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Unconditionally-secure and reusable public-key authentication 1

6th Conference on the Theory of quantum Computation, Communication, and Cryptography, TQC 2011

作者： Ioannou, Lawrence M. Mosca, Michele Institute for Quantum Computing University of Waterloo 200 University Avenue Waterloo ON N2L 3G1 Canada Department of Combinatorics and Optimization University of Waterloo 200 University Avenue Waterloo ON N2L 3G1 Canada Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo ON N2L 2Y5 Canada

We present a quantum-public-key identification protocol and show that it is secure against a computationally-unbounded adversary. This demonstrates for the first time that unconditionally-secure and reusable public-ke... 详细信息

ISBN: (数字)9783642544293

ISBN: (纸本)9783642544286

关键词： Authentication

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Hamiltonian Learning and Certification Using quantum Resources

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Physical Review Letters 2014年第19期112卷 190501-190501页

作者： Nathan Wiebe Christopher Granade Christopher Ferrie D. G. Cory Quantum Architectures and Computation Group Microsoft Research Redmond Washington 98052 USA Department of Combinatorics & Optimization University of Waterloo Ontario N2L 3G1 Canada Institute for Quantum Computing University of Waterloo Ontario N2L 3G1 Canada Department of Physics University of Waterloo Ontario N2L 3G1 Canada Center for Quantum Information and Control University of New Mexico Albuquerque New Mexico 87131-0001 USA Department of Chemistry University of Waterloo Ontario N2L 3G1 Canada Perimeter Institute University of Waterloo Ontario N2L 2Y5 Canada

In recent years quantum simulation has made great strides, culminating in experiments that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum simulator using a trusted quantum simulator. We illustrate the power of this approach by showing numerically that it can inexpensively learn the Hamiltonians for large frustrated Ising models, demonstrating that quantum resources can make certifying analog quantum simulators tractable.

关键词： quantum theory RESEARCH SUPERCOMPUTERS HAMILTONIAN systems ALGORITHMS -- Research PHYSICS research

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quantum Hamiltonian learning using imperfect quantum resources

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Physical Review A 2014年第4期89卷 042314-042314页

作者： Nathan Wiebe Christopher Granade Christopher Ferrie David Cory Quantum Architectures and Computation Group Microsoft Research Redmond Washington 98052 USA Department of Combinatorics & Optimization University of Waterloo Ontario Canada N2L 3G1 Institute for Quantum Computing University of Waterloo Ontario Canada N2L 3G1 Department of Physics University of Waterloo Ontario Canada N2L 3G1 Center for Quantum Information and Control University of New Mexico Albuquerque New Mexico 87131-0001 USA Department of Chemistry University of Waterloo Ontario Canada N2L 3G1 Perimeter Institute University of Waterloo Ontario Canada N2L 2Y5

Identifying an accurate model for the dynamics of a quantum system is a vexing problem that underlies a range of problems in experimental physics and quantum information theory. Recently, a method called quantum Hamiltonian learning has been proposed by the present authors that uses quantum simulation as a resource for modeling an unknown quantum system. This approach can, under certain circumstances, allow such models to be efficiently identified. A major caveat of that work is the assumption of that all elements of the protocol are noise free. Here we show that quantum Hamiltonian learning can tolerate substantial amounts of depolarizing noise and show numerical evidence that it can tolerate noise drawn from other realistic models. We further provide evidence that the learning algorithm will find a model that is maximally close to the true model in cases where the hypothetical model lacks terms present in the true model. Finally, we also provide numerical evidence that the algorithm works for noncommuting models. This work illustrates that quantum Hamiltonian learning can be performed using realistic resources and suggests that even imperfect quantum resources may be valuable for characterizing quantum systems.

