Electro-optomechanical equivalent circuits for quantum transduction - Emil Zeuthen; Albert Schliesser; J. M. Taylor; Anders S. Sørensen (2018)
Using the techniques of optomechanics, a high-Q mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical (OM) systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input/output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.

Energy-level statistics in strongly disordered systems with power-law hopping - Paraj Titum; Victor L. Quito; Sergey V. Syzranov (Phys. Rev., 2018)
Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian ∝1/rα in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function R2(ω) in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by R2(ω,V)=A3ωωV for small frequencies ω≪ωV and R2(ω,V)=1−(α−d)A1(ωVω)dα−A2(ωVω)2 for large frequencies ω≫ωV, where ωV∝V−αd is the characteristic matrix element of excitation hopping in a system of volume V, and A1, A2 and A3 are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.

Entanglement of purification: from spin chains to holography - Phuc Nguyen; Trithep Devakul; Matthew G. Halbasch; Michael P. Zaletel; Brian Swingle (Journal of High Energy Physics, 2018)
Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

Exact entanglement cost of quantum states and channels under PPT-preserving operations - Xin Wang; Mark M. Wilde (2018)
This paper establishes single-letter formulas for the exact entanglement cost of generating bipartite quantum states and simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we establish that the exact entanglement cost of any bipartite quantum state under PPT-preserving operations is given by a single-letter formula, here called the <span class="MathJax" id="MathJax-Element-1-Frame" style="box-sizing: inherit; display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(51, 51, 51); font-family: "Open Sans", "Lucida Grande", "Helvetica Neue", Helvetica, Arial, sans-serif;" tabindex="0"><nobr style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;"><span class="math" id="MathJax-Span-1" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: static; vertical-align: 0px; line-height: normal; width: 0.752em;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 0.579em; height: 0px; font-size: 17.36px;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; position: absolute; vertical-align: 0px; line-height: normal; clip: rect(1.731em, 1000.58em, 2.537em, -999.997em); top: -2.359em; left: 0em;"><span class="mrow" id="MathJax-Span-2" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="texatom" id="MathJax-Span-3" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="mrow" id="MathJax-Span-4" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="mo" id="MathJax-Span-5" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-family: MathJax_Math-italic;">κ-entanglement of a quantum state. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum states. Notably, this is the first time that an entanglement measure for general bipartite states has been proven not only to possess a direct operational meaning but also to be efficiently computable, thus solving a question that has remained open since the inception of entanglement theory over two decades ago. Next, we introduce and solve the exact entanglement cost for simulating quantum channels in both the parallel and sequential settings, along with the assistance of free PPT-preserving operations. The entanglement cost in both cases is given by the same single-letter formula and is equal to the largest <span class="MathJax" id="MathJax-Element-2-Frame" style="box-sizing: inherit; display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(51, 51, 51); font-family: "Open Sans", "Lucida Grande", "Helvetica Neue", Helvetica, Arial, sans-serif;" tabindex="0"><nobr style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;"><span class="math" id="MathJax-Span-6" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: static; vertical-align: 0px; line-height: normal; width: 0.752em;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 0.579em; height: 0px; font-size: 17.36px;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; position: absolute; vertical-align: 0px; line-height: normal; clip: rect(1.731em, 1000.58em, 2.537em, -999.997em); top: -2.359em; left: 0em;"><span class="mrow" id="MathJax-Span-7" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="texatom" id="MathJax-Span-8" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="mrow" id="MathJax-Span-9" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="mo" id="MathJax-Span-10" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-family: MathJax_Math-italic;">κ-entanglement that can be shared by the sender and receiver of the channel. It is also efficiently computable by a semidefinite program.

Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals - Peter Bierhorst; Emanuel Knill; Scott Glancy; Yanbao Zhang; Alan Mink; Stephen Jordan; Andrea Rommal; Yi-Kai Liu; Bradley Christensen; Sae Woo Nam; Martin J. Stevens; Lynden K. Shalm (Nature, 2018)
From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within 10−12. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory - Moosavian, Ali Hamed; Stephen Jordan (Phys. Rev. A 98, 012332 (2018), 2018)
In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum Field Theory (QFT) on a quantum computer, which is based on the matrix product state ansatz. We apply this to the massive Gross-Neveu model in one spatial dimension to illustrate the algorithm, but we believe the same algorithm with slight modifications can be used to simulate any one-dimensional massive Fermionic QFT. In the case where the number of particle species is one, our algorithm can prepare particle states using O(ε−3.23…) gates, which is much faster than previous known results, namely O(ε−8−o(1)). Furthermore, unlike previous methods which were based on adiabatic state preparation, the method given here should be able to simulate quantum phases unconnected to the free theory.

Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers - Constantinos Makrides; Ming Li; Eite Tiesinga; Svetlana Kotochigova (Science Advances, 2018)
Ergodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external magnetic field. As recently shown, colliding ultracold magnetic dysprosium atoms display a soft chaotic behavior with a small degree of disorder. We broaden this classification by investigating the generalized inverse participation ratio and fractal dimensions for large sets of molecular wave functions. Our exact close-coupling simulations reveal a dynamic phase transition from partially localized states to totally delocalized states and universality in its distribution by increasing the magnetic field strength to only a hundred Gauss (or 10 mT). Finally, we prove the existence of nonergodic delocalized phase in the system and explain the violation of ergodicity by strong coupling between near-threshold molecular states and the nearby continuum.

Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal - Tobias Graß; Przemyslaw Bienias; Michael Gullans; Rex Lundgren; Joseph Maciejko; Alexey V. Gorshkov (2018)
Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems, and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half-filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal phase, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

Geometry of the quantum set of correlations - Koon Tong Goh; Jedrzej Kaniewski; Elie Wolfe; Tamás Vértesi; Xingyao Wu; Yu Cai; Yeong-Cherng Liang; Valerio Scarani (Physical Review A, 2018)
It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

High Purity Single Photons Entangled with an Atomic Memory - Clayton Crocker; Martin Lichtman; Ksenia Sosnova; Allison Carter; Sophia Scarano; Christopher Monroe (2018)
Trapped atomic ions are an ideal candidate for quantum network nodes, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. The integrity of this photonic interface is generally reliant on purity of single photons produced by the quantum memory. Here we demonstrate a single-photon source for quantum networking based on a trapped 138Ba+ ion with a single photon purity of g2(0)=(8.1±2.3)×10−5 without background subtraction. We further optimize the tradeoff between the photonic generation rate and the memory-photon entanglement fidelity for the case of polarization photonic qubits by tailoring the spatial mode of the collected light.

High-fidelity quantum gates in Si/SiGe double quantum dots - Maximilian Russ; D. M. Zajac; A. J. Sigillito; F. Borjans; J. M. Taylor; J. R. Petta; Guido Burkard (Physical Review B, 2018)
Motivated by recent experiments of Zajac et al. [<a href="http://dx.doi.org/10.1126/science.aao5965" style="box-sizing: border-box; background-image: initial; background-position: 0px 0px; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; color: rgb(50, 148, 216); line-height: inherit; font-family: "Helvetica Neue", Helvetica, Roboto, Arial, sans-serif; font-size: 14px;">Science 359, 439 (2018)], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due to residual exchange interaction, nonadiabatic pulses, and off-resonant driving. By adjusting the gate times, synchronizing the resonant and off-resonant transitions, and compensating these phase mismatches by phase control, the overall gate fidelity can be increased significantly.

Holographic Complexity of Einstein-Maxwell-Dilaton Gravity - Brian Swingle; Yixu Wang (J. High Energ. Phys., 2018)
We study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed "complexity = volume" and "complexity = action" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.

Implicit regularization and solution uniqueness in over-parameterized matrix sensing - Anastasios Kyrillidis; Amir Kalev (2018)
We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-r positive semi-definite (PSD) matrices in Rn×n, with a sensing mechanism that satisfies the restricted isometry property (RIP). The algorithm we study is that of factored gradient descent, where we model the low-rankness and PSD constraints with the factorization UU⊤, where U∈Rn×r. Surprisingly, recent work argues that the choice of r≤n is not pivotal: even setting U∈Rn×n is sufficient for factored gradient descent to find the rank-r solution, which suggests that operating over the factors leads to an implicit regularization. In this note, we provide a different perspective. We show that, in the noiseless case, under certain conditions, the PSD constraint by itself is sufficient to lead to a unique rank-r matrix recovery, without implicit or explicit low-rank regularization. I.e., under assumptions, the set of PSD matrices, that are consistent with the observed data, is a singleton, irrespective of the algorithm used.

In Defense of a "Single-World" Interpretation of Quantum Mechanics - Jeffrey Bub (forthcoming in Studies in History and Philosophy of Modern Physics, 2018)
In a recent result, Frauchiger and Renner argue that if quantum theory accurately describes complex systems like observers who perform measurements, then "we are forced to give up the view that there is one single reality." Following a review of the Frauchiger-Renner argument, I argue that quantum mechanics should be understood probabilistically, as a new sort of non-Boolean probability theory, rather than representationally, as a theory about the elementary constituents of the physical world and how these elements evolve dynamically over time. I show that this way of understanding quantum mechanics is not in conflict with a consistent "single-world" interpretation of the theory.

Information-Theoretic Privacy For Distributed Average Consensus: Bounded Integral Inputs - Nirupam Gupta; Jonathan Katz; Nikhil Chopra (2018)
We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents' inputs against colluding passive adversarial agents, as long as the set of colluding passive adversarial agents is not a vertex cut in the underlying communication network. This implies that a network with (t+1)-connectivity guarantees information-theoretic privacy of honest agents' inputs against any t colluding agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm. The agent' inputs are bounded integers, where the bounds are apriori known to all the agents.

Information-Theoretic Privacy in Distributed Average Consensus - Nirupam Gupta; Jonathan Katz; Nikhil Chopra (2018)
We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents' inputs against colluding semi-honest (passively adversarial) agents, as long as the set of colluding semi-honest agents is not a vertex cut in the underlying communication network. This implies that a network with <span class="MathJax" id="MathJax-Element-2-Frame" style="box-sizing: inherit; display: inline; line-height: normal; font-size: 14px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(51, 51, 51); font-family: "Open Sans", "Lucida Grande", "Helvetica Neue", Helvetica, Arial, sans-serif;" tabindex="0"><nobr style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;"><span class="math" id="MathJax-Span-8" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: static; vertical-align: 0px; line-height: normal; width: 3.574em;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 2.883em; height: 0px; font-size: 17.36px;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; position: absolute; vertical-align: 0px; line-height: normal; clip: rect(1.443em, 1002.77em, 2.768em, -999.997em); top: -2.359em; left: 0em;"><span class="mrow" id="MathJax-Span-9" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="mo" id="MathJax-Span-10" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-family: MathJax_Main;">(<span class="mi" id="MathJax-Span-11" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-family: MathJax_Math-italic;">t<span class="mo" id="MathJax-Span-12" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; padding-left: 0.233em; vertical-align: 0px; line-height: normal; font-family: MathJax_Main;">+<span class="mn" id="MathJax-Span-13" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; padding-left: 0.233em; vertical-align: 0px; line-height: normal; font-family: MathJax_Main;">1<span class="mo" id="MathJax-Span-14" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-family: MathJax_Main;">)-connectivity guarantees information-theoretic privacy of honest agents' inputs against any <span class="MathJax" id="MathJax-Element-3-Frame" style="box-sizing: inherit; display: inline; line-height: normal; font-size: 14px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(51, 51, 51); font-family: "Open Sans", "Lucida Grande", "Helvetica Neue", Helvetica, Arial, sans-serif;" tabindex="0"><nobr style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;"><span class="math" id="MathJax-Span-15" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: static; vertical-align: 0px; line-height: normal; width: 0.464em;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 0.349em; height: 0px; font-size: 17.36px;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; position: absolute; vertical-align: 0px; line-height: normal; clip: rect(1.558em, 1000.29em, 2.537em, -999.997em); top: -2.359em; left: 0em;"><span class="mrow" id="MathJax-Span-16" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="mi" id="MathJax-Span-17" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-family: MathJax_Math-italic;">t colluding semi-honest agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm.

Keyring models: an approach to steerability - Carl Miller; Roger Colbeck; Yaoyun Shi (Journal of Mathematical Physics, 2018)
If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation — that is, if shared randomness cannot produce these reduced states for all possible measurements — the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models — a special class of local hidden state model. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels. Our results imply that Werner states, which are a special case of the previous states, are unsteerable under real projective measurements if and only if their efficiency is at most 2/π.

Local randomness: Examples and application - Honghao Fu; Carl Miller (Phys. Rev. A, 2018)
When two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

Machine learning assisted readout of trapped-ion qubits - Alireza Seif; Kevin A. Landsman; Norbert M. Linke; Caroline Figgatt; C. Monroe; Mohammad Hafezi (J. Phys. B: At. Mol. Opt. Phys., 2018)
We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.

Mathematical methods for resource-based type theories - Aarthi Sundaram; Brad Lackey (2018)
With the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a quantum program. In this work, we make progress towards a program verification approach using the formalism of operational quantum mechanics and resource theories. We present a logical framework that captures two mathematical approaches to resource theory based on monoids (algebraic) and monoidal categories (categorical). We develop the syntax of this framework as an intuitionistic sequent calculus, and prove soundness and completeness of an algebraic and categorical semantics that recover these approaches. We also provide a cut-elimination theorem, normal form, and analogue of Lambek's lifting theorem for polynomial systems over the logics. Using these approaches along with the Curry-Howard-Lambek correspondence for programs, proofs and categories, this work lays the mathematical groundwork for a type checker for some resource theory based frameworks, with the possibility of extending it other quantum programming languages.

Measurement Contextuality and Planck's Constant - Lucas Kocia; Peter Love (New Journal of Physics, 2018)
Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, ℏ, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of ℏ---all orders higher than ℏ0 can be interpreted as quantum corrections to the order ℏ0 term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order ℏ0 terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is equivalent to orders of ℏ as a resource within the WWM formalism. This explains why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres-Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, we find that qubit Pauli observables lack an order ℏ0 contribution in their Weyl symbol and so exhibit contextuality regardless of the state being measured. On the other hand, odd-dimensional qudit observables generally possess non-zero order ℏ0 terms, and higher, in their WWM formulation, and so exhibit contextuality depending on the state measured: odd-dimensional qudit states that exhibit measurement contextuality have an order ℏ1 contribution that allows for the violation of classical bounds while states that do not exhibit measurement contextuality have insufficiently large order ℏ1 contributions.

More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting - Hubert Chan; Jonathan Katz; Kartik Nayak; Antigoni Polychroniadou; Elaine Shi (2018)
The problem of Oblivious RAM (ORAM) has traditionally been studied in a single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case. In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process, we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.

Morphisms in categories of nonlocal games - Brad Lackey; Nishant Rodrigues (2018)
Synchronous correlations provide a class of nonlocal games that behave like functions between finite sets. In this work we examine categories whose morphisms are games with synchronous classical, quantum, or general nonsignaling correlations. In particular, we characterize when morphisms in these categories are monic, epic, sections, or retractions.

Multiparty quantum data hiding with enhanced security and remote deletion - Xingyao Wu; Jianxin Chen (2018)
One of the applications of quantum technology is to use quantum states and measurements to communicate which offers more reliable security promises. Quantum data hiding, which gives the source party the ability of sharing data among multiple receivers and revealing it at a later time depending on his/her will, is one of the promising information sharing schemes which may address practical security issues. In this work, we propose a novel quantum data hiding protocol. By concatenating different subprotocols which apply to rather symmetric hiding scenarios, we cover a variety of more general hiding scenarios. We provide the general requirements for constructing such protocols and give explicit examples of encoding states for five parties. We also proved the security of the protocol in sense that the achievable information by unauthorized operations asymptotically goes to zero. In addition, due to the capability of the sender to manipulate his/her subsystem, the sender is able to abort the protocol remotely at any time before he/she reveals the information.

On the need for soft dressing - Daniel Carney; Laurent Chaurette; Dominik Neuenfeld; Gordon Semenoff (High Energ. Phys., 2018)
In order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

The Non-Disjoint Ontic States of the Grassmann Ontological Model, Transformation Contextuality, and the Single Qubit Stabilizer Subtheory - Lucas Kocia; Peter Love (2018)
We show that it is possible to construct a preparation non-contextual ontological model that does not exhibit "transformation contextuality" for single qubits in the stabilizer subtheory. In particular, we consider the "blowtorch" map and show that it does not exhibit transformation contextuality under the Grassmann Wigner-Weyl-Moyal (WWM) qubit formalism. Furthermore, the transformation in this formalism can be fully expressed at order ℏ0 and so does not qualify as a candidate quantum phenomenon. In particular, we find that the Grassmann WWM formalism at order ℏ0 corresponds to an ontological model governed by an additional set of constraints arising from the relations defining the Grassmann algebra. Due to this additional set of constraints, the allowed probability distributions in this model do not form a single convex set when expressed in terms of disjoint ontic states and so cannot be mapped to models whose states form a single convex set over disjoint ontic states. However, expressing the Grassmann WWM ontological model in terms of non-disjoint ontic states corresponding to the monomials of the Grassmann algebra results in a single convex set. We further show that a recent result by Lillystone et al. that proves a broad class of preparation and measurement non-contextual ontological models must exhibit transformation contextuality lacks the generality to include the ontological model considered here; Lillystone et al.'s result is appropriately limited to ontological models whose states produce a single convex set when expressed in terms of disjoint ontic states. Therefore, we prove that for the qubit stabilizer subtheory to be captured by a preparation, transformation and measurement non-contextual ontological theory, it must be expressed in terms of non-disjoint ontic states, unlike the case for the odd-dimensional single-qudit stabilizer subtheory.

