Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new non-equilibrium phases of matter. In particular, we focus on "discrete time crystals", which are many-body phases of matter characterized by a spontaneously broken discrete time translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a non-equilibrium phenomenon, which is stabilized by many-body interactions, with no analog in non-interacting systems. We explain the theory behind several proposed models of discrete time crystals, and compare a number of recent realizations, in different experimental contexts.

%8 05/30/2019 %G eng %U https://arxiv.org/abs/1905.13232 %0 Journal Article %D 2019 %T Ground-state energy estimation of the water molecule on a trapped ion quantum computer %A Yunseong Nam %A Jwo-Sy Chen %A Neal C. Pisenti %A Kenneth Wright %A Conor Delaney %A Dmitri Maslov %A Kenneth R. Brown %A Stewart Allen %A Jason M. Amini %A Joel Apisdorf %A Kristin M. Beck %A Aleksey Blinov %A Vandiver Chaplin %A Mika Chmielewski %A Coleman Collins %A Shantanu Debnath %A Andrew M. Ducore %A Kai M. Hudek %A Matthew Keesan %A Sarah M. Kreikemeier %A Jonathan Mizrahi %A Phil Solomon %A Mike Williams %A Jaime David Wong-Campos %A Christopher Monroe %A Jungsang Kim %XQuantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

%8 03/07/2019 %G eng %U https://arxiv.org/abs/1902.10171 %0 Journal Article %J Commun. Math. Phys. %D 2019 %T Limitations of semidefinite programs for separable states and entangled games %A Aram W. Harrow %A Anand Natarajan %A Xiaodi Wu %XSemidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These are based on new limitations on the sum-of-squares (SoS) hierarchy in approximating two particularly important sets in quantum information theory, where previously no ω(1)-round integrality gaps were known: the set of separable (i.e. unentangled) states, or equivalently, the 2→4 norm of a matrix, and the set of quantum correlations; i.e. conditional probability distributions achievable with local measurements on a shared entangled state. In both cases no-go theorems were previously known based on computational assumptions such as the Exponential Time Hypothesis (ETH) which asserts that 3-SAT requires exponential time to solve. Our unconditional results achieve the same parameters as all of these previous results (for separable states) or as some of the previous results (for quantum correlations). In some cases we can make use of the framework of Lee-Raghavendra-Steurer (LRS) to establish integrality gaps for any SDP, not only the SoS hierarchy. Our hardness result on separable states also yields a dimension lower bound of approximate disentanglers, answering a question of Watrous and Aaronson et al. These results can be viewed as limitations on the monogamy principle, the PPT test, the ability of Tsirelson-type bounds to restrict quantum correlations, as well as the SDP hierarchies of Doherty-Parrilo-Spedalieri, Navascues-Pironio-Acin and Berta-Fawzi-Scholz.

%B Commun. Math. Phys. %V 366 %8 03/04/2019 %G eng %U https://arxiv.org/abs/1612.09306 %N 2 %& 423-468 %R https://doi.org/10.1007/s00220-019-03382-y %0 Journal Article %D 2019 %T Toward convergence of effective field theory simulations on digital quantum computers %A Omar Shehab %A Kevin A. Landsman %A Yunseong Nam %A Daiwei Zhu %A Norbert M. Linke %A Matthew J. Keesan %A Raphael C. Pooser %A Christopher R. Monroe %XWe report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansaetze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of E4=−2.220±0.179MeV may be compared with the exact Deuteron ground-state energy −2.224MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps for the first time. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.

%8 04/18/2019 %G eng %U https://arxiv.org/abs/1904.04338 %0 Journal Article %D 2018 %T Approximate Quantum Fourier Transform with O(nlog(n)) T gates %A Yunseong Nam %A Yuan Su %A Dmitri Maslov %XThe ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer enables the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete logarithm over Abelian groups, and phase estimation. The standard fault-tolerant implementation of an n-qubit QFT approximates the desired transformation by removing small-angle controlled rotations and synthesizing the remaining ones into Clifford+t gates, incurring the t-count complexity of O(n log2 (n)). In this paper we show how to obtain approximate QFT with the t-count of O(n log(n)). Our approach relies on quantum circuits with measurements and feedforward, and on reusing a special quantum state that induces the phase gradient transformation. We report asymptotic analysis as well as concrete circuits, demonstrating significant advantages in both theory and practice.