关键词： quantum information theory HAMILTON'S principle function quantum systems EMISSION tomography quantum computing BAYESIAN analysis

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Easy and hard functions for the Boolean hidden shift problem 8

Easy and hard functions for the Boolean hidden shift problem

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8th Conference on the Theory of quantum Computation, Communication and Cryptography, TQC 2013

作者： Childs, Andrew M. Kothari, Robin Ozols, Maris Roetteler, Martin Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo 200 University Avenue West WaterlooONN2L 3G1 Canada David R. Cheriton School of Computer Science Institute for Quantum Computing University of Waterloo 200 University Avenue West WaterlooONN2L 3G1 Canada IBM TJ Watson Research Center 1101 Kitchawan Road Yorktown HeightsNY10598 United States NEC Laboratories America 4 Independence Way PrincetonNJ08540 United States

ISBN: (纸本)9783939897552

We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x + s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact onequery algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta functions. Moreover, we show that the problem is easy for random functions, since two queries suffice. Our algorithm for random functions is based on performing the pretty good measurement on several copies of a certain state;its analysis relies on the Fourier transform. We also use this approach to improve the quantum rejection sampling approach to the Boolean hidden shift problem. © Andrew M. Childs, Robin Kothari, Maris Ozols, and Martin Roetteler.

关键词： Boolean functions

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quantum query complexity of minor-closed graph properties

Quantum query complexity of minor-closed graph properties

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作者： Childs, Andrew M. Kothari, Robin Department of Combinatorics and Optimization and Institute for Quantum Computing University of Waterloo Waterloo ON N2L 3G1 Canada David R. Cheriton School of Computer Science and Institute for Quantum Computing University of Waterloo Waterloo ON N2L 3G1 Canada

We study the quantum query complexity of m inor-closed graph properties, which include such problems as determining whether an n-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most minor-closed properties-those that cannot be characterized by a finite set of forbidden subgraphs-have quantum query complexity Θ(n3/2). To establish this, we prove an adversary lower bound using a detailed analysis of the structure of minor-closed properties with respect to forbidden topological minors and forbidden subgraphs. On the other hand, we show that minor-closed properties (and more generally, sparse graph properties) that can be characterized by finitely many forbidden subgraphs can be solved strictly faster, in o(n3/2) queries. Our algorithms are a novel application of the quantum walk search framework and give improved upper bounds for several subgraph-finding problems. © 2012 Societ y for Industrial and Applied Mathematics.

关键词： Graph theory

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Information-Theoretic Equilibration: The Appearance of Irreversibility under Complex quantum Dynamics

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Physical Review Letters 2013年第8期111卷 080403-080403页

作者： Cozmin Ududec Nathan Wiebe Joseph Emerson Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L3G1 Canada Institute for Quantum Computing 200 University Avenue West Waterloo Ontario N2L3G1 Canada Department of Combinatics and Optimization University of Waterloo Waterloo Ontario N2L3G1 Canada Department of Applied Math University of Waterloo Waterloo Ontario N2L3G1 Canada

The question of how irreversibility can emerge as a generic phenomenon when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the appearance of irreversibility that applies to coherent, isolated systems in a pure quantum state. This equilibration mechanism requires only an assumption of sufficiently complex internal dynamics and natural information-theoretic constraints arising from the infeasibility of collecting an astronomical amount of measurement data. Remarkably, we are able to prove that irreversibility can be understood as typical without assuming decoherence or restricting to coarse-grained observables, and hence occurs under distinct conditions and time scales from those implied by the usual decoherence point of view. We illustrate the effect numerically in several model systems and prove that the effect is typical under the standard random-matrix conjecture for complex quantum systems.

关键词： quantum mechanics CLASSICAL mechanics quantum states ISOLATED systems (Thermodynamics) DECOHERENCE (quantum mechanics)

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Number-Theoretic Nature of Communication in quantum Spin Systems

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Physical Review Letters 2012年第5期109卷 050502-050502页

作者： Chris Godsil Stephen Kirkland Simone Severini Jamie Smith Combinatorics & Optimization University of Waterloo N2L 3G1 Waterloo Canada Hamilton Institute National University of Ireland Maynooth County Kildare Ireland Department of Computer Science and Department of Physics & Astronomy University College London WC1E 6BT London United Kingdom Institute for Quantum Computing and Combinatorics & Optimization University of Waterloo N2L 3G1 Waterloo Canada

The last decade has witnessed substantial interest in protocols for transferring information on networks of quantum mechanical objects. A variety of control methods and network topologies have been proposed, on the basis that transfer with perfect fidelity—i.e., deterministic and without information loss—is impossible through unmodulated spin chains with more than a few particles. Solving the original problem formulated by Bose [Phys. Rev. Lett. 91, 207901 (2003)], we determine the exact number of qubits in unmodulated chains (with an XY Hamiltonian) that permit transfer with a fidelity arbitrarily close to 1, a phenomenon called pretty good state transfer. We prove that this happens if and only if the number of nodes is n=p−1, 2p−1, where p is a prime, or n=2m−1. The result highlights the potential of quantum spin system dynamics for reinterpreting questions about the arithmetic structure of integers and, in this case, primality.