Observation of bound state self-interaction in a nano-eV atom collider - Ryan Thomas; Matthew Chilcott; Eite Tiesinga; Amita B. Deb; Niels Kjærgaard (Nature Communications, 2018)
Quantum mechanical scattering resonances for colliding particles occur when a continuum scattering state couples to a discrete bound state between them. The coupling also causes the bound state to interact with itself via the continuum and leads to a shift in the bound state energy, but, lacking knowledge of the bare bound state energy, measuring this self-energy via the resonance position has remained elusive. Here, we report on the direct observation of self-interaction by using a nano-eV atom collider to track the position of a magnetically-tunable Feshbach resonance through a parameter space spanned by energy and magnetic field. Our system of potassium and rubidium atoms displays a strongly non-monotonic resonance trajectory with an exceptionally large self-interaction energy arising from an interplay between the Feshbach bound state and a different, virtual bound state at a fixed energy near threshold.

Observation of three-photon bound states in a quantum nonlinear medium - Qi-Yu Liang; Aditya V. Venkatramani; Sergio H. Cantu; Travis L. Nicholson; Michael Gullans; Alexey V. Gorshkov; Jeff D. Thompson; Cheng Chin; Mikhail D. Lukin; Vladan Vuletic (Science, 2018)
Bound states of massive particles, such as nuclei, atoms or molecules, are ubiquitous in nature and constitute the bulk of the visible world around us. In contrast, photons typically only weakly influence each other due to their very weak interactions and vanishing mass. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. In particular, photon correlation and conditional phase measurements reveal the distinct features associated with three-photon and two-photon bound states. Such photonic trimers and dimers can be viewed as quantum solitons with shape-preserving wavefunctions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are quantitatively described by an effective field theory (EFT) of Rydberg-induced photon-photon interactions, which demonstrates the presence of a substantial effective three-body force between the photons. These observations pave the way towards the realization, studies, and control of strongly interacting quantum many-body states of light.

Optimal and Secure Measurement Protocols for Quantum Sensor Networks - Zachary Eldredge; Michael Foss-Feig; Steven L. Rolston; Alexey V. Gorshkov (2018)
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting where the quantity to be measured is a linear function of parameters coupled to each qubit individually. We first generalize the Heisenberg limit to the measurement of non-local observables in a quantum network, deriving a bound based on the multi-parameter quantum Fisher information. We then propose a protocol that can make use of GHZ states or spin-squeezed states, and show that in the case of GHZ states the procedure is optimal, i.e., it saturates our bound.

Optimal Pure-State Qubit Tomography via Sequential Weak Measurements - Ezad Shojaee; Christopher S. Jackson; Carlos A. Riofrio; Amir Kalev; Ivan H. Deutsch (Phys. Rev. Lett., 2018)
The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound.

Optimization of photon storage fidelity in ordered atomic arrays - M. T. Manzoni; M. Moreno-Cardoner; A. Asenjo-Garcia; J. V. Porto; Alexey V. Gorshkov; D. E. Chang (New Journal of Physics, 2018)
A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. The validity of this model can break down, however, in systems such as dense, ordered atomic arrays, where strong interference in emission can give rise to phenomena such as subradiance and "selective" radiance. Here, we develop a general formalism that finds the maximum storage efficiency for a collection of atoms with discrete, known positions, and a given spatial mode in which an optical field is sent. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number Na like ∼(logNa)2/N2a, and that, remarkably, an array of just 4×4 atoms in principle allows for an efficiency comparable to a disordered ensemble with optical depth of around 600.

Optomechanical approach to controlling the temperature and chemical potential of light - Chiao-Hsuan Wang; J. M. Taylor (Phys. Rev. A 97, 033850, 2018)
Massless particles, including photons, are not conserved even at low energies and thus have no chemical potential. However, in driven systems, near equilibrium dynamics can lead to equilibration of photons with a finite number, describable using an effective chemical potential. Here we build upon this general concept with an implementation appropriate for a nonlinear photon-based quantum simulator. We consider how laser cooling of a well-isolated mechanical mode can provide an effective low-frequency bath for the quantum simulator system. We show that the use of auxiliary photon modes, coupled by the mechanical system, enables control of both the chemical potential, by drive frequency, and temperature, by drive amplitude, of the resulting photonic quantum simulator's grand canonical ensemble.

Orbital quantum magnetism in spin dynamics of strongly interacting magnetic lanthanide atoms - Ming Li; Eite Tiesinga; Svetlana Kotochigova (2018)
Laser cooled lanthanide atoms are ideal candidates with which to study strong and unconventional quantum magnetism with exotic phases. Here, we use state-of-the-art closed-coupling simulations to model quantum magnetism for pairs of ultracold spin-6 erbium lanthanide atoms placed in a deep optical lattice. In contrast to the widely used single-channel Hubbard model description of atoms and molecules in an optical lattice, we focus on the single-site multi-channel spin evolution due to spin-dependent contact, anisotropic van der Waals, and dipolar forces. This has allowed us to identify the leading mechanism, orbital anisotropy, that governs molecular spin dynamics among erbium atoms. The large magnetic moment and combined orbital angular momentum of the 4f-shell electrons are responsible for these strong anisotropic interactions and unconventional quantum magnetism. Multi-channel simulations of magnetic Cr atoms under similar trapping conditions show that their spin-evolution is controlled by spin-dependent contact interactions that are distinct in nature from the orbital anisotropy in Er. The role of an external magnetic field and the aspect ratio of the lattice site on spin dynamics is also investigated.

Parallel Entangling Operations on a Universal Ion Trap Quantum Computer - C. Figgatt; A. Ostrander; N. M. Linke; K. A. Landsman; D. Zhu; D. Maslov; C. Monroe (2018)
The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

Phase Retrieval Without Small-Ball Probability Assumptions - Felix Krahmer; Yi-Kai Liu (IEEE Transactions on Information Theory, 2018)
In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even in combination with certain practically feasible random masks. To avoid this difficulty, the analysis is often restricted to measurement ensembles (or masks) that satisfy a small-ball probability condition, in order to ensure that the reconstruction is unique. This paper shows a complementary result: for random Bernoulli measurements, there is still a large class of signals that can be reconstructed uniquely, namely, those signals that are non-peaky. In fact, this result is much more general: it holds for random measurements sampled from any subgaussian distribution 2), without any small-ball conditions. This is demonstrated in two ways: 1) a proof of stability and uniqueness and 2) a uniform recovery guarantee for the PhaseLift algorithm. In all of these cases, the number of measurements m approaches the information-theoretic lower bound. Finally, for random Bernoulli measurements with erasures, it is shown that PhaseLift achieves uniform recovery of all signals (including peaky ones).

Photon propagation through dissipative Rydberg media at large input rates - Przemyslaw Bienias; James Douglas; Asaf Paris-Mandoki; Paraj Titum; Ivan Mirgorodskiy; Christoph Tresp; Emil Zeuthen; Michael Gullans; Marco Manzoni; Sebastian Hofferberth; Darrick Chang; Alexey V. Gorshkov (2018)
We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency (EIT). Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail for the first time the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly-stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.

Photon Subtraction by Many-Body Decoherence - Callum R. Murray; Ivan Mirgorodskiy; Christoph Tresp; Christoph Braun; Asaf Paris-Mandoki; Alexey V. Gorshkov; Sebastian Hofferberth; Thomas Pohl (2018)
We present an experimental and theoretical investigation of the scattering-induced decoherence of multiple photons stored in a strongly interacting atomic ensemble. We derive an exact solution to this many-body problem, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis demonstrates a correlated coherence-protection process, in which the induced decoherence of one photon can preserve the spatial coherence of all others. We discuss how this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability.

Photon thermalization via laser cooling of atoms - Chiao-Hsuan Wang; Michael Gullans; J. V. Porto; William D. Phillips; J. M. Taylor (Phys. Rev. A 98, 013834, 2018)
Laser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that non-interacting photons can thermalize with the atoms to a grand canonical ensemble with a non-zero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential set by the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare earth atoms. With the addition of photon-photon interactions, this system could provide a new platform for exploring many-body physics.

Practitioner's guide to social network analysis: Examining physics anxiety in an active-learning setting - Remy Dou; Justyna P. Zwolak (2018)
The application of social network analysis (SNA) has recently grown prevalent in science, technology, engineering, and mathematics education research. Research on classroom networks has led to greater understandings of student persistence in physics majors, changes in their career-related beliefs (e.g., physics interest), and their academic success. In this paper, we aim to provide a practitioner's guide to carrying out research using SNA, including how to develop data collection instruments, set up protocols for gathering data, as well as identify network methodologies relevant to a wide range of research questions beyond what one might find in a typical primer. We illustrate these techniques using student anxiety data from active-learning physics classrooms. We explore the relationship between students' physics anxiety and the social networks they participate in throughout the course of a semester. We find that students' with greater numbers of outgoing interactions are more likely to experience negative anxiety shifts even while we control for {\it pre} anxiety, gender, and final course grade. We also explore the evolution of student networks and find that the second half of the semester is a critical period for participating in interactions associated with decreased physics anxiety. Our study further supports the benefits of dynamic group formation strategies that give students an opportunity to interact with as many peers as possible throughout a semester. To complement our guide to SNA in education research, we also provide a set of tools for letting other researchers use this approach in their work -- the {\it SNA toolbox} -- that can be accessed on GitHub.

Probing electron-phonon interactions in the charge-photon dynamics of cavity-coupled double quantum dots - Michael Gullans; J. M. Taylor; J. R. Petta (Physical Review B, 2018)
Electron-phonon coupling is known to play an important role in the charge dynamics of semiconductor quantum dots. Here we explore its role in the combined charge-photon dynamics of cavity-coupled double quantum dots. Previous work on these systems has shown that strong electron-phonon coupling leads to a large contribution to photoemission and gain from phonon-assisted emission and absorption processes. We compare the effects of this phonon sideband in three commonly investigated gate-defined quantum dot material systems: InAs nanowires and GaAs and Si two-dimensional electron gases (2DEGs). We compare our theory with existing experimental data from cavity-coupled InAs nanowire and GaAs 2DEG double quantum dots and find quantitative agreement only when the phonon sideband and photoemission processes during lead tunneling are taken into account. Finally, we show that the phonon sideband also leads to a sizable renormalization of the cavity frequency, which allows for direct spectroscopic probes of the electron-phonon coupling in these systems.

Pseudorandom States, Non-Cloning Theorems and Quantum Money - Zhengfeng Ji; Yi-Kai Liu; Fang Song (In: Shacham H., Boldyreva A. (eds) Advances in Cryptology – CRYPTO 2018. CRYPTO 2018. Lecture Notes in Computer Science., 2018)
We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study—it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.

QFlow lite dataset: A machine-learning approach to the charge states in quantum dot experiments - Justyna P. Zwolak; Sandesh S. Kalantre; Xingyao Wu; Stephen Ragole; J. M. Taylor (PLOS ONE, 2018)
Over the past decade, machine learning techniques have revolutionized how research is done, from designing new materials and predicting their properties to assisting drug discovery to advancing cybersecurity. Recently, we added to this list by showing how a machine learning algorithm (a so-called learner) combined with an optimization routine can assist experimental efforts in the realm of tuning semiconductor quantum dot (QD) devices. Among other applications, semiconductor QDs are a candidate system for building quantum computers. The present-day tuning techniques for bringing the QD devices into a desirable configuration suitable for quantum computing that rely on heuristics do not scale with the increasing size of the quantum dot arrays required for even near-term quantum computing demonstrations. Establishing a reliable protocol for tuning that does not rely on the gross-scale heuristics developed by experimentalists is thus of great importance. To implement the machine learning-based approach, we constructed a dataset of simulated QD device characteristics, such as the conductance and the charge sensor response versus the applied electrostatic gate voltages. Here, we describe the methodology for generating the dataset, as well as its validation in training convolutional neural networks. We show that the learner's accuracy in recognizing the state of a device is ~96.5 % in both current- and charge-sensor-based training. We also introduce a tool that enables other researchers to use this approach for further research: QFlow lite - a Python-based mini-software suite that uses the dataset to train neural networks to recognize the state of a device and differentiate between states in experimental data. This work gives the definitive reference for the new dataset that will help enable researchers to use it in their experiments or to develop new machine learning approaches and concepts

Quantitative Robustness Analysis of Quantum Programs (Extended Version) - Shih-Han Hung; Kesha Hietala; Shaopeng Zhu; Mingsheng Ying; Michael Hicks; Xiaodi Wu (Proc. ACM Program. Lang., 2018)
Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called ε-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.

Quantum adiabatic optimization without heuristics - Michael Jarret; Brad Lackey; Aike Liu; Kianna Wan (2018)
Quantum adiabatic optimization (QAO) is performed using a time-dependent Hamiltonian H(s) with spectral gap γ(s). Assuming the existence of an oracle Γ such that γ(s)=Θ(Γ(s)), we provide an algorithm that reliably performs QAO in time Oγ−1minlog(γ−1min) with Olog(γ−1min) oracle queries, where γmin=minsγ(s). Our strategy is not heuristic and does not require guessing time parameters or annealing paths. Rather, our algorithm naturally produces an annealing path such that dH/ds≈γ(s) and chooses its own runtime T to be as close as possible to optimal while promising convergence to the ground state. We then demonstrate the feasibility of this approach in practice by explicitly constructing a gap oracle Γ for the problem of finding a vertex m=argminuW(u) of the cost function W:V⟶[0,1], restricting ourselves to computational basis measurements and driving Hamiltonian H(0)=I−V−1∑u,v∈V|u⟩⟨v|, with V=|V|. Requiring only that W have a constant lower bound on its spectral gap and upper bound κ on its spectral ratio, our QAO algorithm returns m using Γ with probability (1−ε)(1−e−1/ε) in time O˜(ε−1[V−−√+(κ−1)2/3V2/3]). This achieves a quantum advantage for all κ, and when κ≈1, recovers Grover scaling up to logarithmic factors. We implement the algorithm as a subroutine in an optimization procedure that produces m with exponentially small failure probability and expected runtime O˜(ε−1[V−−√+(κ−1)2/3V2/3]), even when κ is not known beforehand.

Quantum algorithm for multivariate polynomial interpolation - Jianxin Chen; Andrew M. Childs; Shih-Han Hung (Proceedings of The Royal Society A, 2018)
How many quantum queries are required to determine the coefficients of a degree-d polynomial in n variables? We present and analyze quantum algorithms for this multivariate polynomial interpolation problem over the fields Fq, R, and C. We show that kC and 2kC queries suffice to achieve probability 1 for C and R, respectively, where kC = ⌈ 1 n+1 ( n+d d )⌉ except for d = 2 and four other special cases. For Fq, we show that ⌈ d n+d ( n+d d )⌉ queries suffice to achieve probability approaching 1 for large field order q. The classical query complexity of this problem is ( n+d d ), so our result provides a speedup by a factor of n + 1, n+1 2 , and n+d d for C, R, and Fq, respectively. Thus we find a much larger gap between classical and quantum algorithms than the univariate case, where the speedup is by a factor of 2. For the case of Fq, we conjecture that 2kC queries also suffice to achieve probability approaching 1 for large field order q, although we leave this as an open problem.

Quantum Channel Simulation and the Channel's Smooth Max-Information - Kun Fang; Xin Wang; Marco Tomamichel; Mario Berta (2018)
We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel's smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel's smooth max-information as the one-shot quantum simulation cost under no-signalling assisted codes. Third, we derive the asymptotic equipartition property of the channel's smooth max-information, i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels.

Quantum Cryptanalysis: Shor, Grover, and Beyond - Stephen P. Jordan; Yi-Kai Liu (IEEE Security & Privacy, 2018)

Quantum field theory for the chiral clock transition in one spatial dimension - Seth Whitsitt; Rhine Samajdar; Subir Sachdev (Phys. Rev., 2018)
We describe the quantum phase transition in the N-state chiral clock model in spatial dimension d=1. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and N=3, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ZN symmetry, to a gapped phase with the ZN symmetry restored. The transition has dynamical critical exponent z≠1, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in d=1, involving the onset of a single boson condensate in the background of a higher-dimensional N-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in 2−d, with 4−N chosen to be of order 2−d. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for N=3, finding good evidence for a direct phase transition, and obtain estimates for z and the correlation length exponent ν.