%8 2018/03/13 %G eng %U https://arxiv.org/abs/1803.04933 %0 Journal Article %J npj:Quantum Information %D 2018 %T Automated optimization of large quantum circuits with continuous parameters %A Yunseong Nam %A Neil J. Ross %A Yuan Su %A Andrew M. Childs %A Dmitri Maslov %XWe develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale quantum circuits. For the suite of benchmarks considered, we obtain substantial reductions in gate counts. In particular, we provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. Our results help bridge the gap between the computations that can be run on existing hardware and those that are expected to outperform classical computers.

%B npj:Quantum Information %V 4 %8 2017/10/19 %G eng %U https://arxiv.org/abs/1710.07345 %N 23 %R https://doi.org/10.1038/s41534-018-0072-4 %0 Journal Article %D 2018 %T An autonomous single-piston engine with a quantum rotor %A Alexandre Roulet %A Stefan Nimmrichter %A Jacob M. Taylor %XPistons are elementary components of a wide variety of thermal engines, converting input fuel into rotational motion. Here, we propose a single-piston engine where the rotational degree of freedom is effectively realized by the flux of a superconducting island -- a quantum rotor -- while the working volume corresponds to the effective length of a superconducting resonator. Our autonomous design implements a Carnot cycle, relies solely on standard thermal baths and can be implemented with circuit quantum electrodynamics. We demonstrate how the piston is able to extract a net positive work via its built-in synchronicity using a filter cavity as an effective valve, eliminating the need for external control.

%8 2018/02/15 %G eng %U https://arxiv.org/abs/1802.05486 %R https://doi.org/10.1088/2058-9565/aac40d %0 Conference Paper %B Annual ACM Symposium on the Theory of Computing STOC 2018 %D 2018 %T Capacity Approaching Codes for Low Noise Interactive Quantum Communication %A Debbie Leung %A Ashwin Nayak %A Ala Shayeghi %A Dave Touchette %A Penghui Yao %A Nengkun Yu %XWe consider the problem of implementing two-party interactive quantum

communication over noisy channels, a necessary endeavor if we wish to

fully reap quantum advantages for communication.

For an arbitrary protocol with n messages, designed for

noiseless qudit channels, our main result is a simulation method that fails with probability less than

$2^{-\Theta(n\epsilon)}$ and uses a qudit channel $n(1 + \Theta

(\sqrt{\epsilon}))$ times, of which an $\epsilon$ fraction can be

corrupted adversarially.

The simulation is thus capacity achieving to leading order, and

we conjecture that it is optimal up to a constant factor in

the $\sqrt{\epsilon}$ term.

Furthermore, the simulation is in a model that does not require

pre-shared resources such as randomness or entanglement between the

communicating parties.

Surprisingly, this outperforms the best-known overhead of $1 +

O(\sqrt{\epsilon \log \log 1/\epsilon})$ in the corresponding

\emph{classical} model, which is also conjectured to be optimal

[Haeupler, FOCS'14].

Our work also improves over the best previously known quantum result

where the overhead is a non-explicit large constant [Brassard \emph{et

al.}, FOCS'14] for low $\epsilon$.

%B Annual ACM Symposium on the Theory of Computing STOC 2018
%8 2018/01/01
%G eng
%U http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html
%0 Journal Article
%J Phys. Rev. B 98, 060501
%D 2018
%T Circuit QED-based measurement of vortex lattice order in a Josephson junction array
%A R. Cosmic
%A Hiroki Ikegami
%A Zhirong Lin
%A Kunihiro Inomata
%A Jacob M. Taylor
%A Yasunobu Nakamura
%X Superconductivity provides a canonical example of a quantum phase of matter. When superconducting islands are connected by Josephson junctions in a lattice, the low temperature state of the system can map to the celebrated XY model and its associated universality classes. This has been used to experimentally implement realizations of Mott insulator and Berezinskii--Kosterlitz--Thouless (BKT) transitions to vortex dynamics analogous to those in type-II superconductors. When an external magnetic field is added, the effective spins of the XY model become frustrated, leading to the formation of topological defects (vortices). Here we observe the many-body dynamics of such an array, including frustration, via its coupling to a superconducting microwave cavity. We take the design of the transmon qubit, but replace the single junction between two antenna pads with the complete array. This allows us to probe the system at 10 mK with minimal self-heating by using weak coherent states at the single (microwave) photon level to probe the resonance frequency of the cavity. We observe signatures of ordered vortex lattice at rational flux fillings of the array.

