TY - JOUR T1 - Free Quantum Codes from Twisted Unitary $t$-groups Y1 - 2024 A1 - Eric Kubischta A1 - Ian Teixeira AB -

We introduce twisted unitary t-groups, a generalization of unitary t-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that twisted unitary t-groups automatically correspond to quantum codes with distance d=t+1. By construction these codes have many transversal gates, which are naturally fault tolerant.

UR - https://arxiv.org/abs/2402.01638 ER - TY - JOUR T1 - A family of permutationally invariant quantum codes Y1 - 2023 A1 - Arda Aydin A1 - Max A. Alekseyev A1 - Alexander Barg AB -

We construct a new family of permutationally invariant codes that correct t Pauli errors for any t≥1. We also show that codes in the new family correct spontaneous decay errors as well as deletion errors. In many cases the codes in this family are shorter than the best previously known explicit families of permutationally invariant codes both for Pauli errors, deletions, and for the amplitude damping channel. As a separate result, we generalize the conditions for permutationally invariant codes to correct t Pauli errors from the previously known results for t=1 to any number of errors. For small t, these conditions can be used to construct new examples of codes by computer.

UR - https://arxiv.org/abs/2310.05358 ER - TY - JOUR T1 - A Family of Quantum Codes with Exotic Transversal Gates Y1 - 2023 A1 - Eric Kubischta A1 - Ian Teixeira AB -

Recently it has been shown that the binary icosahedral group 2I together with a certain involution forms the most efficient single-qubit universal gate set. In order for this to be viable, one must construct a quantum code with transversal gate group 2I, however, no such code has ever been demonstrated explicitly. We fill this void by constructing a novel family of quantum codes that all have transversal gate group 2I.

UR - https://arxiv.org/abs/2305.07023 ER - TY - JOUR T1 - Fat Pointers for Temporal Memory Safety of C JF - Proceedings of the ACM on Programming Languages Y1 - 2023 A1 - Zhou, Jie A1 - Criswell, John A1 - Hicks, Michael KW - Cryptography and Security (cs.CR) KW - FOS: Computer and information sciences AB -

Temporal memory safety bugs, especially use-after-free and double free bugs, pose a major security threat to C programs. Real-world exploits utilizing these bugs enable attackers to read and write arbitrary memory locations, causing disastrous violations of confidentiality, integrity, and availability. Many previous solutions retrofit temporal memory safety to C, but they all either incur high performance overhead and/or miss detecting certain types of temporal memory safety bugs.
In this paper, we propose a temporal memory safety solution that is both efficient and comprehensive. Specifically, we extend Checked C, a spatially-safe extension to C, with temporally-safe pointers. These are implemented by combining two techniques: fat pointers and dynamic key-lock checks. We show that the fat-pointer solution significantly improves running time and memory overhead compared to the disjoint-metadata approach that provides the same level of protection. With empirical program data and hands-on experience porting real-world applications, we also show that our solution is practical in terms of backward compatibility -- one of the major complaints about fat pointers.

VL - 7 U4 - 316-347 UR - https://arxiv.org/abs/2208.12900 CP - 1 U5 - 10.1145/3586038 ER - TY - JOUR T1 - Fault-tolerant hyperbolic Floquet quantum error correcting codes Y1 - 2023 A1 - Ali Fahimniya A1 - Hossein Dehghani A1 - Kishor Bharti A1 - Sheryl Mathew A1 - Alicia J. Kollár A1 - Alexey V. Gorshkov A1 - Michael J. Gullans AB -

A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes." These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for n qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate (1/8+2/n) and have a depth-3 syndrome extraction circuit. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in n. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1% in a phenomenological noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a [[400,52,8]] code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.

UR - https://arxiv.org/abs/2309.10033 ER - TY - JOUR T1 - Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes Y1 - 2023 A1 - Jon Nelson A1 - Gregory Bentsen A1 - Steven T. Flammia A1 - Michael J. Gullans AB -

Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless. In this work, we design a fault-tolerant distillation protocol for preparing encoded states of one-dimensional random circuit codes even when all gates and measurements are subject to noise. This is sufficient for fault-tolerant quantum memory since these encoded states can then be used as ancillas for Steane error correction. We show through numerical simulations that our protocol can correct erasure errors up to an error rate of 2%. In addition, we also extend results in the code capacity setting by developing a maximum likelihood decoder for depolarizing noise similar to work by Darmawan et al. As in their work, we formulate the decoding problem as a tensor network contraction and show how to contract the network efficiently by exploiting the low-depth structure. Replacing the tensor network with a so-called ''tropical'' tensor network, we also show how to perform minimum weight decoding. With these decoders, we are able to numerically estimate the depolarizing error threshold of finite-rate random circuit codes and show that this threshold closely matches the hashing bound even when the decoding is sub-optimal.