Quantum generalizations of the polynomial hierarchy with applications to QMA(2) - Sevag Gharibian; Miklos Santha; Jamie Sikora; Aarthi Sundaram; Justin Yirka (Proceedings of 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), 2018)
The polynomial-time hierarchy (PH) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as PH does not collapse). Here, we study whether two quantum generalizations of PH can similarly prove separations in the quantum setting. The first generalization, QCPH, uses classical proofs, and the second, QPH, uses quantum proofs. For the former, we show quantum variants of the Karp-Lipton theorem and Toda's theorem. For the latter, we place its third level, QΣ3, into NEXP {using the Ellipsoid Method for efficiently solving semidefinite programs}. These results yield two implications for QMA(2), the variant of Quantum Merlin-Arthur (QMA) with two unentangled proofs, a complexity class whose characterization has proven difficult. First, if QCPH=QPH (i.e., alternating quantifiers are sufficiently powerful so as to make classical and quantum proofs "equivalent"), then QMA(2) is in the Counting Hierarchy (specifically, in PPPPP). Second, unless QMA(2)=QΣ3 (i.e., alternating quantifiers do not help in the presence of "unentanglement"), QMA(2) is strictly contained in NEXP.

Quantum SDP Solvers: Large Speed-ups, Optimality, and Applications to Quantum Learning - Fernando G. S. L. Brandão; Amir Kalev; Tongyang Li; Cedric Yen-Yu Lin; Krysta M. Svore; Xiaodi Wu (To appear at the 46th International Colloquium on Automata, Languages and Programming (ICALP 2019), 2018)
We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with m constraint matrices, each of dimension n, rank r, and sparsity s. The first algorithm assumes an input model where one is given access to entries of the matrices at unit cost. We show that it has run time O~(s2(m−−√ε−10+n−−√ε−12)), where ε is the error. This gives an optimal dependence in terms of m,n and quadratic improvement over previous quantum algorithms when m≈n. The second algorithm assumes a fully quantum input model in which the matrices are given as quantum states. We show that its run time is O~(m−−√+poly(r))⋅poly(logm,logn,B,ε−1), with B an upper bound on the trace-norm of all input matrices. In particular the complexity depends only poly-logarithmically in n and polynomially in r. We apply the second SDP solver to the problem of learning a good description of a quantum state with respect to a set of measurements: Given m measurements and copies of an unknown state ρ, we show we can find in time m−−√⋅poly(logm,logn,r,ε−1) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as ρ on the m measurements, up to error ε. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes' principle from statistical mechanics. As in previous work, we obtain our algorithm by "quantizing" classical SDP solvers based on the matrix multiplicative weight method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians with a poly-logarithmic dependence on its dimension, which could be of independent interest.

Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics - Andras Gilyen; Yuan Su; Guang Hao Low; Nathan Wiebe (Proceedings of the 51st ACM Symposium on Theory of Computing, 2018)
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation" algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while usually only use a constant number of ancilla qubits. We show that singular value transformation leads to novel algorithms. We give an efficient solution to a certain "non-commutative" measurement problem and propose a new method for singular value estimation. We also show how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum. Finally, as a quantum machine learning application we show how to efficiently implement principal component regression. "Singular value transformation" is conceptually simple and efficient, and leads to a unified framework of quantum algorithms incorporating a variety of quantum speed-ups. We illustrate this by showing how it generalizes a number of prominent quantum algorithms, including: optimal Hamiltonian simulation, implementing the Moore-Penrose pseudoinverse with exponential precision, fixed-point amplitude amplification, robust oblivious amplitude amplification, fast QMA amplification, fast quantum OR lemma, certain quantum walk results and several quantum machine learning algorithms. In order to exploit the strengths of the presented method it is useful to know its limitations too, therefore we also prove a lower bound on the efficiency of singular value transformation, which often gives optimal bounds.

Quantum Supremacy and the Complexity of Random Circuit Sampling - Adam Bouland; Bill Fefferman; Chinmay Nirkhe; Umesh Vazirani (2018)
A critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB team, is sampling from the probability distributions of randomly chosen quantum circuits, which we call Random Circuit Sampling (RCS). In this paper we study both the hardness and verification of RCS. While RCS was defined with experimental realization in mind, we show complexity theoretic evidence of hardness that is on par with the strongest theoretical proposals for supremacy. Specifically, we show that RCS satisfies an average-case hardness condition - computing output probabilities of typical quantum circuits is as hard as computing them in the worst-case, and therefore #P-hard. Our reduction exploits the polynomial structure in the output amplitudes of random quantum circuits, enabled by the Feynman path integral. In addition, it follows from known results that RCS satisfies an anti-concentration property, making it the first supremacy proposal with both average-case hardness and anti-concentration.

Quantum-secure message authentication via blind-unforgeability - Gorjan Alagic; Christian Majenz; Alexander Russell; Fang Song (2018)
Formulating and designing unforgeable authentication of classical messages in the presence of quantum adversaries has been a challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of "predicting an unqueried value" when the adversary can query in quantum superposition. In this work, we uncover serious shortcomings in existing approaches, and propose a new definition. We then support its viability by a number of constructions and characterizations. Specifically, we demonstrate a function which is secure according to the existing definition by Boneh and Zhandry, but is clearly vulnerable to a quantum forgery attack, whereby a query supported only on inputs that start with 0 divulges the value of the function on an input that starts with 1. We then propose a new definition, which we call "blind-unforgeability" (or BU.) This notion matches "intuitive unpredictability" in all examples studied thus far. It defines a function to be predictable if there exists an adversary which can use "partially blinded" oracle access to predict values in the blinded region. Our definition (BU) coincides with standard unpredictability (EUF-CMA) in the classical-query setting. We show that quantum-secure pseudorandom functions are BU-secure MACs. In addition, we show that BU satisfies a composition property (Hash-and-MAC) using "Bernoulli-preserving" hash functions, a new notion which may be of independent interest. Finally, we show that BU is amenable to security reductions by giving a precise bound on the extent to which quantum algorithms can deviate from their usual behavior due to the blinding in the BU security experiment.

The quasiprobability behind the out-of-time-ordered correlator - Nicole Yunger Halpern; Brian Swingle; Justin Dressel (Phys. Rev., 2018)
Two topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC has been shown to equal a moment of a summed quasiprobability. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze the weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.

Recovering quantum gates from few average gate fidelities - Ingo Roth; Richard Kueng; Shelby Kimmel; Yi-Kai Liu; David Gross; Jens Eisert; Martin Kliesch (Phys. Rev. Lett., 2018)
Characterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of today's devices. One method for characterising processes is randomised benchmarking, which is robust against state preparation and measurement (SPAM) errors, and can be used to benchmark Clifford gates. A complementing approach asks for full tomographic knowledge. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. So far, guarantees for compressed sensing protocols rely on unstructured random measurements and can not be applied to the data acquired from randomised benchmarking experiments. It has been an open question whether or not the favourable features of both worlds can be combined. In this work, we give a positive answer to this question. For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries. Moreover, for general unital quantum channels we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity -- a figure of merit that characterises the coherence of a process. In our proofs we exploit recent representation theoretic insights on the Clifford group, develop a version of Collins' calculus with Weingarten functions for integration over the Clifford group, and combine this with proof techniques from compressed sensing.

Recovery Map for Fermionic Gaussian Channels - Brian Swingle; Yixu Wang (2018)
A recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.

Resilience of scrambling measurements - Brian Swingle; Nicole Yunger Halpern (Phys. Rev., 2018)
Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backwards time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum-chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

Resonantly driven CNOT gate for electron spins - D. M. Zajac; A. J. Sigillito; M. Russ; F. Borjans; J. M. Taylor; Guido Burkard; J. R. Petta (Science, 2018)
Single-qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. Although high-fidelity single-qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been challenging because of rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities greater than 99%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 nanoseconds. We used the CNOT gate to generate a Bell state with 78% fidelity (corrected for errors in state preparation and measurement). Our quantum dot device architecture enables multi-qubit algorithms in silicon.

Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force - Pak Hong Leung; Kevin A. Landsman; Caroline Figgatt; Norbert M. Linke; Christopher Monroe; Kenneth R. Brown (Physical Review Letters, 2018)
In an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multi-qubit logical gates. Any residual entanglement between the internal and motional states of the ions will result in decoherence errors, especially when there are many spectator ions in the crystal. We propose using a frequency-modulated (FM) driving force to minimize such errors and implement it experimentally. In simulation, we obtained an optimized FM gate that can suppress decoherence to less than 10−4 and is robust against a frequency drift of more than ±1 kHz. The two-qubit gate was tested in a five-qubit trapped ion crystal, with 98.3(4)% fidelity for a Mølmer-Sørensen entangling gate and 98.6(7)% for a controlled-not (CNOT) gate. We also show an optimized FM two-qubit gate for 17 ions, proving the scalability of our method.

Scrambling dynamics across a thermalization-localization quantum phase transition - Subhayan Sahu; Shenglong Xu; Brian Swingle (2018)
We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the operator dynamics is not very sensitive to the actual eigenstate localization transition. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.

A semiclassical theory of phase-space dynamics of interacting bosons - Ranchu Mathew; Eite Tiesinga (2018)
We study the phase-space representation of dynamics of bosons in the semiclassical regime where the occupation number of the modes is large. To this end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation for the Green's function of the Wigner distribution. The semiclassical analysis incorporates interference of classical paths and reduces to the truncated Wigner approximation (TWA) when the interference is ignored. Furthermore, we identify the Ehrenfest time after which the TWA fails. As a case study, we consider a single-mode quantum nonlinear oscillator, which displays collapse and revival of observables. We analytically show that the interference of classical paths leads to revivals, an effect that is not reproduced by the TWA or a perturbative analysis.

Single-photon bound states in atomic ensembles - Yidan Wang; Michael Gullans; Antoine Browaeys; J. V. Porto; Darrick E. Chang; Alexey V. Gorshkov (2018)
We illustrate the existence of single-excitation bound states for propagating photons interacting with N two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson's theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

Spectrum estimation of density operators with alkaline-earth atoms - Michael E. Beverland; Jeongwan Haah; Gorjan Alagic; Gretchen K. Campbell; Ana Maria Rey; Alexey V. Gorshkov (2018)
We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkalineearth atoms are discussed.

A spinor Bose-Einstein condensate phase-sensitive amplifier for SU(1,1) interferometry - J. P. Wrubel; A. Schwettmann; D. P. Fahey; Z. Glassman; H. K. Pechkis; P. F. Griffin; R. Barnett; E. Tiesinga; P. D. Lett (Phys. Rev, 2018)
The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam-splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F=1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of ⟨F=1,m=±1| atoms. We simulate the effect of single and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single and double-sided seeding we find there exists an optimal phase shift that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of 23Na in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier, and demonstrate sensitivity to initial population fractions as small as 0.1%.

Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits - Lucas Kocia; Peter Love (2018)
We apply the periodized stationary phase method to discrete Wigner functions of systems with odd prime dimension using results from p-adic number theory. We derive the Wigner-Weyl-Moyal (WWM) formalism with higher order ℏ corrections representing contextual corrections to non-contextual Clifford operations. We apply this formalism to a subset of unitaries that include diagonal gates such as the π8 gates. We characterize the stationary phase critical points as a quantum resource injecting contextuality and show that this resource allows for the replacement of the p2t points that represent t magic state Wigner functions on p-dimensional qudits by ≤pt points. We find that the π8 gate introduces the smallest higher order ℏ correction possible, requiring the lowest number of additional critical points compared to the Clifford gates. We then establish a relationship between the stabilizer rank of states and the number of critical points necessary to treat them in the WWM formalism. This allows us to exploit the stabilizer rank decomposition of two qutrit π8 gates to develop a classical strong simulation of a single qutrit marginal on t qutrit π8 gates that are followed by Clifford evolution, and show that this only requires calculating 3t2+1 critical points corresponding to Gauss sums. This outperforms the best alternative qutrit algorithm (based on Wigner negativity and scaling as ∼30.8t for 10−2 precision) for any number of π8 gates to full precision.

Structure of Correlated Worldline Theories of Quantum Gravity - Andrei O. Barvinsky; Daniel Carney; Philip C. E. Stamp (Phys. Rev., 2018)
We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple copies of the coupled matter and gravitational fields. In both versions, the paths in a functional formulation are correlated via gravity itself, causing a breakdown of the superposition principle; however, the product form survives consistency tests not satisfied by the summed form. To better understand the structure of these two theories, we show how to perform diagrammatic expansions in the gravitational coupling for each version of CWL theory, using particle propagation and scalar fields as examples. We explicitly calculate contributions to 2-point and 4-point functions, again for each version of the theory, up to 2nd-order in the gravitational coupling.

Study of radon reduction in gases for rare event search experiments - K. Pushkin; C. Akerlof; D. Anbajagane; J. Armstrong; M. Arthurs; Jacob Bringewatt; T. Edberg; C. Hall; M. Lei; R. Raymond; M. Reh; D. Saini; et al. (2018)
The noble elements, argon and xenon, are frequently employed as the target and event detector for weakly interacting particles such as neutrinos and Dark Matter. For such rare processes, background radiation must be carefully minimized. Radon provides one of the most significant contaminants since it is an inevitable product of trace amounts of natural uranium. To design a purification system for reducing such contamination, the adsorption characteristics of radon in nitrogen, argon, and xenon carrier gases on various types of charcoals with different adsorbing properties and intrinsic radioactive purities have been studied in the temperature range of 190-295 K at flow rates of 0.5 and 2 standard liters per minute. Essential performance parameters for the various charcoals include the average breakthrough times (<span class="MathJax" id="MathJax-Element-1-Frame" style="box-sizing: inherit; display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(51, 51, 51); font-family: "Open Sans", "Lucida Grande", "Helvetica Neue", Helvetica, Arial, sans-serif;" tabindex="0"><nobr style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;"><span class="math" id="MathJax-Span-1" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: static; vertical-align: 0px; line-height: normal; width: 0.579em;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 0.464em; height: 0px; font-size: 17.36px;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; position: absolute; vertical-align: 0px; line-height: normal; clip: rect(1.789em, 1000.52em, 2.537em, -999.997em); top: -2.359em; left: 0em;"><span class="mrow" id="MathJax-Span-2" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="texatom" id="MathJax-Span-3" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="mrow" id="MathJax-Span-4" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="mo" id="MathJax-Span-5" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-family: MathJax_Math-italic;">τ), dynamic adsorption coefficients (k<span class="MathJax" id="MathJax-Element-2-Frame" style="box-sizing: inherit; display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(51, 51, 51); font-family: "Open Sans", "Lucida Grande", "Helvetica Neue", Helvetica, Arial, sans-serif;" tabindex="0"><nobr style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;"><span class="math" id="MathJax-Span-6" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: static; vertical-align: 0px; line-height: normal; width: 0.579em;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 0.464em; height: 0px; font-size: 17.36px;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; position: absolute; vertical-align: 0px; line-height: normal; clip: rect(2.019em, 1000.46em, 2.71em, -999.997em); top: -2.359em; left: 0em;"><span class="mrow" id="MathJax-Span-7" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="msubsup" id="MathJax-Span-8" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 0.464em; height: 0px;"><span class="mi" id="MathJax-Span-10" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-size: 12.2735px; font-family: MathJax_Math-italic;">a) and the number of theoretical stages (n). It is shown that the k<span class="MathJax" id="MathJax-Element-3-Frame" style="box-sizing: inherit; display: inline; line-height: normal; font-size: 14px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; color: rgb(51, 51, 51); font-family: "Open Sans", "Lucida Grande", "Helvetica Neue", Helvetica, Arial, sans-serif;" tabindex="0"><nobr style="box-sizing: inherit; transition: none 0s ease 0s; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;"><span class="math" id="MathJax-Span-11" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: static; vertical-align: 0px; line-height: normal; width: 0.579em;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 0.464em; height: 0px; font-size: 17.36px;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; position: absolute; vertical-align: 0px; line-height: normal; clip: rect(2.019em, 1000.46em, 2.71em, -999.997em); top: -2.359em; left: 0em;"><span class="mrow" id="MathJax-Span-12" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span class="msubsup" id="MathJax-Span-13" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal;"><span style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline-block; position: relative; vertical-align: 0px; line-height: normal; width: 0.464em; height: 0px;"><span class="mi" id="MathJax-Span-15" style="box-sizing: inherit; font-style: inherit; font-weight: inherit; transition: none 0s ease 0s; display: inline; position: static; vertical-align: 0px; line-height: normal; font-size: 12.2735px; font-family: MathJax_Math-italic;">a-values for radon in nitrogen, argon, and xenon increase as the temperature of the charcoal traps decreases, and that they are significantly larger in nitrogen and argon than in xenon gas due to adsorption saturation effects. It is found that, unlike in xenon, the dynamic adsorption coefficients for radon in nitrogen and argon strictly obey the Arrhenius law. The experimental results strongly indicate that nitric acid etched Saratech is the best candidate among all used charcoal brands. It allows reducing total radon concentration in the LZ liquid Xe detector to meet the ultimate goal in the search for Dark Matter.