%B Phys. Rev. B 98, 060501 %8 2018/03/12 %G eng %U https://arxiv.org/abs/1803.04113 %R https://doi.org/10.1103/PhysRevB.98.060501 %0 Journal Article %J Optica %D 2018 %T Electro-mechano-optical NMR detection %A Kazuyuki Takeda %A Kentaro Nagasaka %A Atsushi Noguchi %A Rekishu Yamazaki %A Yasunobu Nakamura %A Eiji Iwase %A Jacob M. Taylor %A Koji Usami %XSignal reception of nuclear magnetic resonance (NMR) usually relies on electrical amplification of the electromotive force caused by nuclear induction. Here, we report up-conversion of a radio-frequency NMR signal to an optical regime using a high-stress silicon nitride membrane that interfaces the electrical detection circuit and an optical cavity through the electro-mechanical and the opto-mechanical couplings. This enables optical NMR detection without sacrificing the versatility of the traditional nuclear induction approach. While the signal-to-noise ratio is currently limited by the Brownian motion of the membrane as well as additional technical noise, we find it can exceed that of the conventional electrical schemes by increasing the electro-mechanical coupling strength. The electro-mechano-optical NMR detection presented here can even be combined with the laser cooling technique applied to nuclear spins.

%B Optica %V 5 %P 152-158 %8 2018/02/01 %G eng %U https://www.osapublishing.org/optica/abstract.cfm?uri=optica-5-2-152 %N 2 %R 10.1364/OPTICA.5.000152 %0 Journal Article %J Journal of High Energy Physics %D 2018 %T Entanglement of purification: from spin chains to holography %A Phuc Nguyen %A Trithep Devakul %A Matthew G. Halbasch %A Michael P. Zaletel %A Brian Swingle %XPurification 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.

%B Journal of High Energy Physics %P 98 %8 2018/01/22 %G eng %U https://link.springer.com/article/10.1007%2FJHEP01%282018%29098#citeas %R 10.1007/JHEP01(2018)098 %0 Journal Article %D 2018 %T Experimental Low-Latency Device-Independent Quantum Randomness %A Yanbao Zhang %A Lynden K. Shalm %A Joshua C. Bienfang %A Martin J. Stevens %A Michael D. Mazurek %A Sae Woo Nam %A Carlos Abellán %A Waldimar Amaya %A Morgan W. Mitchell %A Honghao Fu %A Carl A. Miller %A Alan Mink %A Emanuel Knill %XApplications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of 512 bits with an average experiment time of less than 5 min per block and with certified error bounded by 2−64≈5.42×10−20.

%G eng %U https://arxiv.org/abs/1812.07786 %0 Journal Article %J Nature %D 2018 %T Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals %A Peter Bierhorst %A Emanuel Knill %A Scott Glancy %A Yanbao Zhang %A Alan Mink %A Stephen Jordan %A Andrea Rommal %A Yi-Kai Liu %A Bradley Christensen %A Sae Woo Nam %A Martin J. Stevens %A Lynden K. Shalm %XFrom 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.

%B Nature %V 556 %P 223-226 %8 2018/04/11 %G eng %U https://arxiv.org/abs/1803.06219 %R https://doi.org/10.1038/s41586-018-0019-0 %0 Journal Article %D 2018 %T More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting %A Hubert Chan %A Jonathan Katz %A Kartik Nayak %A Antigoni Polychroniadou %A Elaine Shi %XThe 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.

%G eng %U https://arxiv.org/abs/1809.00825 %0 Journal Article %J High Energ. Phys. %D 2018 %T On the need for soft dressing %A Daniel Carney %A Laurent Chaurette %A Dominik Neuenfeld %A Gordon Semenoff %XIn 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.

%B High Energ. Phys. %V 121 %8 2018 %G eng %0 Journal Article %J Science %D 2018 %T Observation of three-photon bound states in a quantum nonlinear medium %A Qi-Yu Liang %A Aditya V. Venkatramani %A Sergio H. Cantu %A Travis L. Nicholson %A Michael J. Gullans %A Alexey V. Gorshkov %A Jeff D. Thompson %A Cheng Chin %A Mikhail D. Lukin %A Vladan Vuletic %XBound 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.

%B Science %V 359 %P 783-786 %8 2018/02/16 %G eng %U http://science.sciencemag.org/content/359/6377/783 %N 6377 %R 10.1126/science.aao7293 %0 Journal Article %D 2018 %T Quantum Supremacy and the Complexity of Random Circuit Sampling %A Adam Bouland %A Bill Fefferman %A Chinmay Nirkhe %A Umesh Vazirani %XA 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.