UR - https://arxiv.org/abs/2311.17985 ER - TY - JOUR T1 - Feasibility of a trapped atom interferometer with accelerating optical traps Y1 - 2023 A1 - Gayathrini Premawardhana A1 - Jonathan Kunjummen A1 - Sarthak Subhankar A1 - Jacob M. Taylor AB -

In order to increase the measured phase of an atom interferometer and improve its sensitivity, researchers attempt to increase the enclosed space-time area using two methods: creating larger separations between the interferometer arms and having longer evolution times. However, increasing the evolution time reduces the bandwidth that can be sampled, whereas decreasing the evolution time worsens the sensitivity. In this paper, we attempt to address this by proposing a setup for high-bandwidth applications, with improved overall sensitivity. This is realized by accelerating and holding the atoms using optical dipole traps. We find that accelerations of up to 103-105 m/s2 can be achieved using acousto-optic deflectors (AODs) to move the traps. By comparing the sensitivity of our approach to acceleration as a baseline to traditional atom interferometry, we find a substantial improvement to the state of the art. In the limit of appropriate beam and optics stabilization, sensitivities approaching 10−14 (m/s2)/Hz−−−√ may be achievable at 1 Hz, while detection at 1 kHz with a sensitivity an order of magnitude better than traditional free-fall atom interferometers is possible with today's systems.

UR - https://arxiv.org/abs/2308.12246 ER - TY - CONF T1 - Fixing and Mechanizing the Security Proof of Fiat-Shamir with Aborts and Dilithium T2 - Advances in Cryptology – CRYPTO 2023 Y1 - 2023 A1 - Barbosa, Manuel A1 - Barthe, Gilles A1 - Doczkal, Christian A1 - Don, Jelle A1 - Fehr, Serge A1 - Grégoire, Benjamin A1 - Huang, Yu-Hsuan A1 - Hülsing, Andreas A1 - Lee, Yi A1 - Wu, Xiaodi ED - Handschuh, Helena ED - Lysyanskaya, Anna AB -

We extend and consolidate the security justification for the Dilithium signature scheme. In particular, we identify a subtle but crucial gap that appears in several ROM and QROM security proofs for signature schemes that are based on the Fiat-Shamir with aborts paradigm, including Dilithium. The gap lies in the CMA-to-NMA reduction and was uncovered when trying to formalize a variant of the QROM security proof by Kiltz, Lyubashevsky, and Schaffner (Eurocrypt 2018). The gap was confirmed by the authors, and there seems to be no simple patch for it. We provide new, fixed proofs for the affected CMA-to-NMA reduction, both for the ROM and the QROM, and we perform a concrete security analysis for the case of Dilithium to show that the claimed security level is still valid after addressing the gap. Furthermore, we offer a fully mechanized ROM proof for the CMA-security of Dilithium in the EasyCrypt proof assistant. Our formalization includes several new tools and techniques of independent interest for future formal verification results.

JA - Advances in Cryptology – CRYPTO 2023 PB - Springer Nature Switzerland CY - Cham SN - 978-3-031-38554-4 ER - TY - JOUR T1 - FIPS Compliant Quantum Secure Communication using Quantum Permutation Pad Y1 - 2022 A1 - He, Alex A1 - Lou, Dafu A1 - She, Eric A1 - Guo, Shangjie A1 - Watson, Hareesh A1 - Weng, Sibyl A1 - Perepechaenko, Maria A1 - Kuang, Rand KW - Cryptography and Security (cs.CR) KW - FOS: Computer and information sciences KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

Quantum computing has entered fast development track since Shor's algorithm was proposed in 1994. Multi-cloud services of quantum computing farms are currently available. One of which, IBM quantum computing, presented a road map showing their Kookaburra system with over 4158 qubits will be available in 2025. For the standardization of Post-Quantum Cryptography or PQC, the National Institute of Standards and Technology or NIST recently announced the first candidates for standardization with one algorithm for key encapsulation mechanism (KEM), Kyber, and three algorithms for digital signatures. NIST has also issued a new call for quantum-safe digital signature algorithms due June 1, 2023. This timeline shows that FIPS-certified quantum-safe TLS protocol would take a predictably long time. However, "steal now, crack later" tactic requires protecting data against future quantum threat actors today. NIST recommended the use of a hybrid mode of TLS 1.3 with its extensions to support PQC. The hybrid mode works for certain cases but FIPS certification for the hybridized cryptomodule might still be required. This paper proposes to take a nested mode to enable TLS 1.3 protocol with quantum-safe data, which can be made available today and is FIPS compliant. We discussed the performance impacts of the handshaking phase of the nested TLS 1.3 with PQC and the symmetric encryption phase. The major impact on performance using the nested mode is in the data symmetric encryption with AES. To overcome this performance reduction, we suggest using quantum encryption with a quantum permutation pad for the data encryption with a minor performance reduction of less than 10 percent.

UR - https://arxiv.org/abs/2301.00062 U5 - 10.48550/ARXIV.2301.00062 ER - TY - JOUR T1 - Faster Digital Quantum Simulation by Symmetry Protection JF - PRX Quantum Y1 - 2021 A1 - Minh C. Tran A1 - Yuan Su A1 - Daniel Carney A1 - J. M. Taylor AB -

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply our technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, our algorithm can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that our technique can also protect simulation against other types of coherent, temporally correlated errors, such as the 1/f noise commonly found in solid-state experiments.