Studying community development: a network analytical approach - C. A. Hass; Florian Genz; Mary Bridget Kustusch; Pierre-P. A. Ouime; Katarzyna Pomian; Eleanor C. Sayre; Justyna P. Zwolak (2018)
Research shows that community plays a central role in learning, and strong community engages students and aids in student persistence. Thus, understanding the function and structure of communities in learning environments is essential to education. We use social network analysis to explore the community dynamics of students in a pre-matriculation, two-week summer program. Unlike previous network analysis studies in PER, we build our networks from classroom video that has been coded for student interactions using labeled, directed ties. We define 3 types of interaction: on task interactions (regarding the assigned task), on topic interactions (having to do with science, technology, engineering, and mathematics (STEM)), and off topic interactions (unrelated to the assignment or STEM). To study the development of community in this program, we analyze the shift in conversation topicality over the course of the program. Conversations are more on-task toward the end of the program and we propose that this conversational shift represents a change in student membership within their forming community.

Subsystem Complexity and Holography - Cesar A. Agón; Matthew Headrick; Brian Swingle (2018)
We study circuit complexity for spatial regions in holographic field theories. We study analogues based on the entanglement wedge of the bulk quantities appearing in the "complexity = volume" and "complexity = action" conjectures. We calculate these quantities for one exterior region of an eternal static neutral or charged black hole in general dimensions, dual to a thermal state on one boundary with or without chemical potential respectively, as well as for a shock wave geometry. We then define several analogues of circuit complexity for mixed states, and use tensor networks to gain intuition about them. We find a promising qualitative match between the holographic action and what we call the purification complexity, the minimum number of gates required to prepare an arbitrary purification of the given mixed state. On the other hand, the holographic volume does not appear to match any of our definitions of mixed-state complexity.

Tabletop experiments for quantum gravity: a user's manual - Daniel Carney; Philip C. E. Stamp; J. M. Taylor (2018)
Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

Tabletop experiments for quantum gravity: a user's manual - Daniel Carney; Philip C. E. Stamp; J. M. Taylor (2018)
Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

Thermal management and non-reciprocal control of phonon flow via optomechanics - Alireza Seif; Wade DeGottardi; Keivan Esfarjani; Mohammad Hafezi (Nat. Commun., 2018)
Engineering phonon transport in physical systems is a subject of interest in the study of materials and plays a crucial role in controlling energy and heat transfer. Of particular interest are non-reciprocal phononic systems, which in direct analogy to electric diodes, provide a directional flow of energy. Here, we propose an engineered nanostructured material, in which tunable non-reciprocal phonon transport is achieved through optomechanical coupling. Our scheme relies on breaking time-reversal symmetry by a spatially varying laser drive, which manipulates low-energy acoustic phonons. Furthermore, we take advantage of recent developments in the manipulation of high-energy phonons through controlled scattering mechanisms, such as using alloys and introducing disorder. These combined approaches allow us to design an acoustic isolator and a thermal diode. Our proposed device will have potential impact in phonon-based information processing, and heat management in low temperatures.

Time-reversal of rank-one quantum strategy functions - Yuan Su; John Watrous (Quantum, 2018)
The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to the set of rank-one positive semidefinite operators on a certain space. This time-reversal property states that the maximum value obtained by such a function over all valid quantum strategies is also obtained when the direction of time for the function is reversed, despite the fact that the strategies themselves are generally not time reversible. An application of this fact is an alternative proof of a known relationship between the conditional min- and max-entropy of bipartite quantum states, along with generalizations of this relationship.

Totally random: why nobody understands quantum mechanics (a serious comic on entanglement) - Jeffrey Bub; Tanya Bub (Princeton University Press, 2018)

Toward the first quantum simulation with quantum speedup - Andrew M. Childs; Dmitri Maslov; Yunseong Nam; Neil J. Ross; Yuan Su (Proceedings of the National Academy of Sciences, 2018)
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

Two-Dimensional Dilaton Gravity Theory and Lattice Schwarzian Theory - Su-Kuan Chu; Chen-Te Ma; Chih-Hung Wu (2018)
We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of non-vanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of non-vanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term R2, where R is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cut-off ε2 under a constant boundary dilaton field and the non-vanishing cosmological constant by identifying the lattice spacing a of a lattice Schwarzian theory with the boundary cut-off ε of the two-dimensional dilaton gravity theory.

Unforgeable Quantum Encryption - Gorjan Alagic; Tommaso Gagliardoni; Christian Majenz (In: Nielsen J., Rijmen V. (eds) Advances in Cryptology – EUROCRYPT 2018. Lecture Notes in Computer Science, Springer, Cham, 2018)
We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i) ciphertext unforgeability, (ii) indistinguishability under adaptive chosen-ciphertext attack, and (iii) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies   INT-CTXT , (ii) implies   IND-CCA2 , and (iii) implies   AE . All of our new notions also imply   QIND-CPA  privacy. Combining one-time authentication and classical pseudorandomness, we construct symmetric-key quantum encryption schemes for each of these new security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

Unitary Entanglement Construction in Hierarchical Networks - Aniruddha Bapat; Zachary Eldredge; James R. Garrison; Abhinav Desphande; Frederic T. Chong; Alexey V. Gorshkov (2018)
The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

Verified Quantum Information Scrambling - Kevin A. Landsman; Caroline Figgatt; Thomas Schuster; Norbert M. Linke; Beni Yoshida; Norman Y. Yao; Christopher Monroe (2018)
Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically ∼80%, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

3-manifold diagrams and NP vs P - Gorjan Alagic; C. Lo (Quantum Information & Computation, 2017)
The computational complexity class #P captures the di_culty of counting the satisfying assignments to a boolean formula. In this work, we use basic tools from quantum computation to give a proof that the SO(3) Witten-Reshetikhin-Turaev (WRT) invariant of 3-manifolds is #P-hard to calculate. We then apply this result to a question about the combinatorics of Heegaard splittings, motivated by analogous work on link diagrams by M. Freedman. We show that, if #P ⊆ FPNP, then there exist infinitely many Heegaard splittings which cannot be made logarithmically thin by local WRT-preserving moves, except perhaps via a superpolynomial number of steps. We also outline two extensions of the above results. First, adapting a result of Kuperberg, we show that any presentation-independent approximation of WRT is also #P-hard. Second, we sketch out how all of our results can be translated to the setting of triangulations and Turaev-Viro invariants.

Above threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider - Milena S. J. Horvath; Ryan Thomas; Eite Tiesinga; Amita B. Deb; Niels Kjærgaard (Nature Communications, 2017)
Studies of magnetically tunable Feshbach resonances in ultracold atomic gases have predominantly been carried out in the zero collision-energy limit. Here, we explore above threshold collisions at well-defined energies in the vicinity of a narrow magnetic Feshbach resonance by means of a laser-based collider. Our experiment focuses on collisions between ground-state 87Rb atoms in the |F = 2,mF = 0i and |F = 1,mF = 1i hyperfine states, which have a known s-wave resonance at 9.040(7) G at threshold that strongly couples to inelastic channels, where 1 G = 10−4 T. Using our collider we can track the magnetic field shift in resonance position as the energy is tuned. This presents a challenge due to the narrow width of the resonance in conjunction with inherent broadening mechanisms of the collider. We find, however, that the narrow Feshbach scattering feature becomes imprinted on the spatial distribution of atoms in a fashion that allows for an accurate determination of resonance position as a function of collision energy through a shift in center-of-mass position of the outgoing clouds. This shift has a dispersive line shape with a zero value at the resonance position. We obtain excellent agreement with theory on the resonance position.

Advances in Quantum Reinforcement Learning - Vedran Dunjko; J. M. Taylor; Hans J. Briegel (IEEE SMC, Banff, AB, 2017)
In recent times, there has been much interest in quantum enhancements of machine learning, specifically in the context of data mining and analysis. Reinforcement learning, an interactive form of learning, is, in turn, vital in artificial intelligence-type applications. Also in this case, quantum mechanics was shown to be useful, in certain instances. Here, we elucidate these results, and show that quantum enhancements can be achieved in a new setting: the setting of learning models which learn how to improve themselves -- that is, those that meta-learn. While not all learning models meta-learn, all non-trivial models have the potential of being "lifted", enhanced, to meta-learning models. Our results show that also such models can be quantum-enhanced to make even better learners. In parallel, we address one of the bottlenecks of current quantum reinforcement learning approaches: the need for so-called oracularized variants of task environments. Here we elaborate on a method which realizes these variants, with minimal changes in the setting, and with no corruption of the operative specification of the environments. This result may be important in near-term experimental demonstrations of quantum reinforcement learning.

Basic circuit compilation techniques for an ion-trap quantum machine - Dmitri Maslov (New Journal of Physics, 2017)
We study the problem of compilation of quantum algorithms into optimized physical-level circuits executable in a quantum information processing (QIP) experiment based on trapped atomic ions. We report a complete strategy: starting with an algorithm in the form of a quantum computer program, we compile it into a high-level logical circuit that goes through multiple stages of decomposition into progressively lower-level circuits until we reach the physical execution-level specification. We skip the fault-tolerance layer, as it is not necessary in this work. The different stages are structured so as to best assist with the overall optimization while taking into account numerous optimization criteria, including minimizing the number of expensive two-qubit gates, minimizing the number of less expensive single-qubit gates, optimizing the runtime, minimizing the overall circuit error, and optimizing classical control sequences. Our approach allows a trade-off between circuit runtime and quantum error, as well as to accommodate future changes in the optimization criteria that may likely arise as a result of the anticipated improvements in the physical-level control of the experiment.

Complete 3-Qubit Grover Search on a Programmable Quantum Computer - C. Figgatt; Dmitri Maslov; K. A. Landsman; N. M. Linke; S. Debnath; Christopher Monroe (Nature Communications, accepted, 2017)
Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state-marking scheme required to perform a classical search. All quantum solutions are shown to outperform their classical counterparts. We also report the first implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.

Complexity of sampling as an order parameter - Abhinav Deshpande; Bill Fefferman; Michael Foss-Feig; Alexey V. Gorshkov (2017)
We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time <span class="MathJax" id="MathJax-Element-1-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">t. We obtain upper and lower bounds on the scaling of <span class="MathJax" id="MathJax-Element-2-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">twith the number of bosons, <span class="MathJax" id="MathJax-Element-3-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">n, for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian and conjecture a link to dynamical phase transitions. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter systems.

Computational Notions of Quantum Min-Entropy - Yi-Hsiu Chen; Kai-Min Chung; Ching-Yi Lai; Salil P. Vadhan; Xiaodi Wu (2017)
We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold. Our main results are as follows. (1) The classical Leakage Chain Rule for pseudoentropy can be extended to the case that the leakage information is quantum (while the source remains classical). Specifically, if the source has pseudoentropy at least k, then it has pseudoentropy at least k − ℓ conditioned on an ℓ- qubit leakage. (2) As an application of the Leakage Chain Rule, we construct the first quantum leakage-resilient stream-cipher in the bounded-quantum-storage model, assuming the existence of a quantum-secure pseudorandom generator. (3) We show that the general form of the classical Dense Model Theorem (interpreted as the equivalence between two definitions of pseudo-relativemin-entropy) does not extend to quantum states. Along the way, we develop quantum analogues of some classical techniques (e.g., the Leakage Simulation Lemma, which is proven by a Nonuniform Min-Max Theorem or Boosting). On the other hand, we also identify some classical techniques (e.g., Gap Amplification) that do not work in the quantum setting. Moreover, we introduce a variety of notions that combine quantum information and quantum complexity, and this raises several directions for future work.

Cooling a harmonic oscillator by optomechanical modification of its bath - Xunnong Xu; Thomas Purdy; J. M. Taylor (Physical Review Letters, 2017)
Optomechanical systems show tremendous promise for high sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically-induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

Correlated Photon Dynamics in Dissipative Rydberg Media - Emil Zeuthen; Michael Gullans; Mohammad F. Maghrebi; Alexey V. Gorshkov (Physical Review Letters, 2017)
Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative interactions relevant to current experiments. Our model is in good agreement with experimental data. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

Development of a new UHV/XHV pressure standard (cold atom vacuum standard) - Julia Scherschligt; James A Fedchak; Daniel S Barker; Stephen Eckel; Nikolai Klimov; Constantinos Makrides; Eite Tiesinga (Metrologia, 2017)
The National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 x 10-6 to 1 x 10-10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum range and extend into the extreme-high vacuum. This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H2) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H2 system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

Disorder induced transitions in resonantly driven Floquet Topological Insulators - Paraj Titum; Netanel H. Lindner; Gil Refael (Physical Review B, 2017)
We investigate the effects of disorder in Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are induced by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a mobility gap at the resonant quasi-energy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse: we show that in the same quantum well, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). We identify the conditions on the driving field necessary for observing such a transition.

Dispersive optical detection of magnetic Feshbach resonances in ultracold gases - Bianca J. Sawyer; Milena S. J. Horvath; Eite Tiesinga; Amita B. Deb; Niels Kjærgaard (Physical Review A, 2017)
Magnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of <span class="MathJax" id="MathJax-Element-1-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">87Rb, between the <span class="MathJax" id="MathJax-Element-2-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">|F=1,mF=1⟩ and <span class="MathJax" id="MathJax-Element-3-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">|F=2,mF=0⟩ states. Despite the loss features being <span class="MathJax" id="MathJax-Element-4-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">≲100 mG wide, we require only 21 experimental runs to explore a magnetic field range >18 G. The resonances consist of two known s-wave features in the vicinity of 9 G and 18 G and two previously unobserved p-wave features near 5 G and 10 G. We further utilize the dispersive approach to directly characterize the two-body loss dynamics for each Feshbach resonance.

Domination with decay in triangular matchstick arrangement graphs - Jill Cochran; Terry Henderson; Aaron Ostrander; Ron Taylor (Involve, a Journal of Mathematics, 2017)
We provide results for the exponential dominating numbers and total exponential dominating numbers of a family of triangular grid graphs. We then prove inequalities for these numbers and compare them with inequalities that hold more generally for exponential dominating numbers of graphs.

Dynamically induced robust phonon transport and chiral cooling in an optomechanical system - Seunghwi Kim; Xunnong Xu; J. M. Taylor; Gaurav Bahl (Nature Communications, 2017)
The transport of sound and heat, in the form of phonons, has a fundamental material limit: disorder-induced scattering. In electronic and optical settings, introduction of chiral transport - in which carrier propagation exhibits broken parity symmetry - provides robustness against such disorder by preventing elastic backscattering. Here we experimentally demonstrate a path for achieving robust phonon transport even in the presence of material disorder, by dynamically inducing chirality through traveling-wave optomechanical coupling. Using this approach, we demonstrate dramatic optically-induced chiral transport for clockwise and counterclockwise phonons in a symmetric resonator. This induced chirality also enhances isolation from the thermal bath and leads to gain-free reduction of the intrinsic damping of the phonons. Surprisingly, this passive mechanism is also accompanied by a chiral reduction in heat load leading to a novel optical cooling of the mechanics. This technique has the potential to improve upon the fundamental thermal limits of resonant mechanical sensor, which cannot be otherwise attained through conventional optomechanical cooling.

Entanglement area laws for long-range interacting systems - Zhe-Xuan Gong; Michael Foss-Feig; Fernando G. S. L. Brandão; Alexey V. Gorshkov (Physical Review Letters, 2017)
We prove that the entanglement entropy of any state evolved under an arbitrary 1/rα long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any α > D + 1. We also prove that for any α > 2D + 2, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.

Efficient quantum algorithms for analyzing large sparse electrical networks - Guoming Wang (Quantum Information & Computation, 2017)
Analyzing large sparse electrical networks is a fundamental task in physics, electrical engineering and computer science. We propose two classes of quantum algorithms for this task. The first class is based on solving linear systems, and the second class is based on using quantum walks. These algorithms compute various electrical quantities, including voltages, currents, dissipated powers and effective resistances, in time poly(d, c,log(N),1/λ,1/ε), where N is the number of vertices in the network, d is the maximum unweighted degree of the vertices, c is the ratio of largest to smallest edge resistance, λ is the spectral gap of the normalized Laplacian of the network, and ε is the accuracy. Furthermore, we show that the polynomial dependence on 1/λ is necessary. This implies that our algorithms are optimal up to polynomial factors and cannot be signficantly improved.

Efficient simulation of sparse Markovian quantum dynamics - Andrew M. Childs; Tongyang Li (Quantum Information and Computation, 2017)
Quantum algorithms for simulating Hamiltonian dynamics have been extensively developed, but there has been much less work on quantum algorithms for simulating the dynamics of open quantum systems. We give the first efficient quantum algorithms for simulating Markovian quantum dynamics generated by Lindbladians that are not necessarily local. We introduce two approaches to simulating sparse Lindbladians. First, we show how to simulate Lindbladians that act within small invariant subspaces using a quantum algorithm to implement sparse Stinespring isometries. Second, we develop a method for simulating sparse Lindblad operators by concatenating a sequence of short-time evolutions. We also show limitations on Lindbladian simulation by proving a no-fast-forwarding theorem for simulating sparse Lindbladians in a black-box model.

Efimov States of Strongly Interacting Photons - Michael Gullans; S. Diehl; S. T. Rittenhouse; B. P. Ruzic; J. P. D'Incao; P. Julienne; Alexey V. Gorshkov; J. M. Taylor (Physical Review Letters, 2017)
We demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity, but with spatially anisotropic wavefunctions in the original coordinates. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the non-equilbrium, many-body regime.