%G eng %U https://arxiv.org/abs/1803.04402 %0 Journal Article %J Proceedings of the National Academy of Sciences %D 2018 %T Toward the first quantum simulation with quantum speedup %A Andrew M. Childs %A Dmitri Maslov %A Yunseong Nam %A Neil J. Ross %A Yuan Su %XWith 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.

%B Proceedings of the National Academy of Sciences %V 115 %P 9456-9461 %G eng %U https://arxiv.org/abs/1711.10980 %R https://doi.org/10.1073/pnas.1801723115 %0 Journal Article %J Physical Review A %D 2017 %T Emergent equilibrium in many-body optical bistability %A Michael Foss-Feig %A Pradeep Niroula %A Jeremy T. Young %A Mohammad Hafezi %A Alexey V. Gorshkov %A Ryan M. Wilson %A Mohammad F. Maghrebi %XMany-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.

%B Physical Review A %V 95 %P 043826 %8 2017/04/17 %G eng %U https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826 %R doi.org/10.1103/PhysRevA.95.043826 %0 Journal Article %D 2017 %T Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling %A Peter Bierhorst %A Emanuel Knill %A Scott Glancy %A Alan Mink %A Stephen P. Jordan %A Andrea Rommal %A Yi-Kai Liu %A Bradley Christensen %A Sae Woo Nam %A Lynden K. Shalm %XRandom 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.

%8 2017/02/16 %G eng %U https://arxiv.org/abs/1702.05178# %0 Journal Article %J Quantum Information Processing %D 2017 %T Optimal length of decomposition sequences composed of imperfect gates %A Yunseong Nam %A R. Blümel %XQuantum 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 of the length *L* of the decomposition sequence. The existence of 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 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.

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.

%8 2017/08/31 %G eng %U https://arxiv.org/abs/1708.09780 %0 Journal Article %J New Journal of Physics %D 2017 %T Use of global interactions in efficient quantum circuit constructions %A Dmitri Maslov %A Yunseong Nam %XIn 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.

%B New Journal of Physics %8 2017/12/21 %G eng %U http://iopscience.iop.org/article/10.1088/1367-2630/aaa398 %R 10.1088/1367-2630/aaa398 %0 Journal Article %J Nature Photonics %D 2016 %T High resolution adaptive imaging of a single atom %A J. D. Wong-Campos %A K. G. Johnson %A Brian Neyenhuis %A J. Mizrahi %A Chris Monroe %XWe 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.

%B Nature Photonics %P 606-610 %8 2016/07/18 %G eng %U https://www.nature.com/nphoton/journal/v10/n9/full/nphoton.2016.136.html %N 10 %R 10.1038/nphoton.2016.136 %0 Journal Article %J Journal of Statistical Mechanics: Theory and Experiment %D 2016 %T Lattice Laughlin states on the torus from conformal field theory %A Abhinav Deshpande %A Anne E B Nielsen %X 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. %B Journal of Statistical Mechanics: Theory and Experiment %V 2016 %P 013102 %8 2016/01/28 %G eng %U http://stacks.iop.org/1742-5468/2016/i=1/a=013102 %0 Journal Article %J Nature Physics %D 2016 %T Many-body localization in a quantum simulator with programmable random disorder %A Jacob Smith %A Aaron Lee %A Philip Richerme %A Brian Neyenhuis %A Paul W. Hess %A Philipp Hauke %A Markus Heyl %A David A. Huse %A Christopher Monroe %XWhen 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.

%B Nature Physics %8 2016/06/06 %G eng %U http://arxiv.org/abs/1508.07026v1 %R 10.1038/nphys3783 %0 Journal Article %D 2016 %T Observation of Prethermalization in Long-Range Interacting Spin Chains %A B. Neyenhuis %A J. Smith %A A. C. Lee %A J. Zhang %A P. Richerme %A P. W. Hess %A Z. -X. Gong %A Alexey V. Gorshkov %A C. Monroe %XStatistical mechanics can predict thermal equilibrium states for most classical systems, but for an isolated quantum system there is no general understanding on how equilibrium states dynamically emerge from the microscopic Hamiltonian. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale and, instead, relax to quasi-stationary prethermal states that can be described by statistical mechanics when approximately conserved quantities are appropriately included in a generalized Gibbs ensemble (GGE). Here we experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse field Ising Hamiltonian following a sudden quench. For sufficiently long-ranged interactions the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. In this case, the prethermal state cannot be described by a GGE, but rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a significantly broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.