VL - 2 UR - https://arxiv.org/abs/2006.16248 U5 - http://dx.doi.org/10.1103/PRXQuantum.2.010323 ER - TY - JOUR T1 - Feedback-stabilized dynamical steady states in the Bose-Hubbard model JF - Phys. Rev. Research Y1 - 2021 A1 - Jeremy T. Young A1 - Alexey V. Gorshkov A1 - I. B. Spielman AB -

The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this work, we investigate the potential of this approach from three perspectives. First, we consider a double-well system in the classical large-atom-number limit, deriving the exact equations of motion in the presence of feedback. Second, we consider the same system in the limit of small atom number, revealing the effect that quantum fluctuations have on the feedback scheme. Finally, we explore the behavior of modest sized Hubbard chains using exact numerics, demonstrating the near-deterministic preparation of number states, a tradeoff between local and non-local feedback for state preparation, and evidence of a feedback-driven symmetry-breaking phase transition.

VL - 3 U4 - 043075 UR - https://arxiv.org/abs/2106.09744 CP - 4 U5 - https://doi.org/10.1103/PhysRevResearch.3.043075 ER - TY - JOUR T1 - From Quantum Codes to Gravity: A Journey of Gravitizing Quantum Mechanics Y1 - 2021 A1 - ChunJun Cao AB -

In this note, I review a recent approach to quantum gravity that "gravitizes" quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that approximate quantum error correction codes, when re-adapted into the aforementioned framework, also has promise in emerging gravity in near-flat geometries.

UR - https://arxiv.org/abs/2112.00199 ER - TY - JOUR T1 - Frustration-induced anomalous transport and strong photon decay in waveguide QED JF - Phys. Rev. Research Y1 - 2021 A1 - Ron Belyansky A1 - Seth Whitsitt A1 - Rex Lundgren A1 - Yidan Wang A1 - Andrei Vrajitoarea A1 - Andrew A. Houck A1 - Alexey V. Gorshkov AB -

We study the propagation of photons in a one-dimensional environment consisting of two non-interacting species of photons frustratingly coupled to a single spin-1/2. The ultrastrong frustrated coupling leads to an extreme mixing of the light and matter degrees of freedom, resulting in the disintegration of the spin and a breakdown of the "dressed-spin", or polaron, description. Using a combination of numerical and analytical methods, we show that the elastic response becomes increasingly weak at the effective spin frequency, showing instead an increasingly strong and broadband response at higher energies. We also show that the photons can decay into multiple photons of smaller energies. The total probability of these inelastic processes can be as large as the total elastic scattering rate, or half of the total scattering rate, which is as large as it can be. The frustrated spin induces strong anisotropic photon-photon interactions that are dominated by inter-species interactions. Our results are relevant to state-of-the-art circuit and cavity quantum electrodynamics experiments.

VL - 3 UR - https://arxiv.org/abs/2007.03690 CP - 032058 U5 - https://doi.org/10.1103/PhysRevResearch.3.L032058 ER - TY - JOUR T1 - Fully device-independent quantum key distribution using synchronous correlations Y1 - 2021 A1 - Rodrigues, Nishant A1 - Lackey, Brad KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

We derive a device-independent quantum key distribution protocol based on synchronous correlations and their Bell inequalities. This protocol offers several advantages over other device-independent schemes including symmetry between the two users and no need for preshared randomness. We close a "synchronicity" loophole by showing that an almost synchronous correlation inherits the self-testing property of the associated synchronous correlation. We also pose a new security assumption that closes the "locality" (or "causality") loophole: an unbounded adversary with even a small uncertainty about the users' choice of measurement bases cannot produce any almost synchronous correlation that approximately maximally violates a synchronous Bell inequality.

UR - https://arxiv.org/abs/2110.14530 U5 - 10.48550/ARXIV.2110.14530 ER - TY - JOUR T1 - Fault-Tolerant Operation of a Quantum Error-Correction Code Y1 - 2020 A1 - Laird Egan A1 - Dripto M. Debroy A1 - Crystal Noel A1 - Andrew Risinger A1 - Daiwei Zhu A1 - Debopriyo Biswas A1 - Michael Newman A1 - Muyuan Li A1 - Kenneth R. Brown A1 - Marko Cetina A1 - Christopher Monroe AB -

Quantum error correction protects fragile quantum information by encoding it in a larger quantum system whose extra degrees of freedom enable the detection and correction of errors. An encoded logical qubit thus carries increased complexity compared to a bare physical qubit. Fault-tolerant protocols contain the spread of errors and are essential for realizing error suppression with an error-corrected logical qubit. Here we experimentally demonstrate fault-tolerant preparation, rotation, error syndrome extraction, and measurement on a logical qubit encoded in the 9-qubit Bacon-Shor code. For the logical qubit, we measure an average fault-tolerant preparation and measurement error of 0.6% and a transversal Clifford gate with an error of 0.3% after error correction. The result is an encoded logical qubit whose logical fidelity exceeds the fidelity of the entangling operations used to create it. We compare these operations with non-fault-tolerant protocols capable of generating arbitrary logical states, and observe the expected increase in error. We directly measure the four Bacon-Shor stabilizer generators and are able to detect single qubit Pauli errors. These results show that fault-tolerant quantum systems are currently capable of logical primitives with error rates lower than their constituent parts. With the future addition of intermediate measurements, the full power of scalable quantum error-correction can be achieved. 