An Elementary Proof of Private Random Number Generation from Bell Inequalities - Carl Miller (2017)
The field of device-independent quantum cryptography has seen enormous success in the past several years, including security proofs for key distribution and random number generation that account for arbitrary imperfections in the devices used. Full security proofs in the field so far are long and technically deep. In this paper we show that the concept of the mirror adversary can be used to simplify device-independent proofs. We give a short proof that any bipartite Bell violation can be used to generate private random numbers. The proof is based on elementary techniques and is self-contained.

Emergent equilibrium in many-body optical bistability - Michael Foss-Feig; Pradeep Niroula; Jeremy T. Young; Mohammad Hafezi; Alexey V. Gorshkov; Ryan M. Wilson; Mohammad F. Maghrebi (Physical Review A, 2017)
Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

Entanglement Wedge Reconstruction via Universal Recovery Channels - Jordan Cotler; Patrick Hayden; Geoffrey Penington; Grant Salton; Brian Swingle; Michael Walter (2017)
We apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region's entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region's entanglement wedge can be expressed as the response of the boundary region's modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes' rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra

Exact sampling hardness of Ising spin models - Bill Fefferman; Michael Foss-Feig; Alexey V. Gorshkov (Physical Review A, 2017)
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

Exactly soluble model of boundary degeneracy - Sriram Ganeshan; Alexey V. Gorshkov; Victor Gurarie; Victor M. Galitski (Physical Review B, 2017)
We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

Experimental Comparison of Two Quantum Computing Architectures - N.M. Linke; Dmitri Maslov; Martin Roetteler; S. Debnath; C. Figgatt; K. A. Landsman; K. Wright; Christopher Monroe (Proceedings of the National Academy of Sciences, 2017)
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device [1] with limited connectivity, and the other is a fully connected trapped-ion system [2]. Even though the two systems have different native quantum interactions, both can be programmed in a way that is blind to the underlying hardware, thus allowing the first comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that employ more connectivity clearly benefit from a better connected system of qubits. While the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that co-designing particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

Experimental demonstration of cheap and accurate phase estimation - Kenneth Rudinger; Shelby Kimmel; Daniel Lobser; Peter Maunz (Physical Review Letters, 2017)
We demonstrate experimental implementation of robust phase estimation (RPE) to learn the phases of X and Y rotations on a trapped Yb+ ion qubit. We estimate these phases with uncertainties less than 4 · 10−4 radians using as few as 176 total experimental samples per phase, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We cross-validate the results of RPE with the more resource-intensive protocol of gate set tomography.

Experimental Study of Optimal Measurements for Quantum State Tomography - Sosa-Martinez, H.; Lysne, N. K.; Baldwin, C. H.; Kalev, A.; Deutsch, I. H.; Jessen, P. S. (Physical Review Letters, 2017)
Quantum tomography is a critically important tool to evaluate quantum hardware, making it essential to develop optimized measurement strategies that are both accurate and efficient. We compare a variety of strategies using nearly pure test states. Those that are informationally complete for all states are found to be accurate and reliable even in the presence of errors in the measurements themselves, while those designed to be complete only for pure states are far more efficient but highly sensitive to such errors. Our results highlight the unavoidable trade-offs inherent in quantum tomography.

Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling - Peter Bierhorst; Emanuel Knill; Scott Glancy; Alan Mink; Stephen P. Jordan; Andrea Rommal; Yi-Kai Liu; Bradley Christensen; Sae Woo Nam; Lynden K. Shalm (2017)
Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.

Exponential improvements for quantum-accessible reinforcement learning - Vedran Dunjko; Yi-Kai Liu; Xingyao Wu; J. M. Taylor (2017)
Quantum computers can offer dramatic improvements over classical devices for data analysis tasks such as prediction and classification. However, less is known about the advantages that quantum computers may bring in the setting of reinforcement learning, where learning is achieved via interaction with a task environment. Here, we consider a special case of reinforcement learning, where the task environment allows quantum access. In addition, we impose certain "naturalness" conditions on the task environment, which rule out the kinds of oracle problems that are studied in quantum query complexity (and for which quantum speedups are well-known). Within this framework of quantum-accessible reinforcement learning environments, we demonstrate that quantum agents can achieve exponential improvements in learning efficiency, surpassing previous results that showed only quadratic improvements. A key step in the proof is to construct task environments that encode well-known oracle problems, such as Simon's problem and Recursive Fourier Sampling, while satisfying the above "naturalness" conditions for reinforcement learning. Our results suggest that quantum agents may perform well in certain game-playing scenarios, where the game has recursive structure, and the agent can learn by playing against itself

Exponential Quantum Speed-ups for Semidefinite Programming with Applications to Quantum Learning - Fernando G. S. L. Brandão; Amir Kalev; Tongyang Li; Cedric Yen-Yu Lin; Krysta M. Svore; Xiaodi Wu (2017)
We give semidefinite program (SDP) quantum solvers with an exponential speed-up over classical ones. Specifically, we consider SDP instances with m constraint matrices of dimension n, each of rank at most r, and assume that the input matrices of the SDP are given as quantum states (after a suitable normalization). Then we show there is a quantum algorithm that solves the SDP feasibility problem with accuracy ǫ by using √ m log m · poly(log n,r, ǫ −1 ) quantum gates. The dependence on n provides an exponential improvement over the work of Brand ˜ao and Svore [6] and the work of van Apeldoorn et al. [23], and demonstrates an exponential quantum speed-up when m and r are small. We apply the SDP solver to the problem of learning a good description of a quantum state with respect to a set of measurements: Given m measurements and a supply of copies of an unknown state ρ, we show we can find in time √ m log m · poly(log n,r, ǫ −1 ) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as ρ on the m measurements up to error ǫ. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes’ principle. As in previous work, we obtain our algorithm by “quantizing” classical SDP solvers based on the matrix multiplicative weight update method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians with a poly-logarithmic dependence on its dimension based on the techniques developed in quantum principal component analysis, which could be of independent interest. Our quantum SDP solver is different from previous ones in the following two aspects: (1) it follows from a zero-sum game approach of Hazan [11] of solving SDPs rather than the primal-dual approach by Arora and Kale [5]; and (2) it does not rely on any sparsity assumption of the input matrices.

Extracting entanglement geometry from quantum states - Katharine Hyatt; James R. Garrison; Bela Bauer (Physical Review Letters, 2017)
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network - and hence the geometry - is largely fixed a priori by the choice of tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of non-interacting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.

Extreme learning machines for regression based on V-matrix method - Yang, Zhiyong; Zhang, Taohong; Lu, Jingcheng; Yuan Su; Zhang, Dezheng; Duan, Yaowu (Cognitive Neurodynamics, 2017)
This paper studies the joint effect of V-matrix, a recently proposed framework for statistical inferences, and extreme learning machine (ELM) on regression problems. First of all, a novel algorithm is proposed to efficiently evaluate the V-matrix. Secondly, a novel weighted ELM algorithm called V-ELM is proposed based on the explicit kernel mapping of ELM and the V-matrix method. Though V-matrix method could capture the geometrical structure of training data, it tends to assign a higher weight to instance with smaller input value. In order to avoid this bias, a novel method called VI-ELM is proposed by minimizing both the regression error and the V-matrix weighted error simultaneously. Finally, experiment results on 12 real world benchmark datasets show the effectiveness of our proposed methods.

Fast optimization algorithms and the cosmological constant - Ning Bao; Raphael Bousso; Stephen P. Jordan; Brad Lackey (Physical Review D, 2017)
Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10−120 in a randomly generated 109 -dimensional ADK landscape.

Fast quantum computation at arbitrarily low energy - Stephen P. Jordan (Physical Review A, 2017)
One version of the energy-time uncertainty principle states that the minimum time <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-1-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.12em; box-sizing: content-box !important;">T⊥ for a quantum system to evolve from a given state to any orthogonal state is <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-2-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; box-sizing: content-box !important;">h/(4Δ<span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.026em; box-sizing: content-box !important;">E), where <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-3-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0">Δ<span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.026em; box-sizing: content-box !important;">E is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-4-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.12em; box-sizing: content-box !important;">T⊥≥<span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; box-sizing: content-box !important;">h/(2⟨<span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.026em; box-sizing: content-box !important;">E⟩), where <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-5-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0">⟨<span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.026em; box-sizing: content-box !important;">E⟩ is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-6-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.12em; box-sizing: content-box !important;">T⊥ as defining a minimal time for an elementary computational operation and correspondingly a fundamental limit on clock speed determined by a system's energy. Here we present local time-independent Hamiltonians in which computational clock speed becomes arbitrarily large relative to <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-7-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0">⟨<span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.026em; box-sizing: content-box !important;">E⟩ and <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-8-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0">Δ<span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.026em; box-sizing: content-box !important;">E as the number of computational steps goes to infinity. We argue that energy considerations alone are not sufficient to obtain an upper bound on computational speed, and that additional physical assumptions such as limits to information density and information transmission speed are necessary to obtain such a bound.

Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions - Zachary Eldredge; Zhe-Xuan Gong; Ali Hamed Moosavian; Michael Foss-Feig; Alexey V. Gorshkov (Physical Review Letters, 2017)
In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance <span class="MathJax" id="MathJax-Element-1-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">L in <span class="MathJax" id="MathJax-Element-2-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">d dimensions using long-range interactions with strength bounded by <span class="MathJax" id="MathJax-Element-3-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">1/rα. If <span class="MathJax" id="MathJax-Element-4-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">α<d, the state transfer time is asymptotically independent of <span class="MathJax" id="MathJax-Element-5-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">L; if <span class="MathJax" id="MathJax-Element-6-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">α=d, the time is logarithmic in distance <span class="MathJax" id="MathJax-Element-7-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">L; if <span class="MathJax" id="MathJax-Element-8-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">d<α<d+1, transfer occurs in time proportional to <span class="MathJax" id="MathJax-Element-9-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">Lα−d; and if <span class="MathJax" id="MathJax-Element-10-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">α≥d+1, it occurs in time proportional to <span class="MathJax" id="MathJax-Element-11-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">L. We then use this protocol to upper bound the time required to create a state specified by a MERA (multiscale entanglement renormalization ansatz) tensor network, and show that, if the linear size of the MERA state is <span class="MathJax" id="MathJax-Element-12-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">L, then it can be created in time that scales with <span class="MathJax" id="MathJax-Element-13-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">L identically to state transfer up to multiplicative logarithmic corrections.

Genuine N -partite entanglement without N -partite correlation functions - Minh C. Tran; Margherita Zuppardo; Anna de Rosier; Lukas Knips; Wieslaw Laskowski; Tomasz Paterek; Harald Weinfurter (Physical Review A, 2017)
A genuinely <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-3-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.085em; box-sizing: content-box !important;">N-partite entangled state may display vanishing <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-4-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.085em; box-sizing: content-box !important;">N-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-5-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.085em; box-sizing: content-box !important;">N is to design an “antistate” in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its antistate then produces a mixed state with no <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-6-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.085em; box-sizing: content-box !important;">N-partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of “entanglement without correlations” involve an odd number of particles. Here we further develop the idea of antistates, thereby shedding light on the different properties of even and odd particle systems. We conjecture that there is no antistate to any pure even-<span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-7-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.085em; box-sizing: content-box !important;">N-party entangled state making the simple construction scheme unfeasible. However, as we prove by construction, higher-rank examples of entanglement without correlations for arbitrary even <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-8-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.085em; box-sizing: content-box !important;">N indeed exist. These classes of states exhibit genuine entanglement and even violate an <span class="mjx-chtml MathJax_CHTML" id="MathJax-Element-9-Frame" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 14.84px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; padding-top: 1px; padding-bottom: 1px;" tabindex="0"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.475em; padding-bottom: 0.273em; padding-right: 0.085em; box-sizing: content-box !important;">N-partite Bell inequality, clearly demonstrating the nonclassical features of these states as well as showing their applicability for quantum information processing.

Hamiltonian Simulation with Optimal Sample Complexity - Shelby Kimmel; Cedric Yen-Yu Lin; Guang Hao Low; Maris Ozols; Theodore J. Yoder (npj Quantum Information, 2017)
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631--633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.

High-Order Multipole Radiation from Quantum Hall States in Dirac Materials - Michael Gullans; J. M. Taylor; Atac Imamoglu; Pouyan Ghaemi; Mohammad Hafezi (Physical Review B, 2017)
Topological states can exhibit electronic coherence on macroscopic length scales. When the coherence length exceeds the wavelength of light, one can expect new phenomena to occur in the optical response of these states. We theoretically characterize this limit for integer quantum Hall states in two-dimensional Dirac materials. We find that the radiation from the bulk is dominated by dipole emission, whose spectral properties vary with the local disorder potential. On the other hand, the radiation from the edge is characterized by large multipole moments in the far-field associated with the efficient transfer of angular momentum from the electrons into the scattered light. These results demonstrate that high-order multipole transitions are a necessary component for the optical spectroscopy and control of quantum Hall and related topological states in electronic systems.

Input-output theory for spin-photon coupling in Si double quantum dots - Benito, M.; Mi, X.; J. M. Taylor; Petta, J. R.; Burkard, Guido (Physical Review B, 2017)
The interaction of qubits via microwave frequency photons enables long-distance qubit-qubit coupling and facilitates the realization of a large-scale quantum processor. However, qubits based on electron spins in semiconductor quantum dots have proven challenging to couple to microwave photons. In this theoretical work we show that a sizable coupling for a single electron spin is possible via spin-charge hybridization using a magnetic field gradient in a silicon double quantum dot. Based on parameters already shown in recent experiments, we predict optimal working points to achieve a coherent spin-photon coupling, an essential ingredient for the generation of long-range entanglement. Furthermore, we employ input-output theory to identify observable signatures of spin-photon coupling in the cavity output field, which may provide guidance to the experimental search for strong coupling in such spin-photon systems and opens the way to cavity-based readout of the spin qubit.

Lieb-Robinson bounds on n-partite connected correlation functions - Minh C. Tran; James R. Garrison; Zhe-Xuan Gong; Alexey V. Gorshkov (Phys. Rev. A 96, 052334, 2017)
Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

Lieb-Robinson bounds on n-partite connected correlations - Minh C. Tran; James R. Garrison; Zhe-Xuan Gong; Alexey V. Gorshkov (Physical Review A, 2017)
Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an <span class="MathJax" id="MathJax-Element-2-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an <span class="MathJax" id="MathJax-Element-3-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

Light-induced fractional quantum Hall phases in graphene - Areg Ghazaryan; Tobias Graß; Michael Gullans; Pouyan Ghaemi; Mohammad Hafezi (Physical Review Letters, 2017)
We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

Machine Learning techniques for state recognition and auto-tuning in quantum dots - Sandesh S. Kalantre; Justyna P. Zwolak; Stephen Ragole; Xingyao Wu; Neil M. Zimmerman; M. D. Stewart; J. M. Taylor (2017)
Recent progress in building large-scale quantum devices for exploring quantum computing and simulation paradigms has relied upon effective tools for achieving and maintaining good experimental parameters, i.e. tuning up devices. In many cases, including in quantum-dot based architectures, the parameter space grows substantially with the number of qubits, and may become a limit to scalability. Fortunately, machine learning techniques for pattern recognition and image classification using so-called deep neural networks have shown surprising successes for computer-aided understanding of complex systems. In this work, we use deep and convolutional neural networks to characterize states and charge configurations of semiconductor quantum dot arrays when one can only measure a current-voltage characteristic of transport (here conductance) through such a device. For simplicity, we model a semiconductor nanowire connected to leads and capacitively coupled to depletion gates using the Thomas-Fermi approximation and Coulomb blockade physics. We then generate labeled training data for the neural networks, and find at least 90 % accuracy for charge and state identification for single and double dots purely from the dependence of the nanowire’s conductance upon gate voltages. Using these characterization networks, we can then optimize the parameter space to achieve a desired configuration of the array, a technique we call ‘auto-tuning’. Finally, we show how such techniques can be implemented in an experimental setting by applying our approach to an experimental data set, and outline further problems in this domain, from using charge sensing data to extensions to full one and two-dimensional arrays, that can be tackled with machine learning.

Modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum Hamiltonians - Michael Jarret; Stephen P. Jordan (Journal of Mathematical Analysis and Applications, 2017)
We adapt modulus of continuity estimates to the study of spectra of combinatorial graph Laplacians, as well as the Dirichlet spectra of certain weighted Laplacians. The latter case is equivalent to stoquastic Hamiltonians and is of current interest in both condensed matter physics and quantum computing. In particular, we introduce a new technique which bounds the spectral gap of such Laplacians (Hamiltonians) by studying the limiting behavior of the oscillations of their eigenvectors when introduced into the heat equation. Our approach is based on recent advances in the PDE literature, which include a proof of the fundamental gap theorem by Andrews and Clutterbuck.