%8 2016/08/02 %G eng %U https://arxiv.org/abs/1608.00681 %0 Journal Article %J 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) %D 2016 %T Space-Efficient Error Reduction for Unitary Quantum Computations %A Bill Fefferman %A Hirotada Kobayashi %A Cedric Yen-Yu Lin %A Tomoyuki Morimae %A Harumichi Nishimura %XThis paper develops general space-efficient methods for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness

We determine the exact time evolution of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a hexagonal optical lattice. The dynamical evolution is triggered by ramping the lattice potential up, such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency |Uf|/(2π) in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the order parameter Δ. The latter is not reproduced by treating the time evolution in mean-field theory. The momentum density-density or noise correlation functions oscillate at frequency |Uf|/2π as well as its second harmonic. For a very deep lattice, with negligible tunneling energy, the oscillations of momentum occupation numbers are undamped. Non-zero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. This occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. We therefore propose to use this dephasing to detect a BCS state. Finally, we predict that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point.

%B Physical Review A %V 94 %P 023607 %8 2016/08/05 %G eng %U http://arxiv.org/abs/1602.00979 %N 2 %R http://dx.doi.org/10.1103/PhysRevA.94.023607 %0 Journal Article %J Quantum Information and Computation %D 2015 %T Momentum switches %A Andrew M. Childs %A David Gosset %A Daniel Nagaj %A Mouktik Raha %A Zak Webb %X Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct momentum switches, graphs that route particles depending on their momenta. We also give an example where there is no exact momentum switch, although we construct an arbitrarily good approximation. %B Quantum Information and Computation %V 15 %P 601-621 %8 2015/05/01 %G eng %U http://arxiv.org/abs/1406.4510v1 %N 7-8 %! Quantum Information and Computation 15 %0 Journal Article %J Physical Review A %D 2015 %T Optimization of collisional Feshbach cooling of an ultracold nondegenerate gas %A Marlon Nuske %A Eite Tiesinga %A L. Mathey %X We optimize a collision-induced cooling process for ultracold atoms in the nondegenerate regime. It makes use of a Feshbach resonance, instead of rf radiation in evaporative cooling, to selectively expel hot atoms from a trap. Using functional minimization we analytically show that for the optimal cooling process the resonance energy must be tuned such that it linearly follows the temperature. Here, optimal cooling is defined as maximizing the phase-space density after a fixed cooling duration. The analytical results are confirmed by numerical Monte-Carlo simulations. In order to simulate more realistic experimental conditions, we show that background losses do not change our conclusions, while additional non-resonant two-body losses make a lower initial resonance energy with non-linear dependence on temperature preferable. %B Physical Review A %V 91 %P 043626 %8 2015/04/20 %G eng %U http://arxiv.org/abs/1412.8473v1 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.91.043626 %0 Journal Article %J Physical Review Letters %D 2013 %T Dissipative Many-body Quantum Optics in Rydberg Media %A Alexey V. Gorshkov %A Rejish Nath %A Thomas Pohl %X We develop a theoretical framework for the dissipative propagation of quantized light in interacting optical media under conditions of electromagnetically induced transparency (EIT). The theory allows us to determine the peculiar spatiotemporal structure of the output of two complementary Rydberg-EIT-based light-processing modules: the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. In addition to being crucial for applications of these and other optical quantum devices, the theory opens the door to the study of exotic dissipative many-body dynamics of strongly interacting photons in nonlinear nonlocal media. %B Physical Review Letters %V 110 %8 2013/4/9 %G eng %U http://arxiv.org/abs/1211.7060v1 %N 15 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.110.153601 %0 Journal Article %J Quantum Information and Computation %D 2012 %T Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems %A Stephen P. Jordan %A Hirotada Kobayashi %A Daniel Nagaj %A Harumichi Nishimura %X This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations can be exactly implemented, e.g., {Hadamard, Toffoli, NOT}. The proof is quantumly nonrelativizing, and uses a simple but novel quantum technique that additively adjusts the success probability, which may be of independent interest. %B Quantum Information and