UR - https://arxiv.org/abs/2009.11482 ER - TY - JOUR T1 - Feedback Induced Magnetic Phases in Binary Bose-Einstein Condensates Y1 - 2020 A1 - Hilary M. Hurst A1 - Shangjie Guo A1 - I. B. Spielman AB -

Weak measurement in tandem with real-time feedback control is a new route toward engineering novel non-equilibrium quantum matter. Here we develop a theoretical toolbox for quantum feedback control of multicomponent Bose-Einstein condensates (BECs) using backaction-limited weak measurements in conjunction with spatially resolved feedback. Feedback in the form of a single-particle potential can introduce effective interactions that enter into the stochastic equation governing system dynamics. The effective interactions are tunable and can be made analogous to Feshbach resonances -- spin-independent and spin-dependent -- but without changing atomic scattering parameters. Feedback cooling prevents runaway heating due to measurement backaction and we present an analytical model to explain its effectiveness. We showcase our toolbox by studying a two-component BEC using a stochastic mean-field theory, where feedback induces a phase transition between easy-axis ferromagnet and spin-disordered paramagnet phases. We present the steady-state phase diagram as a function of intrinsic and effective spin-dependent interaction strengths. Our result demonstrates that closed-loop quantum control of Bose-Einstein condensates is a powerful new tool for quantum engineering in cold-atom systems.

UR - https://arxiv.org/abs/2007.07266 ER - TY - JOUR T1 - Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries JF - Phys. Rev. Lett. Y1 - 2020 A1 - Luis Pedro García-Pintos A1 - Alioscia Hamma A1 - Adolfo del Campo AB -

We study the connection between the charging power of quantum batteries and the fluctuations of the stored work. We prove that in order to have a non-zero rate of change of the extractable work, the state ρW of the battery cannot be an eigenstate of a `\emph{work operator}', defined by F ≡ HW + β−1log(ρW), where HW is the Hamiltonian of the battery and β is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the stored work upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine. 

VL - 125 UR - https://arxiv.org/abs/1909.03558 CP - 040601 U5 - 10.1103/PhysRevLett.125.040601 ER - TY - JOUR T1 - Faster quantum simulation by randomization JF - Quantum Y1 - 2019 A1 - Andrew M. Childs A1 - Aaron Ostrander A1 - Yuan Su AB -

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation and thereby give more efficient simulations. Indeed, we show that these bounds can be asymptotically better than previous bounds that exploit commutation between the summands, despite using much less information about the structure of the Hamiltonian. Numerical evidence suggests that our randomized algorithm may be advantageous even for near-term quantum simulation.

VL - 3 UR - https://arxiv.org/abs/1805.08385 CP - 182 U5 - https://doi.org/10.22331/q-2019-09-02-182 ER - TY - JOUR T1 - Feshbach resonances in p-wave three-body recombination within Fermi-Fermi mixtures of open-shell 6Li and closed-shell 173Yb atoms Y1 - 2019 A1 - Alaina Green A1 - Hui Li A1 - Jun Hui See Toh A1 - Xinxin Tang A1 - Katherine McCormick A1 - Ming Li A1 - Eite Tiesinga A1 - Svetlana Kotochigova A1 - Subhadeep Gupta AB -

We report on observations and modeling of interspecies magnetic Feshbach resonances in dilute ultracold mixtures of open-shell alkali-metal 6Li and closed-shell 173Yb atoms with temperatures just above quantum degeneracy for both fermionic species. Resonances are located by detecting magnetic-field-dependent atom loss due to three-body recombination. We resolve closely-located resonances that originate from a weak separation-dependent hyperfine coupling between the electronic spin of 6Li and the nuclear spin of 173Yb, and confirm their magnetic field spacing by ab initio electronic-structure calculations. Through quantitative comparisons of theoretical atom-loss profiles and experimental data at various temperatures between 1 μK and 20 μK, we show that three-body recombination in fermionic mixtures has a p-wave Wigner threshold behavior leading to characteristic asymmetric loss profiles. Such resonances can be applied towards the formation of ultracold doublet ground-state molecules and quantum simulation of superfluid p-wave pairing.

UR - https://arxiv.org/abs/1912.04874 ER - TY - JOUR T1 - Floquet engineering of optical lattices with spatial features and periodicity below the diffraction limit Y1 - 2019 A1 - S. Subhankar A1 - P. Bienias A1 - P. Titum A1 - T-C. Tsui A1 - Y. Wang A1 - Alexey V. Gorshkov A1 - S. L. Rolston A1 - J. V. Porto AB -

Floquet engineering or coherent time periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological band structures, and observation of dynamical localization, to name just a few. Here we present a Floquet-based framework to stroboscopically engineer Hamiltonians with spatial features and periodicity below the diffraction limit of light used to create them by time-averaging over various configurations of a 1D optical Kronig-Penney (KP) lattice. The KP potential is a lattice of narrow subwavelength barriers spaced by half the optical wavelength (λ/2) and arises from the non-linear optical response of the atomic dark state. Stroboscopic control over the strength and position of this lattice requires time-dependent adiabatic manipulation of the dark state spin composition. We investigate adiabaticity requirements and shape our time-dependent light fields to respect the requirements. We apply this framework to show that a λ/4-spaced lattice can be synthesized using realistic experimental parameters as an example, discuss mechanisms that limit lifetimes in these lattices, explore candidate systems and their limitations, and treat adiabatic loading into the ground band of these lattices.