Multicritical behavior in dissipative Ising models - Vincent R. Overbeck; Mohammad F. Maghrebi; Alexey V. Gorshkov; Hendrik Weimer (Physical Review A, 2017)
We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

Nonlocal games, synchronous correlations, and Bell inequalities - Brad Lackey; Nishant Rodrigues (2017)
A nonlocal game with a synchronous correlation is a natural generalization of a function between two finite sets, and has recently appeared in the context of quantum graph homomorphisms. In this work we examine analogues of Bell's inequalities for synchronous correlations. We show that, unlike general correlations and the CHSH inequality, there can be no quantum Bell violation among synchronous correlations with two measurement settings. However we exhibit explicit analogues of Bell's inequalities for synchronous correlations with three measurement settings and two outputs, provide an analogue of Tsirl'son's bound in this setting, and give explicit quantum correlations that saturate this bound.

Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator - J. Zhang; G. Pagano; P. W. Hess; A. Kyprianidis; P. Becker; H. Kaplan; Alexey V. Gorshkov; Z. -X. Gong; C. Monroe (Nature, 2017)
A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.

Optimal length of decomposition sequences composed of imperfect gates - Yunseong Nam; R. Blümel (Quantum Information Processing, 2017)
Quantum error correcting circuitry is both a resource for correcting errors and a source for generating errors. A balance has to be struck between these two aspects. Perfect quantum gates do not exist in nature. Therefore, it is important to investigate how flaws in the quantum hardware affect quantum computing performance. We do this in two steps. First, in the presence of realistic, faulty quantum hardware, we establish how quantum error correction circuitry achieves reduction in the extent of quantum information corruption. Then, we investigate fault-tolerant gate sequence techniques that result in an approximate phase rotation gate, and establish the existence of an optimal length <span class="MathJax" data-mathml="L<mtext>opt</mtext>" id="MathJax-Element-1-Frame" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" tabindex="0"><nobr aria-hidden="true" style="box-sizing: border-box; transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;">L<span class="mtext" id="MathJax-Span-7" style="box-sizing: border-box; transition: none; display: inline; position: static; vertical-align: 0px; line-height: normal; font-size: 13.3411px; font-family: MathJax_Main;">opt<span class="MJX_Assistive_MathML" role="presentation" style="box-sizing: border-box; top: 0px; left: 0px; clip: rect(1px 1px 1px 1px); user-select: none; position: static; display: inline; transition: none; vertical-align: 0px; line-height: normal; height: 1px !important; width: 1px !important; overflow: hidden !important;">L<mtext>opt</mtext> of the length L of the decomposition sequence. The existence of <span class="MathJax" data-mathml="L<mtext>opt</mtext>" id="MathJax-Element-2-Frame" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" tabindex="0"><nobr aria-hidden="true" style="box-sizing: border-box; transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;">L<span class="mtext" id="MathJax-Span-14" style="box-sizing: border-box; transition: none; display: inline; position: static; vertical-align: 0px; line-height: normal; font-size: 13.3411px; font-family: MathJax_Main;">opt<span class="MJX_Assistive_MathML" role="presentation" style="box-sizing: border-box; top: 0px; left: 0px; clip: rect(1px 1px 1px 1px); user-select: none; position: static; display: inline; transition: none; vertical-align: 0px; line-height: normal; height: 1px !important; width: 1px !important; overflow: hidden !important;">L<mtext>opt</mtext> is due to the competition between the increase in gate accuracy with increasing L, but the decrease in gate performance due to the diffusive proliferation of gate errors due to faulty basis gates. We present an analytical formula for the gate fidelity as a function of L that is in satisfactory agreement with the results of our simulations and allows the determination of <span class="MathJax" data-mathml="L<mtext>opt</mtext>" id="MathJax-Element-3-Frame" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" tabindex="0"><nobr aria-hidden="true" style="box-sizing: border-box; transition: none; border: 0px; padding: 0px; margin: 0px; max-width: none; max-height: none; min-width: 0px; min-height: 0px; vertical-align: 0px; line-height: normal;">L<span class="mtext" id="MathJax-Span-21" style="box-sizing: border-box; transition: none; display: inline; position: static; vertical-align: 0px; line-height: normal; font-size: 13.3411px; font-family: MathJax_Main;">opt<span class="MJX_Assistive_MathML" role="presentation" style="box-sizing: border-box; top: 0px; left: 0px; clip: rect(1px 1px 1px 1px); user-select: none; position: static; display: inline; transition: none; vertical-align: 0px; line-height: normal; height: 1px !important; width: 1px !important; overflow: hidden !important;">L<mtext>opt</mtext> via the solution of a transcendental equation. Our result is universally applicable since gate sequence approximations also play an important role, e.g., in atomic and molecular physics and in nuclear magnetic resonance.

Optomechanical Analogy for Toy Cosmology with Quantized Scale Factor - Smiga, Joseph A.; J. M. Taylor (Entropy, 2017)
The simplest cosmology—the Friedmann–Robertson–Walker–Lemaître (FRW) model— describes a spatially homogeneous and isotropic universe where the scale factor is the only dynamical parameter. Here we consider how quantized electromagnetic fields become entangled with the scale factor in a toy version of the FRW model. A system consisting of a photon, source, and detector is described in such a universe, and we find that the detection of a redshifted photon by the detector system constrains possible scale factor superpositions. Thus, measuring the redshift of the photon is equivalent to a weak measurement of the underlying cosmology. We also consider a potential optomechanical analogy system that would enable experimental exploration of these concepts. The analogy focuses on the effects of photon redshift measurement as a quantum back-action on metric variables, where the position of a movable mirror plays the role of the scale factor. By working in the rotating frame, an effective Hubble equation can be simulated with a simple free moving mirror.

Optomechanically-induced chiral transport of phonons in one dimension - Xunnong Xu; J. M. Taylor (2017)
Non-reciprocal devices, with one-way transport properties, form a key component for isolating and controlling light in photonic systems. Optomechanical systems have emerged as a potential platform for optical non-reciprocity, due to ability of a pump laser to break time and parity symmetry in the system. Here we consider how the non-reciprocal behavior of light can also impact the transport of sound in optomechanical devices. We focus on the case of a quasi one dimensional optical ring resonator with many mechanical modes coupled to light via the acousto-optic effect. The addition of disorder leads to finite diffusion for phonon transport in the material, largely due to elastic backscattering between clockwise and counter-clockwise phonons. We show that a laser pump field, along with the assumption of high quality-factor, sideband-resolved optical resonances, suppresses the effects of disorder and leads to the emergence of chiral diffusion, with direction-dependent diffusion emerging in a bandwidth similar to the phase-matching bandwidth for Brillouin scattering. A simple diagrammatic theory connects the observation of reduced mechanical linewidths directly to the associated phonon diffusion properties, and helps explain recent experimental results.

Out-of-time-order correlators in finite open systems - S. V. Syzranov; Alexey V. Gorshkov; V. Galitski (2017)
We study out-of-time order correlators (OTOCs) of the form hAˆ(t)Bˆ(0)Cˆ(t)Dˆ(0)i for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially ∝ Paie −t/τi + const to a constant value at t → ∞, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focussing on the case of a two-level system, we calculate microscopically the decay times τi and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.

Partial breakdown of quantum thermalization in a Hubbard-like model - James R. Garrison; Ryan V. Mishmash; Matthew P. A. Fisher (Physical Review B, 2017)
We study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain without disorder, with both spin and charge degrees of freedom. The eigenstates of this model exhibit peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a “volume law” to an “area law” after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, nonthermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.

Penalty models for bitstrings of constant Hamming weight - Brad Lackey (2017)
To program a quantum annealer, one must construct objective functions whose minima encode hard constraints imposed by the underlying problem. For such "penalty models," one desires the additional property that the gap in the objective value between such minima and states that fail the constraints is maximized amongst the allowable objective functions. In this short note, we prove the standard penalty model for the constraint that a bitstring has given Hamming weight is optimal with respect to objective value gap.

Pendular trapping conditions for ultracold polar molecules enforced by external electric fields - Ming Li; Alexander Petrov; Constantinos Makrides; Eite Tiesinga; Svetlanta Kotochigova (Physical Review A, 2017)
We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar <span class="MathJax" id="MathJax-Element-1-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">23Na<span class="MathJax" id="MathJax-Element-2-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">40K polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of <span class="MathJax" id="MathJax-Element-3-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">5.26(15) kV/cm and an angle of <span class="MathJax" id="MathJax-Element-4-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">54.7∘ between this field and the polarization of the optical laser lead to a trapping design for <span class="MathJax" id="MathJax-Element-5-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">23Na<span class="MathJax" id="MathJax-Element-6-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">40K molecules where decoherences due laser-intensity fluctuations and fluctuations in the direction of its polarization are kept to a minimum. One standard deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions pairs of hyperfine-rotational states of <span class="MathJax" id="MathJax-Element-7-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">v=0 molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.

Phase retrieval using unitary 2-designs - Shelby Kimmel; Yi-Kai Liu (SampTA 2017, 2017)
We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |tr(C†U)|2 with unitary matrices C that are chosen by the observer. This problem has applications to quantum process tomography, when the unknown process is a unitary operation. We show that PhaseLift, a convex programming algorithm for phase retrieval, can be adapted to this matrix setting, using measurements that are sampled from unitary 4- and 2-designs. In the case of unitary 4-design measurements, we show that PhaseLift can reconstruct all unitary matrices, using a nearoptimal number of measurements. This extends previous work on PhaseLift using spherical 4-designs. In the case of unitary 2-design measurements, we show that PhaseLift still works pretty well on average: it recovers almost all signals, up to a constant additive error, using a near-optimal number of measurements. These 2-design measurements are convenient for quantum process tomography, as they can be implemented via randomized benchmarking techniques. This is the first positive result on PhaseLift using 2-designs.

Phase-space mixing in dynamically unstable, integrable few-mode quantum systems - Ranchu Mathew; Eite Tiesinga (Physical Review A, 2017)
Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA) and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as 1/O(ln N), where N is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady state value is a damped oscillation and the damping is Gaussian in time. We confirm our results with numerical TWA simulations.

Provable quantum state tomography via non-convex methods - Anastasios Kyrillidis; Amir Kalev; Dohuyng Park; Srinadh Bhojanapalli; Constantine Caramanis; Sujay Sanghavi (2017)
With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from non-convex optimization. The algorithm excels in the compressed-sensing-like setting, where only a few data points are measured from a lowrank or highly-pure quantum state of a high-dimensional system. We show that the algorithm can practically be used in quantum tomography problems that are beyond the reach of convex solvers, and, moreover, is faster than other state-of-the-art non-convex approaches. Crucially, we prove that, despite being a non-convex program, under mild conditions, the algorithm is guaranteed to converge to the global minimum of the problem; thus, it constitutes a provable quantum state tomography protocol.

Quantum algorithm for linear differential equations with exponentially improved dependence on precision - Dominic W. Berry; Andrew M. Childs; Aaron Ostrander; Guoming Wang (Communications in Mathematical Physics, 2017)
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time. The complexity of the algorithm is polynomial in the logarithm of the inverse error, an exponential improvement over previous quantum algorithms for this problem. Our result builds upon recent advances in quantum linear systems algorithms by encoding the simulation into a sparse, well-conditioned linear system that approximates evolution according to the propagator using a Taylor series. Unlike with finite difference methods, our approach does not require additional hypotheses to ensure numerical stability.

Quantum Algorithm for Linear Regression - Guoming Wang (Physical Review A, 2017)
We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which only yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at negligible cost. Moreover, our algorithm does not require the design matrix to be sparse or need any help from additional state preparation procedures. It runs in time poly(log(N), d, κ, 1/), where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit without computing its parameters explicitly. This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

Quantum algorithm for systems of linear equations with exponentially improved dependence on precision - Andrew M. Childs; Robin Kothari; Rolando D. Somma (SIAM Journal on Computing, 2017)
Harrow, Hassidim, and Lloyd showed that for a suitably specified N×N matrix A and N-dimensional vector b⃗ , there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of equations Ax⃗ =b⃗ . If A is sparse and well-conditioned, their algorithm runs in time poly(logN,1/ϵ), where ϵ is the desired precision in the output state. We improve this to an algorithm whose running time is polynomial in log(1/ϵ), exponentially improving the dependence on precision while keeping essentially the same dependence on other parameters. Our algorithm is based on a general technique for implementing any operator with a suitable Fourier or Chebyshev series representation. This allows us to bypass the quantum phase estimation algorithm, whose dependence on ϵ is prohibitive.

Quantum Algorithms for Graph Connectivity and Formula Evaluation - Stacey Jeffery; Shelby Kimmel (2017)
We give a new upper bound on the quantum query complexity of deciding st-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation reduces to deciding connectivity on just such a class of graphs. Applying the algorithm for st-connectivity to Boolean formula evaluation problems, we match the O( √ N) bound on the quantum query complexity of evaluating formulas on N variables, give a quadratic speed-up over the classical query complexity of a certain class of promise Boolean formulas, and show this approach can yield superpolynomial quantum/classical separations. These results indicate that this st-connectivity-based approach may be the “right” way of looking at quantum algorithms for formula evaluation.

Quantum Fully Homomorphic Encryption With Verification - Gorjan Alagic; Yfke Dulek; Christian Schaffner; Florian Speelman (Proceedings of ASIACRYPT 2017, 2017)
Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is reasonable to hope that quantum FHE (or QFHE) will lead to many new results in the quantum setting. However, a crucial ingredient in almost all applications of FHE is circuit verification. Classically, verification is performed by checking a transcript of the homomorphic computation. Quantumly, this strategy is impossible due to no-cloning. This leads to an important open question: can quantum computations be delegated and verified in a non-interactive manner? In this work, we answer this question in the affirmative, by constructing a scheme for QFHE with verification (vQFHE). Our scheme provides authenticated encryption, and enables arbitrary polynomial-time quantum computations without the need of interaction between client and server. Verification is almost entirely classical; for computations that start and end with classical states, it is completely classical. As a first application, we show how to construct quantum one-time programs from classical one-time programs and vQFHE.

Quantum Non-malleability and Authentication - Gorjan Alagic; Christian Majenz (In: Katz J., Shacham H. (eds) Advances in Cryptology – CRYPTO 2017. Lecture Notes in Computer Science. Springer, Cham, 2017)
In encryption, non-malleability is a highly desirable property: it ensures that adversaries cannot manipulate the plaintext by acting on the ciphertext. In [6], Ambainis et al. gave a definition of non-malleability for the encryption of quantum data. In this work, we show that this definition is too weak, as it allows adversaries to “inject” plaintexts of their choice into the ciphertext. We give a new definition of quantum non-malleability which resolves this problem. Our definition is expressed in terms of entropic quantities, considers stronger adversaries, and does not assume secrecy. Rather, we prove that quantum non-malleability implies secrecy; this is in stark contrast to the classical setting, where the two properties are completely independent. For unitary schemes, our notion of non-malleability is equivalent to encryption with a two-design (and hence also to the definition of [6]). Our techniques also yield new results regarding the closely-related task of quantum authentication. We show that “total authentication” (a notion recently proposed by Garg et al. [18]) can be satisfied with two-designs, a significant improvement over the eight-design construction of [18]. We also show that, under a mild adaptation of the rejection procedure, both total authentication and our notion of non-malleability yield quantum authentication as defined by Dupuis et al. [16].

Quantum simulation of ferromagnetic Heisenberg model - Yiping Wang; Minh C. Tran; J. M. Taylor (2017)
Large quantum simulators, with sufficiently many qubits to be impossible to simulate classically, become hard to experimentally validate. We propose two tests of a quantum simulator with Heisenberg interaction in a linear chain of spins. In the first, we propagate half of a singlet state through a chain of spin with a ferromagnetic interaction and subsequently recover the state with an antiferromagnetic interaction. The antiferromagnetic interaction is intrinsic to the system while the ferromagnetic one can be simulated by a sequence of time-dependent controls of the antiferromagnetic interaction and Suzuki-Trotter approximations. In the second test, we use the same technique to transfer a spin singlet state from one end of a spin chain to the other. We show that the tests are robust against parametric errors in operation of the simulator and may be applicable even without error correction.

Quantum state tomography via reduced density matrices - Tao Xin; Dawei Lu; Joel Klassen; Nengkun Yu; Zhengfeng Ji; Jianxin Chen; Xian Ma; Guilu Long; Bei Zeng; Raymond Laflamme (Physical Review Letters, 2017)
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

Quantum-Secure Symmetric-Key Cryptography Based on Hidden Shifts - Gorjan Alagic; Alexander Russell (In: Coron JS., Nielsen J. (eds) Advances in Cryptology – EUROCRYPT 2017. Lecture Notes in Computer Science, Springer, Cham, 2017)
Recent results of Kaplan et al., building on work by Kuwakado and Morii, have shown that a wide variety of classically-secure symmetric-key cryptosystems can be completely broken by quantum chosen-plaintext attacks (qCPA). In such an attack, the quantum adversary has the ability to query the cryptographic functionality in superposition. The vulnerable cryptosystems include the Even-Mansour block cipher, the three-round Feistel network, the Encrypted-CBC-MAC, and many others. In this article, we study simple algebraic adaptations of such schemes that replace   (Z/2)n  addition with operations over alternate finite groups—such as   Z/2n —and provide evidence that these adaptations are qCPA-secure. These adaptations furthermore retain the classical security properties and basic structural features enjoyed by the original schemes. We establish security by treating the (quantum) hardness of the well-studied Hidden Shift problem as a cryptographic assumption. We observe that this problem has a number of attractive features in this cryptographic context, including random self-reducibility, hardness amplification, and—in many cases of interest—a reduction from the “search version” to the “decisional version.” We then establish, under this assumption, the qCPA-security of several such Hidden Shift adaptations of symmetric-key constructions. We show that a Hidden Shift version of the Even-Mansour block cipher yields a quantum-secure pseudorandom function, and that a Hidden Shift version of the Encrypted CBC-MAC yields a collision-resistant hash function. Finally, we observe that such adaptations frustrate the direct Simon’s algorithm-based attacks in more general circumstances, e.g., Feistel networks and slide attacks.