关键词： KNOWLEDGE transfer (Communication) quantum theory INFORMATION networks NATURAL numbers ARITHMETIC

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quantum Algorithm for Data Fitting

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Physical Review Letters 2012年第5期109卷 050505-050505页

作者： Nathan Wiebe Daniel Braun Seth Lloyd Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo 200 University Ave. West Waterloo Ontario Canada Laboratoire de Physique Théorique Université Paul Sabatier 118 Route de Narbonne F-31062 Toulouse France CNRS LPT (IRSAMC) F-31062 Toulouse France Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA

We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)]. In many cases, our algorithm can also efficiently find a concise function that approximates the data to be fitted and bound the approximation error. In cases where the input data are pure quantum states, the algorithm can be used to provide an efficient parametric estimation of the quantum state and therefore can be applied as an alternative to full quantum-state tomography given a fault tolerant quantum computer.

关键词： LEAST squares LINEAR algebras APPROXIMATION error PARAMETER estimation COMPUTER algorithms

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Experimental implementation of a codeword-stabilized quantum code

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Physical Review A 2012年第6期85卷 062312-062312页

作者： Jingfu Zhang Markus Grassl Bei Zeng Raymond Laflamme Institute for Quantum Computing and Department of Physics University of Waterloo Waterloo Ontario N2L 3G1 Canada Centre for Quantum Technologies National University of Singapore Singapore 117543 Singapore Department of Mathematics & Statistics University of Guelph Guelph Ontario N1G 2W1 Canada Institute for Quantum Computing and Department of Combinatorics & Optimization University of Waterloo Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics Waterloo Ontario N2J 2W9 Canada

A five-qubit-codeword-stabilized quantum code is implemented in a seven-qubit system using nuclear magnetic resonance. Our experiment implements a good nonadditive quantum code which encodes a larger Hilbert space than any stabilizer code with the same length and capable of correcting the same kind of errors. The experimentally measured quantum coherence is shown to be robust against artificially introduced errors, benchmarking the success in implementing the quantum error correction code. Given the typical decoherence time of the system, our experiment illustrates the ability of coherent control to implement complex quantum circuits for demonstrating interesting results in spin qubits for quantum computing.

关键词： quantum error correcting codes QUBITS NUCLEAR magnetic resonance COHERENCE (Optics) quantum information theory MATHEMATICAL physics

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Tight Bell inequalities with no quantum violation from qubit unextendible product bases

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Physical Review A 2012年第4期85卷 042113-042113页

作者： R. Augusiak T. Fritz Ma. Kotowski Mi. Kotowski M. Pawłowski M. Lewenstein A. Acín ICFO–Institut de Ciències Fotòniques 08860 Castelldefels (Barcelona) Spain Department of Combinatorics and Optimization and Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada N2L 3G1 Department of Mathematics University of Bristol Bristol BS8 1TW United Kingdom ICREA–Institució Catalana de Recerca i Estudis Avançats 08010 Barcelona Spain

We investigate the relation between unextendible product bases (UPB) and Bell inequalities found recently in R. Augusiak et al. [Phys. Rev. Lett. 107, 070401 (2011)]. We, first, review the procedure introduced there that associates to any set of mutually orthogonal product vectors in a many-qubit Hilbert space a Bell inequality. We then show that if a set of mutually orthogonal product vectors can be completed to a full basis, then the associated Bell inequality is trivial, in the sense of not being violated by any nonsignalling correlations. This implies that the relevant Bell inequalities that arise from the construction all come from UPBs, which adds additional weight to the significance of UPBs for Bell inequalities. Then, we provide additional examples of tight Bell inequalities with no quantum violation constructed from UPBs in this way. Finally, it is proven that the Bell inequalities with no quantum violation introduced recently in M. Almeida et al. [Phys. Rev. Lett. 104, 230404 (2010)] are tight for any odd number of parties.

关键词： Bells

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