UR - https://arxiv.org/abs/1906.07646 ER - TY - JOUR T1 - Fluctuation-induced torque on a topological insulator out of thermal equilibrium JF - Phys. Rev. Lett. Y1 - 2019 A1 - M. F. Maghrebi A1 - Alexey V. Gorshkov A1 - J. D. Sau AB -

Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well-understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. Utilizing the Keldysh framework, we investigate the universal nonequilibrium response of the TI to the temperature difference with the environment. Finally, we argue that experimental observation of this effect is within reach.

VL - 123 UR - https://arxiv.org/abs/1811.06080 CP - 055901 U5 - https://doi.org/10.1103/PhysRevLett.123.055901 ER - TY - JOUR T1 - Framework for Hamiltonian simulation and beyond: standard-form encoding, qubitization, and quantum signal processing JF - Quantum Views Y1 - 2019 A1 - Yuan Su AB -
This is a Perspective on "Hamiltonian Simulation by Qubitization" by Guang Hao Low and Isaac L. Chuang, published in Quantum 3, 163 (2019).
VL - 3 UR - https://quantum-journal.org/views/qv-2019-08-13-21/ CP - 21 U5 - https://doi.org/10.22331/qv-2019-08-13-21 ER - TY - JOUR T1 - Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory JF - Phys. Rev. A 98, 012332 (2018) Y1 - 2018 A1 - Moosavian, Ali Hamed A1 - Stephen Jordan AB -

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.

VL - A U4 - 012332 UR - https://arxiv.org/abs/1711.04006 CP - 98 U5 - https://doi.org/10.1103/PhysRevA.98.012332 ER - TY - JOUR T1 - Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers JF - Science Advances Y1 - 2018 A1 - Constantinos Makrides A1 - Ming Li A1 - Eite Tiesinga A1 - Svetlana Kotochigova AB -

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.

VL - 4 U4 - eaap8308 UR - https://arxiv.org/abs/1802.09586 CP - 2 U5 - https://doi.org/10.1126/sciadv.aap8308 ER - TY - JOUR T1 - Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal Y1 - 2018 A1 - Tobias Graß A1 - Przemyslaw Bienias A1 - Michael Gullans A1 - Rex Lundgren A1 - Joseph Maciejko A1 - Alexey V. Gorshkov AB -

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.

UR - https://arxiv.org/abs/1809.04493 ER - TY - JOUR T1 - Fast optimization algorithms and the cosmological constant JF - Physical Review D Y1 - 2017 A1 - Ning Bao A1 - Raphael Bousso A1 - Stephen P. Jordan A1 - Brad Lackey AB -

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.

VL - 96 U4 - 103512 UR - https://arxiv.org/abs/1706.08503 CP - 10 U5 - 10.1103/PhysRevD.96.103512 ER - TY - JOUR T1 - Fast quantum computation at arbitrarily low energy JF - Physical Review A Y1 - 2017 A1 - Stephen P. Jordan AB -

One version of the energy-time uncertainty principle states that the minimum time T for a quantum system to evolve from a given state to any orthogonal state is h/(4ΔE), where ΔE is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that Th/(2E), where E is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted 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 E and ΔE 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.

VL - 95 U4 - 032305 UR - http://link.aps.org/doi/10.1103/PhysRevA.95.032305 U5 - 10.1103/PhysRevA.95.032305 ER - TY - JOUR T1 - Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions JF - Physical Review Letters Y1 - 2017 A1 - Zachary Eldredge A1 - Zhe-Xuan Gong A1 - Ali Hamed Moosavian A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -

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 L in d dimensions using long-range interactions with strength bounded by 1/rα. If α<d, the state transfer time is asymptotically independent of L; if α=d, the time is logarithmic in distance L; if d<α<d+1, transfer occurs in time proportional to Lαd; and if αd+1, it occurs in time proportional to 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 L, then it can be created in time that scales with L identically to state transfer up to multiplicative logarithmic corrections.

VL - 119 U4 - 170503 UR - https://arxiv.org/abs/1612.02442 CP - 17 U5 - 10.1103/PhysRevLett.119.170503 ER - TY - JOUR T1 - Figures of merit for quantum transducers Y1 - 2016 A1 - Emil Zeuthen A1 - Albert Schliesser A1 - Anders S. Sørensen A1 - J. M. Taylor AB -

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 η and the added noise N.

UR - https://arxiv.org/abs/1610.01099 ER - TY - JOUR T1 - A finite presentation of CNOT-dihedral operators Y1 - 2016 A1 - Matthew Amy A1 - Jianxin Chen A1 - Neil J. Ross AB -

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.