Computation %V 12 %P 461-471 %8 2012/05/01 %G eng %U http://arxiv.org/abs/1111.5306v2 %N 5-6 %! Quantum Information and Computation Vol. 12 No. 5/6 pg. 461-471 (2012) %0 Journal Article %J Physical Review Letters %D 2012 %T Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice %A Amodsen Chotia %A Brian Neyenhuis %A Steven A. Moses %A Bo Yan %A Jacob P. Covey %A Michael Foss-Feig %A Ana Maria Rey %A Deborah S. Jin %A Jun Ye %X We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of >20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100% efficiency. %B Physical Review Letters %V 108 %8 2012/2/23 %G eng %U http://arxiv.org/abs/1110.4420v1 %N 8 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.108.080405 %0 Journal Article %D 2012 %T Photonic quantum simulation of ground state configurations of Heisenberg square and checkerboard lattice spin systems %A Xiao-song Ma %A Borivoje Dakic %A Sebastian Kropatsche %A William Naylor %A Yang-hao Chan %A Zhe-Xuan Gong %A Lu-ming Duan %A Anton Zeilinger %A Philip Walther %X Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. The available photonic quantum technology is reaching the state where significant advantages arise for the quantum simulation of interesting questions in Heisenberg spin systems. Here we experimentally simulate such spin systems with single photons and linear optics. The effective Heisenberg-type interactions among individual single photons are realized by quantum interference at the tunable direction coupler followed by the measurement process. The effective interactions are characterized by comparing the entanglement dynamics using pairwise concurrence of a four-photon quantum system. We further show that photonic quantum simulations of generalized Heisenberg interactions on a four-site square lattice and a six-site checkerboard lattice are in reach of current technology. %8 2012/05/12 %G eng %U http://arxiv.org/abs/1205.2801v1 %0 Journal Article %D 2011 %T Continuous-variable quantum compressed sensing %A Matthias Ohliger %A Vincent Nesme %A David Gross %A Yi-Kai Liu %A Jens Eisert %X We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise. %8 2011/11/03 %G eng %U http://arxiv.org/abs/1111.0853v3 %0 Journal Article %J Physical Review A %D 2011 %T Fast and robust quantum computation with ionic Wigner crystals %A J. D. Baltrusch %A A. Negretti %A J. M. Taylor %A T. Calarco %X We present a detailed analysis of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps. We elaborate on a recent scheme, proposed by two of the authors, to engineer two-body interactions between ions in such crystals. We analyze for the first time the situation in which the cyclotron (w_c) and the crystal rotation (w_r) frequencies do not fulfill the condition w_c=2w_r. It is shown that even in the presence of the magnetic field in the rotating frame the many-body (classical) Hamiltonian describing small oscillations from the ion equilibrium positions can be recast in canonical form. As a consequence, we are able to demonstrate that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, we describe a realization of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computing scheme. %B Physical Review A %V 83 %8 2011/4/15 %G eng %U http://arxiv.org/abs/1011.5616v2 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.83.042319 %0 Journal Article %J Physical Review A %D 2011 %T Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing %A Nathaniel B. Phillips %A Alexey V. Gorshkov %A Irina Novikova %X We study the modification of a traditional electromagnetically induced transparency (EIT) stored light technique that includes both EIT and four-wave mixing (FWM) in an ensemble of hot Rb atoms. The standard treatment of light storage involves the coherent and reversible mapping of one photonic mode onto a collective spin coherence. It has been shown that unwanted, competing processes such as four-wave mixing are enhanced by EIT and can significantly modify the signal optical pulse propagation. We present theoretical and experimental evidence to indicate that while a Stokes field is indeed detected upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics of the fields and the impact of FWM on the spin wave. %B Physical Review A %V 83 %8 2011/6/20 %G eng %U http://arxiv.org/abs/1103.2131v1 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.83.063823 %0 Journal Article %J Nature %D 2010 %T Quantum Computing %A Thaddeus D. Ladd %A Fedor Jelezko %A Raymond Laflamme %A Yasunobu Nakamura %A Christopher Monroe %A Jeremy L. O'Brien %X Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future. %B Nature %V 464 %P 45 - 53 %8 2010/3/4 %G eng %U http://arxiv.org/abs/1009.2267v1 %N 7285 %! Nature %R 10.1038/nature08812 %0 Journal Article %J