Randomness in nonlocal games between mistrustful players - Carl Miller; Yaoyun Shi (Quantum Information and Computation, 2017)
If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player's input at the conclusion of the game, he cannot perfectly recover her output. Thus some amount of local randomness (i.e., randomness possessed by only one player) is always obtained when randomness is certified from nonlocal games with quantum strategies. This is in contrast to non-signaling game strategies, which may produce global randomness without any local randomness. We discuss potential implications for cryptographic protocols between mistrustful parties.

Raz-McKenzie simulation with the inner product gadget - Xiaodi Wu; Penghui Yao; Henry Yuen (Electronic Colloquium on Computational Complexity (ECCC), 2017)
In this note we show that the Raz-McKenzie simulation algorithm which lifts deterministic query lower bounds to deterministic communication lower bounds can be implemented for functions f composed with the Inner Product gadget 1ip(x, y) = P i xiyi mod 2 of logarithmic size. In other words, given a function f : {0, 1} n → {0, 1} with deterministic query complexity D(f), we show that the deterministic communication complexity of the composed function f ◦ 1 n ip is Θ(D(f) log n), where f ◦ 1 n ip(x, y) = f(1ip(x 1 , y 1 ), . . . , 1ip(x n , y n )) where x = (x 1 , . . . , x n ), y = (y 1 , . . . , y n ) and each x i and y i are O(log n) bit strings. In [RM97] and [GPW15], the simulation algorithm is implemented for functions composed with the Indexing gadget, where the size of the gadget is polynomial in the input length of the outer function f.

On the readiness of quantum optimization machines for industrial applications - Alejandro Perdomo-Ortiz; Alexander Feldman; Asier Ozaeta; Sergei V. Isakov; Zheng Zhu; Bryan O'Gorman; Helmut G. Katzgraber; Alexander Diedrich; Hartmut Neven; Johan de Kleer; Brad Lackey; Rupak Biswas (2017)
There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for near-term quantum annealers.

Rigidity of the magic pentagram game - Amir Kalev; Carl Miller (Quantum Science and Technology, 2017)
A game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it permits a strictly classical user to trust behavior in the quantum realm. This property can be traced back as far as 1998 (Mayers and Yao) and has been proved for multiple classes of games. In this paper we prove ridigity for the magic pentagram game, a simple binary constraint satisfaction game involving two players, five clauses and ten variables. We show that all near-optimal strategies for the pentagram game are approximately equivalent to a unique strategy involving real Pauli measurements on three maximally-entangled qubit pairs.

Robust entanglement renormalization on a noisy quantum computer - Isaac H. Kim; Brian Swingle (2017)
A method to study strongly interacting quantum many-body systems at and away from criticality is proposed. The method is based on a MERA-like tensor network that can be efficiently and reliably contracted on a noisy quantum computer using a number of qubits that is much smaller than the system size. We prove that the outcome of the contraction is stable to noise and that the estimated energy upper bounds the ground state energy. The stability, which we numerically substantiate, follows from the positivity of operator scaling dimensions under renormalization group flow. The variational upper bound follows from a particular assignment of physical qubits to different locations of the tensor network plus the assumption that the noise model is local. We postulate a scaling law for how well the tensor network can approximate ground states of lattice regulated conformal field theories in d spatial dimensions and provide evidence for the postulate. Under this postulate, a O(logd (1/δ))-qubit quantum computer can prepare a valid quantum-mechanical state with energy density δ above the ground state. In the presence of noise, δ = O( logd+1(1/)) can be achieved, where is the noise strength.

Sequential measurements, disturbance and property testing - Aram W. Harrow; Cedric Yen-Yu Lin; Ashley Montanaro (Proceedings of ​the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2017)
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and the case that all of the measurements have low probability of acceptance. The measurements cannot simply be tried in sequence, because early measurements may disturb the state being tested. One procedure is based on a variant of Marriott-Watrous amplification. The other procedure is based on the use of a test for this disturbance, which is applied with low probability. We find a number of applications. First, quantum query complexity separations in the property testing model for testing isomorphism of functions under group actions. We give quantum algorithms for testing isomorphism, linear isomorphism and affine isomorphism of boolean functions which use exponentially fewer queries than is possible classically, and a quantum algorithm for testing graph isomorphism which uses polynomially fewer queries than the best algorithm known. Second, testing properties of quantum states and operations. We show that any finite property of quantum states can be tested using a number of copies of the state which is logarithmic in the size of the property, and give a test for genuine multipartite entanglement of states of n qubits that uses O(n) copies of the state. Third, correcting an error in a result of Aaronson on de-Merlinizing quantum protocols. This result claimed that, in any one-way quantum communication protocol where two parties are assisted by an all-powerful but untrusted third party, the third party can be removed with only a modest increase in the communication cost. We give a corrected proof of a key technical lemma required for Aaronson's result.

Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations - Dmitri Maslov; Martin Roetteler (2017)
In this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004: to implement a general stabilizer circuit, we reduce their 11-stage computation -HC-P-C-P-C-H-P-C-P-C- over the gate set consisting of Hadamard, Controlled-NOT, and Phase gates, into a 7-stage computation of the form -C-CZ-P-H-P-CZ-C-. We show arguments in support of using -CZ- stages over the -C- stages: not only the use of -CZ- stages allows a shorter layered expression, but -CZ- stages are simpler and appear to be easier to implement compared to the -C- stages. Based on this decomposition, we develop a twoqubit gate depth-(14n−4) implementation of stabilizer circuits over the gate library {H, P, CNOT}, executable in the LNN architecture, improving best previously known depth-25n circuit, also executable in the LNN architecture. Our constructions rely on Bruhat decomposition of the symplectic group and on folding arbitrarily long sequences of the form (-P-C-) m into a 3-stage computation -P-CZ-C-. Our results include the reduction of the 11-stage decomposition -H-C-P-C-P-C-H-P-C-P-C- into a 9-stage decomposition of the form -C-P-C-P-H-C-P-C-P-. This reduction is based on the Bruhat decomposition of the symplectic group. This result also implies a new normal form for stabilizer circuits. We show that a circuit in this normal form is optimal in the number of Hadamard gates used. We also show that the normal form has an asymptotically optimal number of parameters.

Simultaneous, Full Characterization of a Single-Photon State - Thomay, Tim; Polyakov, Sergey V.; Gazzano, Olivier; Goldschmidt, Elizabeth; Eldredge, Zachary D.; Huber, Tobias; Loo, Vivien; Solomon, Glenn S. (Physical Review X, 2017)
As single-photon sources become more mature and are used more often in quantum information, communications, and measurement applications, their characterization becomes more important. Singlephoton-like light is often characterized by its brightness, as well as two quantum properties: the suppression of multiphoton content and the photon indistinguishability. While it is desirable to obtain these quantities from a single measurement, currently two or more measurements are required. Here, we show that using two-photon (n ¼ 2) number-resolving detectors, one can completely characterize single-photon-like states in a single measurement, where previously two or more measurements were necessary. We simultaneously determine the brightness, the suppression of multiphoton states, the indistinguishability, and the statistical distribution of Fock states to third order for a quantum light source. We find n ≥ 3 number-resolving detectors provide no additional advantage in the single-photon characterization. The new method extracts more information per experimental trial than a conventional measurement for all input states and is particularly more efficient for statistical mixtures of photon states. Thus, using this n ¼ 2, number-resolving detector scheme will provide advantages in a variety of quantum optics measurements and systems.

A solvable family of driven-dissipative many-body systems - Michael Foss-Feig; Jeremy T. Young; Victor V. Albert; Alexey V. Gorshkov; Mohammad F. Maghrebi (Physical Review Letters, 2017)
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. And conversely, the relative scarcity of solutions for non-equilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently in any number of spatial dimensions. We leverage these solutions to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions, and to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture.

Substochastic Monte Carlo Algorithms - Michael Jarret; Brad Lackey (2017)
In this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than simulated annealing, prove to be worthy optimization algorithms in their own right. In SSMC, a population of walkers is initialized according to a known distribution on an arbitrary search space and varied into the solution of some optimization problem of interest. The first argument of this paper shows how an existing classical algorithm, "Go-With-The-Winners" (GWW), is a limiting case of SSMC when restricted to binary search and particular driving dynamics. Although limiting to GWW, SSMC is more general. We show that (1) GWW can be efficiently simulated within the SSMC framework, (2) SSMC can be exponentially faster than GWW, (3) by naturally incorporating structural information, SSMC can exponentially outperform the quantum algorithm that first inspired it, and (4) SSMC exhibits desirable search features in general spaces. Our approach combines ideas from genetic algorithms (GWW), theoretical probability (Fleming-Viot processes), and quantum computing. Not only do we demonstrate that SSMC is often more efficient than competing algorithms, but we also hope that our results connecting these disciplines will impact each independently. An implemented version of SSMC has previously enjoyed some success as a competitive optimization algorithm for Max-<span class="MathJax" id="MathJax-Element-1-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">k-SAT.

Super-polynomial and exponential improvements for quantum-enhanced reinforcement learning - Vedran Dunjko; Yi-Kai Liu; Xingyao Wu; J. M. Taylor (2017)
Recent work on quantum machine learning has demonstrated that quantum computers can offer dramatic improvements over classical devices for data mining, prediction and classification. However, less is known about the advantages using quantum computers may bring in the more general setting of reinforcement learning, where learning is achieved via interaction with a task environment that provides occasional rewards. Reinforcement learning can incorporate data-analysis-oriented learning settings as special cases, but also includes more complex situations where, e.g., reinforcing feedback is delayed. In a few recent works, Grover-type amplification has been utilized to construct quantum agents that achieve up-to-quadratic improvements in learning efficiency. These encouraging results have left open the key question of whether super-polynomial improvements in learning times are possible for genuine reinforcement learning problems, that is problems that go beyond the other more restricted learning paradigms. In this work, we provide a family of such genuine reinforcement learning tasks. We construct quantum-enhanced learners which learn super-polynomially, and even exponentially faster than any classical reinforcement learning model, and we discuss the potential impact our results may have on future technologies.

Thermodynamic Analysis of Classical and Quantum Search Algorithms - Ray Perlner; Yi-Kai Liu (2017)
We analyze the performance of classical and quantum search algorithms from a thermodynamic perspective, focusing on resources such as time, energy, and memory size. We consider two examples that are relevant to post-quantum cryptography: Grover’s search algorithm, and the quantum algorithm for collisionfinding. Using Bennett’s “Brownian” model of low-power reversible computation, we show classical algorithms that have the same asymptotic energy consumption as these quantum algorithms. Thus, the quantum advantage in query complexity does not imply a reduction in these thermodynamic resource costs. In addition, we present realistic estimates of the resource costs of quantum and classical search, for near-future computing technologies. We find that, if memory is cheap, classical exhaustive search can be surprisingly competitive with Grover’s algorithm.

Thermodynamic limits for optomechanical systems with conservative potentials - Stephen Ragole; Haitan Xu; John Lawall; J. M. Taylor (Physical Review B, 2017)
The mechanical force from light – radiation pressure – provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a function of external parameters. This non-analyticity, a key feature of thermodynamic phase transitions, suggests that there could be an effective thermodynamic description of optomechanical systems. Here we explicitly define the thermodynamic limit for optomechanical systems and derive a set of sufficient constraints on the system parameters as the mechanical system grows large. As an example, we show how these constraints can be satisfied in a system with Z2 symmetry and derive a free energy, allowing us to characterize this as an equilibrium phase transition.

Threshold Dynamics of a Semiconductor Single Atom Maser - Liu, Y.-Y.; Stehlik, J.; Eichler, C.; Mi, X.; Hartke, T. R.; Michael Gullans; J. M. Taylor; Petta, J. R. (Physical Review Letters, 2017)
We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

Unforgeable Quantum Encryption - Gorjan Alagic; Tommaso Gagliardoni; Christian Majenz (2017)
We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i.) ciphertext unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext attack, and (iii.) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All of our new notions also imply QIND-CPA privacy. Combining one-time authentication and classical pseudorandomness, we construct schemes for each of these new quantum security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

Universal Security for Randomness Expansion from the Spot-Checking Protocol - Carl Miller; Yaoyun Shi (SIAM Journal on Computing, 2017)
Colbeck (Thesis, 2006) proposed using Bell inequality violations to generate certified random numbers. While full quantum-security proofs have been given, it remains a major open problem to identify the broadest class of Bell inequalities and lowest performance requirements to achieve such security. In this paper, working within the broad class of spot-checking protocols, we prove exactly which Bell inequality violations can be used to achieve full security. Our result greatly improves the known noise tolerance for secure randomness expansion: for the commonly used CHSH game, full security was only known with a noise tolerance of 1.5%, and we improve this to 10.3%. We also generalize our results beyond Bell inequalities and give the first security proof for randomness expansion based on Kochen-Specker inequalities. The central technical contribution of the paper is a new uncertainty principle for the Schatten norm, which is based on the uniform convexity inequality of Ball, Carlen, and Lieb (Inventiones mathematicae, 115:463-482, 1994).

Use of global interactions in efficient quantum circuit constructions - Dmitri Maslov; Yunseong Nam (New Journal of Physics, 2017)
In this paper we study the ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. In particular, we focus on the circuits composed with global Ising entangling gates and arbitrary addressable single-qubit gates. We show that under certain circumstances the use of global operations can substantially improve the entangling gate count.

Valley Blockade in a Silicon Double Quantum Dot - Justin K. Perron; Michael Gullans; J. M. Taylor; M. D. Stewart, Jr.; Neil M. Zimmerman (Physical Review B, 2017)
Electrical transport in double quantum dots (DQDs) illuminates many interesting features of the dots' carrier states. Recent advances in silicon quantum information technologies have renewed interest in the valley states of electrons confined in silicon. Here we show measurements of DC transport through a mesa-etched silicon double quantum dot. Comparing bias triangles (i.e., regions of allowed current in DQDs) at positive and negative bias voltages we find a systematic asymmetry in the size of the bias triangles at the two bias polarities. Asymmetries of this nature are associated with blocking of tunneling events due to the occupation of a metastable state. Several features of our data lead us to conclude that the states involved are not simple spin states. Rather, we develop a model based on selective filling of valley states in the DQD that is consistent with all of the qualitative features of our data.

Why Bohr was (Mostly) Right - Jeffrey Bub (2017)
After a discussion of the Frauchiger-Renner argument that no “singleworld” interpretation of quantum mechanics can be self-consistent, I propose a “Bohrian” alternative to many-worlds or QBism as the rational option.

Adiabatic optimization versus diffusion Monte Carlo - Michael Jarret; Stephen P. Jordan; Brad Lackey (Physical Review A, 2016)
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here, we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k-SAT at k=2,3,4.

On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization - Dmitri Maslov (Physical Review A, 2016)
Various implementations of the Toffoli gate up to a relative phase have been known for years. The advantage over regular Toffoli gate is their smaller circuit size. However, their use has been often limited to a demonstration of quantum control in designs such as those where the Toffoli gate is being applied last or otherwise for some specific reasons the relative phase does not matter. It was commonly believed that the relative phase deviations would prevent the relative phase Toffolis from being very helpful in practical large-scale designs. In this paper, we report three circuit identities that provide the means for replacing certain configurations of the multiple control Toffoli gates with their simpler relative phase implementations, up to a selectable unitary on certain qubits, and without changing the overall functionality. We illustrate the advantage via applying those identities to the optimization of the known circuits implementing multiple control Toffoli gates, and report the reductions in the CNOT-count, T-count, as well as the number of ancillae used. We suggest that a further study of the relative phase Toffoli implementations and their use may yield other optimizations.

Anomalous broadening in driven dissipative Rydberg systems - E. A. Goldschmidt; T. Boulier; R. C. Brown; S. B. Koller; J. T. Young; Alexey V. Gorshkov; S. L. Rolston; J. V. Porto (Physical Review Letters, 2016)
We observe interaction-induced broadening of the two-photon 5s-18s transition in 87Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly two orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with spontaneously created populations of nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms.

Bananaworld: Quantum Mechanics for Primates - Jeffrey Bub (Oxford University Press, 2016)
This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The 'no go' theorems tell us that we can't shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.