UR - https://arxiv.org/abs/1701.00140 ER - TY - JOUR T1 - Flight of a heavy particle nonlinearly coupled to a quantum bath JF - Physical Review B Y1 - 2016 A1 - Mohammad F. Maghrebi A1 - Matthias Krüger A1 - Mehran Kardar AB - 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 L\'{e}vy flights. We suggest condensed matter analogs where similar effects may arise. VL - 93 U4 - 014309 UR - http://arxiv.org/abs/1508.00582 CP - 1 U5 - 10.1103/PhysRevB.93.014309 ER - TY - JOUR T1 - Fractional Quantum Hall States of Rydberg Polaritons JF - Physical Review A Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Norman Y. Yao A1 - Mohammad Hafezi A1 - Thomas Pohl A1 - Ofer Firstenberg A1 - Alexey V. Gorshkov AB - We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator -- a lattice-based, fractional quantum Hall state of light. VL - 91 U4 - 033838 UR - http://arxiv.org/abs/1411.6624v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.91.033838 ER - TY - JOUR T1 - Framework for learning agents in quantum environments Y1 - 2015 A1 - Vedran Dunjko A1 - J. M. Taylor A1 - Hans J. Briegel AB - In this paper we provide a broad framework for describing learning agents in general quantum environments. We analyze the types of classically specified environments which allow for quantum enhancements in learning, by contrasting environments to quantum oracles. We show that whether or not quantum improvements are at all possible depends on the internal structure of the quantum environment. If the environments are constructed and the internal structure is appropriately chosen, or if the agent has limited capacities to influence the internal states of the environment, we show that improvements in learning times are possible in a broad range of scenarios. Such scenarios we call luck-favoring settings. The case of constructed environments is particularly relevant for the class of model-based learning agents, where our results imply a near-generic improvement. UR - http://arxiv.org/abs/1507.08482v1 ER - TY - JOUR T1 - From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating JF - Annalen der Physik Y1 - 2015 A1 - Corey Stambaugh A1 - Haitan Xu A1 - Utku Kemiktarak A1 - J. M. Taylor A1 - John Lawall AB - We demonstrate a "membrane in the middle" optomechanical system using a silicon nitride membrane patterned as a subwavelength grating. The grating has a reflectivity of over 99.8%, effectively creating two sub-cavities, with free spectral ranges of 6 GHz, optically coupled via photon tunneling. Measurements of the transmission and reflection spectra show an avoided crossing where the two sub-cavities simultaneously come into resonance, with a frequency splitting of 54 MHz. We derive expressions for the lineshapes of the symmetric and antisymmetric modes at the avoided crossing, and infer the grating reflection, transmission, absorption, and scattering through comparison with the experimental data. VL - 527 U4 - 81 - 88 UR - http://arxiv.org/abs/1407.1709v1 CP - 1-2 J1 - ANNALEN DER PHYSIK U5 - 10.1002/andp.201400142 ER - TY - JOUR T1 - The Fundamental Gap for a Class of Schrödinger Operators on Path and Hypercube Graphs JF - Journal of Mathematical Physics Y1 - 2014 A1 - Michael Jarret A1 - Stephen P. Jordan AB - We consider the difference between the two lowest eigenvalues (the fundamental gap) of a Schr\"{o}dinger operator acting on a class of graphs. In particular, we derive tight bounds for the gap of Schr\"{o}dinger operators with convex potentials acting on the path graph. Additionally, for the hypercube graph, we derive a tight bound for the gap of Schr\"{o}dinger operators with convex potentials dependent only upon vertex Hamming weight. Our proof makes use of tools from the literature of the fundamental gap theorem as proved in the continuum combined with techniques unique to the discrete case. We prove the tight bound for the hypercube graph as a corollary to our path graph results. VL - 55 U4 - 052104 UR - http://arxiv.org/abs/1403.1473v1 CP - 5 J1 - J. Math. Phys. U5 - 10.1063/1.4878120 ER - TY - JOUR T1 - Far from equilibrium quantum magnetism with ultracold polar molecules JF - Physical Review Letters Y1 - 2013 A1 - Kaden R. A. Hazzard A1 - Salvatore R. Manmana A1 - Michael Foss-Feig A1 - Ana Maria Rey AB - Recent theory has indicated how to emulate tunable models of quantum magnetism with ultracold polar molecules. Here we show that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate. The first is to verify and benchmark the models proposed to describe these systems. The second is to prepare correlated and possibly useful states in well-understood regimes. The third is to explore many-body physics inaccessible to existing theoretical techniques. Our proposal relies on a non-equilibrium protocol that can be viewed either as Ramsey spectroscopy or an interaction quench. It uses only routine experimental tools available in any ultracold molecule experiment. VL - 110 UR - http://arxiv.org/abs/1209.4076v1 CP - 7 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.110.075301 ER - TY - JOUR T1 - Formation and decay of Bose-Einstein condensates in an excited band of a double-well optical lattice JF - Physical Review A Y1 - 2013 A1 - Saurabh Paul A1 - Eite Tiesinga AB - We study the formation and collision-aided decay of an ultra-cold atomic Bose-Einstein condensate in the first excited band of a double-well 2D-optical lattice with weak harmonic confinement in the perpendicular $z$ direction. This lattice geometry is based on an experiment by Wirth et al. The double well is asymmetric, with the local ground state in the shallow well nearly degenerate with the first excited state of the adjacent deep well. We compare the band structure obtained from a tight-binding (TB) model with that obtained numerically using a plane wave basis. We find the TB model to be in quantitative agreement for the lowest two bands, qualitative for next two bands, and inadequate for even higher bands. The band widths of the excited bands