J. Mod. Opt. %D 2009 %T Slow light propagation and amplification via electromagnetically induced transparency and four-wave mixing in an optically dense atomic vapor %A Phillips, N B %A Alexey V. Gorshkov %A Novikova, I %B J. Mod. Opt. %V 56 %P 1916 %G eng %U http://www.informaworld.com/smpp/content db=all content=a913545405 %0 Journal Article %J Physical Review A %D 2008 %T Optimal light storage in atomic vapor %A Nathaniel B. Phillips %A Alexey V. Gorshkov %A Irina Novikova %X We study procedures for the optimization of efficiency of light storage and retrieval based on the dynamic form of electromagnetically induced transparency (EIT) in warm Rb vapor. We present a detailed analysis of two recently demonstrated optimization protocols: a time-reversal-based iteration procedure, which finds the optimal input signal pulse shape for any given control field, and a procedure based on the calculation of an optimal control field for any given signal pulse shape. We verify that the two procedures are consistent with each other, and that they both independently achieve the maximum memory efficiency for any given optical depth. We observe good agreement with theoretical predictions for moderate optical depths (<25), while at higher optical depths the experimental efficiency falls below the theoretically predicted values. We identify possible effects responsible for this reduction in memory efficiency. %B Physical Review A %V 78 %8 2008/8/1 %G eng %U http://arxiv.org/abs/0805.3348v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.78.023801 %0 Journal Article %J Physical Review A %D 2008 %T Optimal light storage with full pulse shape control %A Irina Novikova %A Nathaniel B. Phillips %A Alexey V. Gorshkov %X We experimentally demonstrate optimal storage and retrieval of light pulses of arbitrary shape in atomic ensembles. By shaping auxiliary control pulses, we attain efficiencies approaching the fundamental limit and achieve precise retrieval into any predetermined temporal profile. Our techniques, demonstrated in warm Rb vapor, are applicable to a wide range of systems and protocols. As an example, we present their potential application to the creation of optical time-bin qubits and to controlled partial retrieval. %B Physical Review A %V 78 %8 2008/8/20 %G eng %U http://arxiv.org/abs/0805.1927v1 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.78.021802 %0 Journal Article %J Phys. Rev. A %D 2008 %T Optimal light storage with full pulse-shape control %A Novikova, I %A Phillips, N B %A Alexey V. Gorshkov %B Phys. Rev. A %V 78 %P 021802(R) %G eng %U http://link.aps.org/abstract/PRA/v78/e021802/ %0 Journal Article %J Proc. SPIE %D 2008 %T Optimizing Slow and Stored Light for Multidisciplinary Applications %A Klein, M %A Xiao, Y %A Alexey V. Gorshkov %A M Hohensee %A C D Leung %A M R Browning %A Phillips, D F %A Novikova, I %A Walsworth, R L %B Proc. SPIE %V 6904 %P 69040C %G eng %U http://spie.org/x648.xml?product_id=772216&Search_Origin=QuickSearch&Search_Results_URL=http://spie.org/x1636.xml&Alternate_URL=http://spie.org/x18509.xml&Alternate_URL_Name=timeframe&Alternate_URL_Value=Exhibitors&UseJavascript=1&Please_Wait_URL=http://s %0 Journal Article %J Physical Review Letters %D 2008 %T Two-body transients in coupled atomic-molecular BECs %A Pascal Naidon %A Eite Tiesinga %A Paul S. Julienne %X We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett., 88, 090403 (2002)], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms. %B Physical Review Letters %V 100 %8 2008/3/3 %G eng %U http://arxiv.org/abs/0707.2963v2 %N 9 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.100.093001 %0 Journal Article %D 2007 %T Coherent, adiabatic and dissociation regimes in coupled atomic-molecular Bose-Einstein condensates %A Pascal Naidon %A Eite Tiesinga %A Paul S. Julienne %X We discuss the dynamics of a Bose-Einstein condensate of atoms which is suddenly coupled to a condensate of molecules by an optical or magnetic Feshbach resonance. Three limiting regimes are found and can be understood from the transient dynamics occuring for each pair of atoms. This transient dynamics can be summarised into a time-dependent shift and broadening of the molecular state. A simple Gross-Pitaevskii picture including this shift and broadening is proposed to describe the system in the three regimes. Finally, we suggest how to explore these regimes experimentally. %8 2007/11/02 %G eng %U http://arxiv.org/abs/0711.0397v2 %0 Journal Article %J New Journal of Physics %D 2007 %T Effective-range description of a Bose gas under strong one- or two-dimensional confinement %A Pascal Naidon %A Eite Tiesinga %A William F. Mitchell %A Paul S. Julienne %X We point out that theories describing s-wave collisions of bosonic atoms