Black Holes, Quantum Mechanics, and the Limits of Polynomial-time Computability - Stephen P. Jordan (XRDS, 2016)
Which computational problems can be solved in polynomial-time and which cannot? Though seemingly technical, this question has wide-ranging implications and brings us to the heart of both theoretical computer science and modern physics.

Causality and quantum criticality in long-range lattice models - Mohammad F. Maghrebi; Zhe-Xuan Gong; Michael Foss-Feig; Alexey V. Gorshkov (Physical Review B, 2016)

Causality and quantum criticality with long-range interactions - Mohammad F. Maghrebi; Zhe-Xuan Gong; Michael Foss-Feig; Alexey V. Gorshkov (Physical Review B, 2016)
Quantum lattice systems with long-range interactions often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model and a fermionic model with long-range interactions, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of long-range interactions, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent.

Co-Designing a Scalable Quantum Computer with Trapped Atomic Ions - Kenneth R. Brown; Jaewan Kim; Christopher Monroe (2016)
The first generation of quantum computers are on the horizon, fabricated from quantum hardware platforms that may soon be able to tackle certain tasks that cannot be performed or modelled with conventional computers. These quantum devices will not likely be universal or fully programmable, but special-purpose processors whose hardware will be tightly co-designed with particular target applications. Trapped atomic ions are a leading platform for first generation quantum computers, but are also fundamentally scalable to more powerful general purpose devices in future generations. This is because trapped ion qubits are atomic clock standards that can be made identical to a part in 10^15, and their quantum circuit connectivity can be reconfigured through the use of external fields, without modifying the arrangement or architecture of the qubits themselves. In this article we show how a modular quantum computer of any size can be engineered from ion crystals, and how the wiring between ion trap qubits can be tailored to a variety of applications and quantum computing protocols.

Collective phases of strongly interacting cavity photons - Ryan M. Wilson; Khan W. Mahmud; Anzi Hu; Alexey V. Gorshkov; Mohammad Hafezi; Michael Foss-Feig (Physical Review A, 2016)
We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-12 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

A Complete Characterization of Unitary Quantum Space - Bill Fefferman; Cedric Yen-Yu Lin (2016)
We give two complete characterizations of unitary quantum space-bounded classes. The first is based on the Matrix Inversion problem for well-conditioned matrices. We show that given the size-n efficient encoding of a 2O(k(n))×2O(k(n)) well-conditioned matrix H, approximating a particular entry of H−1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation. In particular, the problem of computing entries of H−1 for an explicit well-conditioned n×n matrix H is complete for unitary quantum logspace. We then show that the problem of approximating to high precision the least eigenvalue of a positive semidefinite matrix H, encoded as a circuit, gives a second characterization of unitary quantum space complexity. In the process we also establish an equivalence between unitary quantum space-bounded classes and certain QMA proof systems. As consequences, we establish that QMA with exponentially small completeness-soundness gap is equal to PSPACE, that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian.

Complexity of the XY antiferromagnet at fixed magnetization - Andrew M. Childs; David Gosset; Zak Webb (Quantum Information and Computation, 2016)
We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model.

Computational Security of Quantum Encryption - Gorjan Alagic; Anne Broadbent; Bill Fefferman; Tommaso Gagliardoni; Christian Schaffner; Michael St. Jules (Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security., 2016)
Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.

Demonstration of a small programmable quantum computer with atomic qubits - S. Debnath; N. M. Linke; C. Figgatt; K. A. Landsman; K. Wright; C. Monroe (Nature, 2016)
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are native to the hardware and have a mean fidelity of 98 %. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 % and 90 %, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 % and 84 %, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

Detecting Consistency of Overlapping Quantum Marginals by Separability - Jianxin Chen; Zhengfeng Ji; Nengkun Yu; Bei Zeng (Physical Review A, 2016)
The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability.

Double Quantum Dot Floquet Gain Medium - J. Stehlik; Y.-Y. Liu; C. Eichler; T. R. Hartke; X. Mi; Michael Gullans; J. M. Taylor; J. R. Petta (Physical Review X, 2016)
Strongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here we show that a single electron in a periodically driven DQD functions as a "Floquet gain medium," where population imbalances in the DQD Floquet quasi-energy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intra-cavity photon number n_c in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current -- one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of non-classical light and thermalization of driven quantum systems.

Effective Field Theory for Rydberg Polaritons - Michael Gullans; J. D. Thompson; Y. Wang; Q. -Y. Liang; V. Vuletic; M. D. Lukin; Alexey V. Gorshkov (Physical Review Letters, 2016)
We study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.

Entanglement and spin-squeezing without infinite-range interactions - Michael Foss-Feig; Zhe-Xuan Gong; Alexey V. Gorshkov; Charles W. Clark (2016)
Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.

Entangling distant resonant exchange qubits via circuit quantum electrodynamics - V. Srinivasa; J. M. Taylor; C. Tahan (Physical Review B, 2016)
We investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled via a superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubits in silicon triple dots and show that such an implementation is particularly well-suited to achieving the strong coupling regime. Our approach combines the favorable coherence properties of encoded spin qubits in silicon with the rapid and robust long-range entanglement provided by circuit QED systems.

Experimental demonstration of quantum fault tolerance - N. M. Linke; M. Gutierrez; K. A. Landsman; C. Figgatt; S. Debnath; K. R. Brown; C. Monroe (2016)
Quantum computers will eventually reach a size at which quantum error correction (QEC) becomes imperative. In order to make quantum information robust to errors introduced by qubit imperfections and flawed control operations, QEC protocols encode a logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent correction or detection of errors without destroying the logical state itself through direct measurement. While several experiments have shown a reduction of high intrinsic or artificially introduced errors in logical qubits, fault-tolerant encoding of a logical qubit has never been demonstrated. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. This advantage persists in the face of large added error rates and experimental calibration errors.

Exponential Separation of Quantum Communication and Classical Information - Anurag Anshu; Dave Touchette; Penghui Yao; Nengkun Yu (20th Annual Conference on Quantum Information Processing (QIP), 2016)
We exhibit a Boolean function for which the quantum communication complexity is exponentially larger than the classical information complexity. An exponential separation in the other direction was already known from the work of Kerenidis et. al. [SICOMP 44, pp. 1550-1572], hence our work implies that these two complexity measures are incomparable. As classical information complexity is an upper bound on quantum information complexity, which in turn is equal to amortized quantum communication complexity, our work implies that a tight direct sum result for distributional quantum communication complexity cannot hold. The function we use to present such a separation is the Symmetric k-ary Pointer Jumping function introduced by Rao and Sinha [ECCC TR15-057], whose classical communication complexity is exponentially larger than its classical information complexity. In this paper, we show that the quantum communication complexity of this function is polynomially equivalent to its classical communication complexity. The high-level idea behind our proof is arguably the simplest so far for such an exponential separation between information and communication, driven by a sequence of round-elimination arguments, allowing us to simplify further the approach of Rao and Sinha. As another application of the techniques that we develop, we give a simple proof for an optimal trade-off between Alice's and Bob's communication while computing the related Greater-Than function on n bits: say Bob communicates at most b bits, then Alice must send n/exp(O(b)) bits to Bob. This holds even when allowing pre-shared entanglement. We also present a classical protocol achieving this bound.

Figures of merit for quantum transducers - Emil Zeuthen; Albert Schliesser; Anders S. Sørensen; J. M. Taylor (2016)
Recent technical advances have sparked renewed interest in physical systems that couple simultaneously to different parts of the electromagnetic spectrum, thus enabling transduction of signals between vastly different frequencies at the level of single photons. Such hybrid systems have demonstrated frequency conversion of classical signals and have the potential of enabling quantum state transfer, e.g., between superconducting circuits and traveling optical signals. This Letter describes a simple approach for the theoretical characterization of performance for quantum transducers. Given that, in practice, one cannot attain ideal one-to-one quantum conversion, we will explore how well the transducer performs in various scenarios ranging from classical signal detection to applications for quantum information processing. While the performance of the transducer depends on the particular application in which it enters, we show that the performance can be characterized by defining two simple parameters: the signal transfer efficiency <span class="MathJax" id="MathJax-Element-1-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">η and the added noise <span class="MathJax" id="MathJax-Element-2-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">N.

A finite presentation of CNOT-dihedral operators - Matthew Amy; Jianxin Chen; Neil J. Ross (2016)
We give a finite presentation by generators and relations of unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many circuit identities are required to reduce an arbitrary CNOT-dihedral circuit to its normal form. By appropriately restricting our relations, we obtain a finite presentation of unitary operators expressible over the {CNOT, T } gate set as a corollary.

Flight of a heavy particle nonlinearly coupled to a quantum bath - Mohammad F. Maghrebi; Matthias Krüger; Mehran Kardar (Physical Review B, 2016)
Fluctuation and dissipation are by-products of coupling to the `environment.' The Caldeira-Leggett model, a successful paradigm of quantum Brownian motion, views the environment as a collection of harmonic oscillators linearly coupled to the system. However, symmetry considerations may forbid a linear coupling, e.g. for a neutral particle in quantum electrodynamics. We argue that nonlinear couplings can lead to a fundamentally different behavior. Specifically, we consider a heavy particle quadratically coupled to quantum fluctuations of the bath. In one dimension the particle undergoes anomalous diffusion, unfolding as a power-law distribution in space, reminiscent of Lévy flights. We suggest condensed matter analogs where similar effects may arise.

Grover search and the no-signaling principle - Ning Bao; Adam Bouland; Stephen P. Jordan (Physical Review Letters, 2016)
From an information processing point of view, two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox: nonunitary dynamics, non-Born-rule measurement, cloning, and postselection. We find that each model admits superluminal signaling if and only if it admits a query complexity speedup over Grover's algorithm. Furthermore, we show that the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover's algorithm. Hence, one can perform a physically reasonable experiment demonstrating superluminal signaling if and only if one can perform a reasonable experiment inducing a speedup over Grover's algorithm.

High resolution adaptive imaging of a single atom - J. D. Wong-Campos; K. G. Johnson; Brian Neyenhuis; J. Mizrahi; Chris Monroe (Nature Photonics, 2016)
We report the optical imaging of a single atom with nanometer resolution using an adaptive optical alignment technique that is applicable to general optical microscopy. By decomposing the image of a single laser-cooled atom, we identify and correct optical aberrations in the system and realize an atomic position sensitivity of ≈ 0.5 nm/Hz−−−√ with a minimum uncertainty of 1.7 nm, allowing the direct imaging of atomic motion. This is the highest position sensitivity ever measured for an isolated atom, and opens up the possibility of performing out-of-focus 3D particle tracking, imaging of atoms in 3D optical lattices or sensing forces at the yoctonewton (10−24 N) scale.

A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions - Saurabh Paul; P. R. Johnson; Eite Tiesinga (Physical Review A, 2016)
We show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.

Interacting atomic interferometry for rotation sensing approaching the Heisenberg Limit - Stephen Ragole; J. M. Taylor (Physical Review Letters, 2016)
Atom interferometers provide exquisite measurements of the properties of non-inertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory and find an analogy with the superconducting phase-slip qubit, in which the topological charge associated with persistent currents can be put into superposition. In particular, we find that strongly-interacting atoms in such a system could be used for precision rotation sensing. We compare the performance of this new sensor to an equivalent non-interacting atom interferometer, and find improvements in sensitivity and bandwidth beyond the atomic shot-noise limit.

Joint product numerical range and geometry of reduced density matrices - Jianxin Chen; Cheng Guo; Zhengfeng Ji; Yiu-Tung Poon; Nengkun Yu; Bei Zeng; Jie Zhou (2016)
The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that ruled surface emerge naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines.

Kaleidoscope of quantum phases in a long-range interacting spin-1 chain - Zhe-Xuan Gong; Mohammad F. Maghrebi; Anzi Hu; Michael Foss-Feig; Philip Richerme; Christopher Monroe; Alexey V. Gorshkov (Physical Review B, 2016)
Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α≲3, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future.

Landauer formulation of photon transport in driven systems - Chiao-Hsuan Wang; J. M. Taylor (Physical Review B, 2016)
Understanding the behavior of light in non-equilibrium scenarios underpins much of quantum optics and optical physics. While lasers provide a severe example of a non-equilibrium problem, recent interests in the near-equilibrium physics of photon `gases', such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one reexamine some near-equilibrium cases. Here we consider how a sinusoidal parametric coupling between two semi-infinite photonic transmission lines leads to the creation and flow of photons between the two lines. Our approach provides a photonic analogue to the Landauer transport formula, and using non-equilbrium Green's functions, we can extend it to the case of an interacting region between two photonic `leads' where the sinusoid frequency plays the role of a voltage bias. Crucially, we identify both the mathematical framework and the physical regime in which photonic transport is directly analogous to electronic transport, and regimes in which other new behavior such as two-mode squeezing can emerge.

Lattice Laughlin states on the torus from conformal field theory - Abhinav Deshpande; Anne E B Nielsen (Journal of Statistical Mechanics: Theory and Experiment, 2016)
Conformal field theory has turned out to be a powerful tool to derive two-dimensional lattice models displaying fractional quantum Hall physics. So far most of the work has been for lattices with open boundary conditions in at least one of the two directions, but it is desirable to also be able to handle the case of periodic boundary conditions. Here, we take steps in this direction by deriving analytical expressions for a family of conformal field theory states on the torus that is closely related to the family of bosonic and fermionic Laughlin states. We compute how the states transform when a particle is moved around the torus and when the states are translated or rotated, and we provide numerical evidence in particular cases that the states become orthonormal up to a common factor for large lattices. We use these results to find the S -matrix of the states, which turns out to be the same as for the continuum Laughlin states. Finally, we show that when the states are defined on a square lattice with suitable lattice spacing they practically coincide with the Laughlin states restricted to a lattice.

Many-body decoherence dynamics and optimised operation of a single-photon switch - Callum R. Murray; Alexey V. Gorshkov; Thomas Pohl (New Journal of Physics, 2016)
We develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimised switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments [arXiv:1511.09445] and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media.

Many-body localization in a quantum simulator with programmable random disorder - Jacob Smith; Aaron Lee; Philip Richerme; Brian Neyenhuis; Paul W. Hess; Philipp Hauke; Markus Heyl; David A. Huse; Christopher Monroe (Nature Physics, 2016)
When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the essential signatures of MBL: memory retention of the initial state, a Poissonian distribution of energy level spacings, and entanglement growth in the system at long times. Our platform can be scaled to higher numbers of spins, where detailed modeling of MBL becomes impossible due to the complexity of representing such entangled quantum states. Moreover, the high degree of control in our experiment may guide the use of MBL states as potential quantum memories in naturally disordered quantum systems.

Mapping constrained optimization problems to quantum annealing with application to fault diagnosis - Bian, Zhengbing; Chudak, Fabian; Israel, Robert; Lackey, Brad; Macready, William G; Roy, Aidan (2016)
Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave's QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave's hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.

Mapping contrained optimization problems to quantum annealing with application to fault diagnosis - Bian, Zhengbing; Chudak, Fabian; Robert Brian Israel; Brad Lackey; Macready, William G; Aiden Roy (Frontiers in ICT, 2016)
Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping Boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular, we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. By contrast, global embedding techniques generate a hardware-independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of the D-Wave hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D- Wave’s QA hardware to circuit-based fault diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000 N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Furthermore, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.

Measurement Protocol for the Entanglement Spectrum of Cold Atoms - Hannes Pichler; Guanyu Zhu; Alireza Seif; Peter Zoller; Mohammad Hafezi (Phys. Rev. X, 2016)
Entanglement, and, in particular the entanglement spectrum, plays a major role in characterizing many-body quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because of the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian and is based on the ability to produce several copies of the state under investigation together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.

Multiple scattering dynamics of fermions at an isolated p-wave resonance - Ryan Thomas; Kris O. Roberts; Eite Tiesinga; Andrew C.J. Wade; P. Blair Blakie; Amita B. Deb; Niels Kjærgaard (Nature Communications, 2016)
The wavefunction for indistinguishable fermions is anti-symmetric under particle exchange, which directly leads to the Pauli exclusion principle, and hence underlies the structure of atoms and the properties of almost all materials. In the dynamics of collisions between two indistinguishable fermions this requirement strictly prohibits scattering into 90 degree angles. Here we experimentally investigate the collisions of ultracold clouds fermionic <span class="MathJax" id="MathJax-Element-1-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">40K atoms by directly measuring scattering distributions. With increasing collision energy we identify the Wigner threshold for p-wave scattering with its tell-tale dumb-bell shape and no <span class="MathJax" id="MathJax-Element-2-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">90∘ yield. Above this threshold effects of multiple scattering become manifest as deviations from the underlying binary p-wave shape, adding particles either isotropically or axially. A shape resonance for <span class="MathJax" id="MathJax-Element-3-Frame" style="display: inline; line-height: normal; font-size: 14.4px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; font-family: "Lucida Grande", helvetica, arial, verdana, sans-serif;" tabindex="0">40K facilitates the separate observation of these two processes. The isotropically enhanced multiple scattering mode is a generic p-wave threshold phenomenon, while the axially enhanced mode should occur in any colliding particle system with an elastic scattering resonance.