are much larger than the harmonic oscillator energy spacing in the $z$ direction. We then study the thermodynamics of a non-interacting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature, $T_c$, as functions of lattice parameters. For typical atom numbers, the critical energy $k_BT_c$, with $k_B$ the Boltzmann constant, is larger than the excited band widths and harmonic oscillator energy. Using conservation of total energy and atom number, we show that the temperature increases after the lattice transformation. Finally, we estimate the time scale for a two-body collision-aided decay of the condensate as a function of lattice parameters. The decay involves two processes, the dominant one in which both colliding atoms decay to the ground band, and the second involving excitation of one atom to a higher band. For this estimate, we have used TB wave functions for the lowest four bands, and numerical estimates for higher bands. The decay rate rapidly increases with lattice depth, but stays smaller than the tunneling rate between the $s$ and $p$ orbitals in adjacent wells. VL - 88 UR - http://arxiv.org/abs/1308.4449v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.88.033615 ER - TY - JOUR T1 - A framework for bounding nonlocality of state discrimination JF - Communications in Mathematical Physics Y1 - 2013 A1 - Andrew M. Childs A1 - Debbie Leung A1 - Laura Mancinska A1 - Maris Ozols AB - We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99]. VL - 323 U4 - 1121 - 1153 UR - http://arxiv.org/abs/1206.5822v1 CP - 3 J1 - Commun. Math. Phys. U5 - 10.1007/s00220-013-1784-0 ER - TY - JOUR T1 - From Ground States to Local Hamiltonians JF - Physical Review A Y1 - 2012 A1 - Jianxin Chen A1 - Zhengfeng Ji A1 - Bei Zeng A1 - D. L. Zhou AB - Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles. VL - 86 UR - http://arxiv.org/abs/1110.6583v4 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.86.022339 ER - TY - JOUR T1 - Full Abstraction for Set-Based Models of the Symmetric Interaction Combinators JF - Proceedings of the 15th International Conference on Foundations of Software Science and Computation Structures Y1 - 2012 A1 - Damiano Mazza A1 - Neil J. Ross AB - The symmetric interaction combinators are a model of distributed and deterministic computation based on Lafont’s interaction nets, a special form of graph rewriting. The interest of the symmetric interaction combinators lies in their universality, that is, the fact that they may encode all other interaction net systems; for instance, several implementations of the lambda-calculus in the symmetric interaction combinators exist, related to Lamping’s sharing graphs for optimal reduction. A certain number of observational equivalences were introduced for this system, by Lafont, Fernandez and Mackie, and the first author. In this paper, we study the problem of full abstraction with respect to one of these equivalences, using a class of very simple denotational models based on pointed sets. VL - 7213 U4 - 316-330 UR - https://lipn.univ-paris13.fr/~mazza/papers/CombSetSem-FOSSACS2012.pdf ER - TY - JOUR T1 - Fast and robust quantum computation with ionic Wigner crystals JF - Physical Review A Y1 - 2011 A1 - J. D. Baltrusch A1 - A. Negretti A1 - J. M. Taylor A1 - T. Calarco AB - 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. VL - 83 UR - http://arxiv.org/abs/1011.5616v2 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.83.042319 ER - TY - JOUR T1 - Far-field optical imaging and manipulation of individual spins with nanoscale resolution JF - Nature Phys. Y1 - 2010 A1 - Maurer, P C A1 - Maze, J R A1 - Stanwix, P L A1 - Jiang, L A1 - Alexey V. Gorshkov A1 - Zibrov, A A A1 - Harke, B A1 - Hodges, J S A1 - Zibrov, A S A1 - Yacoby, A A1 - Twitchen, D A1 - Hell, S W A1 - Walsworth, R L A1 - Lukin, M D VL - 6 U4 - 912 UR - http://www.nature.com/nphys/journal/v6/n11/abs/nphys1774.html ER - TY - JOUR T1 - Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection JF - Physical Review A Y1 - 2010 A1 - Jonatan B. Brask A1 - Liang Jiang A1 - Alexey V. Gorshkov A1 - Vladan Vuletic A1 - Anders S. Sorensen A1 - Mikhail D. Lukin AB - Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, the entanglement rates and scalability of current approaches are limited by relatively low retrieval and single-photon detector efficiencies. We propose a scheme, which makes use of fluorescent detection of stored excitations to significantly increase the efficiency of connection and hence the rate. Practical performance and possible experimental realizations of the new protocol are discussed. VL - 81 UR - http://arxiv.org/abs/0907.3839v2 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.81.020303 ER - TY - JOUR T1 - Feshbach Resonances in Ultracold Gases JF - Reviews of Modern Physics Y1 - 2010 A1 - Cheng Chin A1 - Rudolf Grimm A1 - Paul Julienne A1 - Eite Tiesinga AB - Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules. VL - 82 U4 - 1225 - 1286 UR - http://arxiv.org/abs/0812.1496v2 CP - 2 J1 - Rev. Mod. Phys. U5 - 10.1103/RevModPhys.82.1225 ER - TY - JOUR T1 - Fast quantum algorithms for approximating some irreducible representations of groups Y1 - 2008 A1 - Stephen P. Jordan AB - We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this problem. Furthermore, quantum Schur transforms yield efficient solutions for certain irreducible representations of the unitary group. Beyond this, we obtain poly(n)-time quantum algorithms for approximating matrix elements from all the irreducible representations of the alternating group A_n, and all the irreducible representations of polynomial highest weight of U(n), SU(n), and SO(n). These quantum algorithms offer exponential speedup in worst case complexity over the fastest known classical algorithms. On the other hand, we show that average case instances are classically easy, and that the techniques analyzed here do not offer a speedup over classical computation for the estimation of group characters. UR - http://arxiv.org/abs/0811.0562v2 ER - TY - JOUR T1 - A fast and robust approach to long-distance quantum communication with atomic ensembles JF - Physical Review A Y1 - 2007 A1 - L. Jiang A1 - J. M. Taylor A1 - M. D. Lukin AB - Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Nature 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3 minutes over 1280 km distance with fidelity (F>78%) sufficient to violate Bell's inequality. VL - 76 UR - http://arxiv.org/abs/quant-ph/0609236v3 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.76.012301 ER - TY - JOUR T1 - Fault-tolerant Quantum Communication with Minimal Physical Requirements JF - Physical Review Letters Y1 - 2006 A1 - L. Childress A1 - J. M. Taylor A1 - A. S. Sorensen A1 - M. D. Lukin AB - We describe a novel protocol for a quantum repeater which enables long distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits. VL - 96 UR - http://arxiv.org/abs/quant-ph/0410123v3 CP - 7 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.96.070504 ER - TY - JOUR T1 - Fast quantum algorithm for numerical gradient estimation JF - Physical Review Letters Y1 - 2005 A1 - Stephen P. Jordan AB - Given a blackbox for f, a smooth real scalar function of d real variables, one wants to estimate the gradient of f at a given point with n bits of precision. On a classical computer this requires a minimum of d+1 blackbox queries, whereas on a quantum computer it requires only one query regardless of d. The number of bits of precision to which f must be evaluated matches the classical requirement in the limit of large n. VL - 95 UR - http://arxiv.org/abs/quant-ph/0405146v2 CP - 5 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.95.050501 ER - TY - JOUR T1 - Fault-tolerant quantum repeaters with minimal physical resources, and implementations based on single photon emitters JF - Physical Review A Y1 - 2005 A1 - L. I. Childress A1 - J. M. Taylor A1 - A. S. Sorensen A1 - M. D. Lukin AB - We analyze a novel method that uses fixed, minimal physical resources to achieve generation and nested purification of quantum entanglement for quantum communication over arbitrarily long distances, and discuss its implementation using realistic photon emitters and photonic channels. In this method, we use single photon emitters with two internal degrees of freedom formed by an electron spin and a nuclear spin to build intermediate nodes in a quantum channel. State-selective fluorescence is used for probabilistic entanglement generation between electron spins in adjacent nodes. We analyze in detail several approaches which are applicable to realistic, homogeneously broadened single photon emitters. Furthermore, the coupled electron and nuclear spins can be used to efficiently implement entanglement swapping and purification. We show that these techniques can be combined to generate high-fidelity entanglement over arbitrarily long distances. We present a specific protocol that functions in polynomial time and tolerates percent-level errors in entanglement fidelity and local operations. The scheme has the lowest requirements on physical resources of any current scheme for fully fault-tolerant quantum repeaters. VL - 72 UR - http://arxiv.org/abs/quant-ph/0502112v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.72.052330 ER - TY - JOUR T1 - From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups Y1 - 2005 A1 - Dave Bacon A1 - Andrew M. Childs A1 - Wim van Dam AB - We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect product of an abelian group and a cyclic group, we show that the pretty good measurement is optimal and that its probability of success and unitary implementation are closely related to an average-case algebraic problem. By solving this problem, we find efficient quantum algorithms for a number of nonabelian hidden subgroup problems, including some for which no efficient algorithm was previously known: certain metacyclic groups as well as all groups of the form (Z_p)^r X| Z_p for fixed r (including the Heisenberg group, r=2). In particular, our results show that entangled measurements across multiple copies of hidden subgroup states can be useful for efficiently solving the nonabelian HSP. UR - http://arxiv.org/abs/quant-ph/0504083v2 J1 - Proc. 46th IEEE Symposium on Foundations of Computer Science (FOCS 2005) U5 - 10.1109/SFCS.2005.38 ER - TY - JOUR T1 - `Flat Phase' Loading of a Bose-Einstein Condensate into an Optical Lattice JF - Physical Review A Y1 - 2002 A1 - Shlomo E. Sklarz A1 - Inbal Friedler A1 - David J. Tannor A1 - Yehuda B. Band A1 - Carl J. Williams AB - It has been proposed that the adiabatic loading of a Bose-Einstein Condensate (BEC) into an optical lattice via the Mott-insulator transition can be used to initialize a quantum computer [D. Jaksch, {\it et al.}, Phys. Rev. Lett. {\bf 81}, 3108 (1998)]. The loading of a BEC into the lattice without causing band excitation is readily achievable; however, unless one switches on an optical lattice very slowly, the optical lattice causes a phase to accumulate across the condensate. We show analytically and numerically that a cancellation of this effect is possible by adjusting the harmonic trap force-constant of the magnetic trap appropriately, thereby facilitating quick loading of an optical lattice for quantum computing purposes. A simple analytical theory is developed for a non-stationary BEC in a harmonic trap. VL - 66 UR - http://arxiv.org/abs/physics/0209071v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.66.053620 ER - TY - JOUR T1 - Finding cliques by quantum adiabatic evolution Y1 - 2000 A1 - Andrew M. Childs A1 - Edward Farhi A1 - Jeffrey Goldstone A1 - Sam Gutmann AB - Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph with high probability and runs in a time polynomial in n. For the small graphs we are able to investigate (n <= 18), the quantum algorithm appears to require only a quadratic run time. UR - http://arxiv.org/abs/quant-ph/0012104v1 J1 - Quantum Information and Computation 2 ER -