confined in one- or two-dimensional geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries. %B New Journal of Physics %V 9 %P 19 - 19 %8 2007/01/29 %G eng %U http://arxiv.org/abs/physics/0607140v2 %N 1 %! New J. Phys. %R 10.1088/1367-2630/9/1/019 %0 Journal Article %J Proc. SPIE %D 2007 %T Multi-photon Entanglement: From Quantum Curiosity to Quantum Computing and Quantum Repeaters %A Walther, P %A Eisaman, M D %A Nemiroski, A %A Alexey V. Gorshkov %A Zibrov, A S %A Zeilinger, A %A Lukin, M D %B Proc. SPIE %V 6664 %P 66640G %G eng %U http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG00666400000166640G000001&idtype=cvips&gifs=Yes&bproc=volrange&scode=6600%20-%206699 %0 Journal Article %J Physical Review Letters %D 2007 %T Optimal control of light pulse storage and retrieval %A Irina Novikova %A Alexey V. Gorshkov %A David F. Phillips %A Anders S. Sorensen %A Mikhail D. Lukin %A Ronald L. Walsworth %X We demonstrate experimentally a procedure to obtain the maximum efficiency for the storage and retrieval of light pulses in atomic media. The procedure uses time reversal to obtain optimal input signal pulse-shapes. Experimental results in warm Rb vapor are in good agreement with theoretical predictions and demonstrate a substantial improvement of efficiency. This optimization procedure is applicable to a wide range of systems. %B Physical Review Letters %V 98 %8 2007/6/15 %G eng %U http://arxiv.org/abs/quant-ph/0702266v1 %N 24 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.98.243602 %0 Journal Article %J Proc. SPIE %D 2007 %T Optimization of slow and stored light in atomic vapor %A Novikova, I %A Alexey V. Gorshkov %A Phillips, D F %A Xiao, Y %A Klein, M %A Walsworth, R L %B Proc. SPIE %V 6482 %P 64820M %G eng %U http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG00648200000164820M000001&idtype=cvips&gifs=Yes&bproc=volrange&scode=6400%20-%206499 %0 Journal Article %J Physical Review A %D 2005 %T Unified derivations of measurement-based schemes for quantum computation %A Andrew M. Childs %A Debbie W. Leung %A Michael A. Nielsen %X We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed entangled state, adaptive measurements on single qubits, and feedforward of the measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308, 96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)]) uses adaptive two-qubit measurements that can be applied to arbitrary pairs of qubits, and feedforward of the measurement results. The underlying principle of our derivations is a variant of teleportation introduced by Zhou, Leung, and Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two measurement-based models of quantum computation and provide significantly simpler schemes. %B Physical Review A %V 71 %8 2005/3/17 %G eng %U http://arxiv.org/abs/quant-ph/0404132v2 %N 3 %! Phys. Rev. A %R 10.1103/PhysRevA.71.032318 %0 Journal Article %J Optics Express %D 2004 %T Quantum key distribution with 1.25 Gbps clock synchronization %A J. C. Bienfang %A A. J. Gross %A A. Mink %A B. J. Hershman %A A. Nakassis %A X. Tang %A R. Lu %A D. H. Su %A Charles W Clark %A Carl J. Williams %A E. W. Hagley %A Jesse Wen %X We have demonstrated the exchange of sifted quantum cryptographic key over a 730 meter free-space link at rates of up to 1.0 Mbps, two orders of magnitude faster than previously reported results. A classical channel at 1550 nm operates in parallel with a quantum channel at 845 nm. Clock recovery techniques on the classical channel at 1.25 Gbps enable quantum transmission at up to the clock rate. System performance is currently limited by the timing resolution of our silicon avalanche photodiode detectors. With improved detector resolution, our technique will yield another order of magnitude increase in performance, with existing technology. %B Optics Express %V 12 %P 2011 %8 2004/05/17 %G eng %U http://arxiv.org/abs/quant-ph/0405097v1 %N 9 %! Opt. Express %R 10.1364/OPEX.12.002011 %0 Journal Article %J Physical Review A %D 2003 %T Lower bounds on the complexity of simulating quantum gates %A Andrew M. Childs %A Henry L. Haselgrove %A Michael A. Nielsen %X We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates. %B Physical Review A %V 68 %8 2003/11/18 %G eng %U http://arxiv.org/abs/quant-ph/0307190v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.68.052311 %0 Journal Article %J Physical Review A %D 2002 %T Universal simulation of Hamiltonian dynamics for qudits %A Michael A. Nielsen %A Michael J. Bremner %A Jennifer L. Dodd %A Andrew M. Childs %A Christopher M. Dawson %X What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries. %B Physical Review A %V 66 %8 2002/8/30 %G eng %U http://arxiv.org/abs/quant-ph/0109064v2 %N 2 %! Phys. Rev. A %R 10.1103/PhysRevA.66.022317