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Physical Review A 2022年第4期106卷 042443-042443页

作者： Andrew Jena Scott N. Genin Michele Mosca Department of Combinatorics and Optimization University of Waterloo Waterloo N2L 3G1 ON Canada Institute for Quantum Computing University of Waterloo Waterloo N2L 3G1 ON Canada OTI Lumionics Inc. 3415 American Drive Unit 1 Mississauga L4V 1T4 ON Canada Perimeter Institute for Theoretical Physics Waterloo N2L 2Y5 ON Canada

Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of Pauli operators allows for fewer measurements and an overall speedup of the measurement process. Using results from coloring random graphs, we give evidence for an upper bound on the expected minimum number of simultaneously measurable parts necessary to partition a set of Pauli operators. By expanding our gate set to allow multiqubit Clifford gates before measurement, we were able to cut down the number of measurements considerably compared to previous approaches. We conjecture that this improvement is, in general, linear with respect to the lengths of the Pauli operators. We conclude by demonstrating the feasibility of this approach by implementing the variational quantum eigensolver on the Aspen-4-4Q-A quantum processor unit. In doing so, we calculate the ground-state energies of H2 using fewer measurements than is possible with single-qubit gates with no statistically significant difference in accuracy.

关键词： Electronic structure Electronic structure of atoms & molecules quantum algorithms quantum computation

Minimal qubit representations of Hamiltonians via conserved charges

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arXiv 2023年

作者： Gunderman, Lane G. Jena, Andrew Dellantonio, Luca Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics and Astronomy University of Exeter Stocker Road ExeterEX4 4QL United Kingdom

In the last years, we have been witnessing a tremendous push to demonstrate that quantum computers can solve classically intractable problems. This effort, initially focused on the hardware, progressively included the simplification of the models to be simulated. We consider Hamiltonians written in terms of Pauli operators and systematically cut all qubits that are not essential to simulate the system. Our approach is universally applicable and lowers the complexity by first ensuring that the largest possible portion of the Hilbert space becomes irrelevant, and then by finding and exploiting all conserved charges of the system, i.e., symmetries that can be expressed as Pauli operators. Remarkably, both processes are classically efficient and optimal. To showcase our algorithm, we simplify chemical molecules, lattice gauge theories, the Hubbard and the Kitaev models. Copyright © 2023, The Authors. All rights reserved.

关键词： Hamiltonians

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

Lieb-Robinson Bounds and the Speed of Light from Topological Order

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Physical Review Letters 2009年第1期102卷 017204-017204页

作者： Alioscia Hamma Fotini Markopoulou Isabeau Prémont-Schwarz Simone Severini Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo Ontario N2L 2Y5 Canada Massachusetts Institute of Technology Research Laboratory of Electronics 77 Massachusetts Avenue Cambridge Massachusetts 02139 USA Department of Physics University of Waterloo Waterloo Ontario N2L 3G1 Canada Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo 200 University Avenue West Waterloo Ontario N2L 3G1 Canada

We apply the Lieb-Robinson bounds technique to find the maximum speed of interaction in a spin model with topological order whose low-energy effective theory describes light [see X.-G. Wen, Phys. Rev. B 68, 115413 (2003)]. The maximum speed of interactions in two dimensions is bounded from above by less than e times the speed of emerging light, giving a strong indication that light is indeed the maximum speed of interactions. This result does not rely on mean field theoretic methods. In higher spatial dimensions, the Lieb-Robinson speed is conjectured to increase linearly with the dimension itself. The implications for the horizon problem in cosmology are discussed.

关键词： Speed

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

Unified approach to data-driven quantum error mitigation

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arXiv 2020年

作者： Lowe, Angus Gordon, Max Hunter Czarnik, Piotr Arrasmith, Andrew Coles, Patrick J. Cincio, Lukasz Department of Combinatorics and Optimization and Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Instituto de Física Teórica UAM/CSIC Universidad Autónoma de Madrid Madrid Spain Theoretical Division Los Alamos National Laboratory Los AlamosNM87545 United States Quantum Science Center Oak RidgeTN37931 United States

Achieving near-term quantum advantage will require effective methods for mitigating hardware noise. Data-driven approaches to error mitigation are promising, with popular examples including zero-noise extrapolation (ZNE) and Clifford data regression (CDR). Here we propose a novel, scalable error mitigation method that conceptually unifies ZNE and CDR. Our approach, called variable-noise Clifford data regression (vnCDR), significantly outperforms these individual methods in numerical benchmarks. vnCDR generates training data first via near-Clifford circuits (which are classically simulable) and second by varying the noise levels in these circuits. We employ a noise model obtained from IBM's Ourense quantum computer to benchmark our method. For the problem of estimating the energy of an 8-qubit Ising model system, vnCDR improves the absolute energy error by a factor of 33 over the unmitigated results and by factors 20 and 1.8 over ZNE and CDR, respectively. For the problem of correcting observables from random quantum circuits with 64 qubits, vnCDR improves the error by factors of 2.7 and 1.5 over ZNE and CDR, respectively. Copyright © 2020, The Authors. All rights reserved.

关键词： Errors

Fast estimation of outcome probabilities for quantum circuits

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arXiv 2021年

作者： Pashayan, Hakop Reardon-Smith, Oliver Korzekwa, Kamil Bartlett, Stephen D. Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Kraków30-348 Poland Centre for Engineered Quantum Systems School of Physics The University of Sydney SydneyNSW2006 Australia

We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like ≈ 1.17t for T gates). Our algorithm is state-of-the-art for this task: as an example, in approximately 13 hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of 0.03, for a 50-qubit, 60 non-Clifford gate quantum circuit with more than 2000 Clifford gates. Our second algorithm, Compute, calculates the probability of a chosen measurement outcome to machine precision with run-time O (2t−rt) where r is an efficiently computable, circuit-specific quantity. With high probability, r is very close to min {t, n − w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n = 55, w = 5, c = 105 and t = 80 T gates, and then compute the Born rule probability with a run-time consistently less than 10 minutes using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms and benchmark them using random circuits, the hidden shift algorithm and the quantum approximate optimization algorithm (QAOA). Copyright © 2021, The Authors. All rights reserved.

关键词： Probability

Device-independent state estimation based on Bell’s inequalities

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Physical Review A 2009年第6期80卷 062327-062327页

作者： C.-E. Bardyn T. C. H. Liew S. Massar M. McKague V. Scarani Centre for Quantum Technologies National University of Singapore Singapore 117543 Singapore Ecole Polytechnique Fédérale de Lausanne (EPFL) 1015 Lausanne Switzerland Laboratoire d’Information Quantique CP 225 Université Libre de Bruxelles Avenue F. D. Roosevelt 50 B-1050 Brussells Belgium Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo 200 University Avenue West Waterloo Ontario Canada N2L 3G1 Department of Physics National University of Singapore Singapore 117542 Singapore

The only information available about an alleged source of entangled quantum states is the amount S by which the Clauser-Horne-Shimony-Holt inequality is violated: nothing is known about the nature of the system or the measurements that are performed. We discuss how the quality of the source can be assessed in this black-box scenario, as compared to an ideal source that would produce maximally entangled states (more precisely, any state for which S=22). To this end, we present several inequivalent notions of fidelity, each one related to the use one can make of the source after having assessed it, and we derive quantitative bounds for each of them in terms of the violation S. We also derive a lower bound on the entanglement of the source as a function of S only.

关键词： quantum entanglement

Asymptotic Bound for Heat-Bath Algorithmic Cooling

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Physical Review Letters 2015年第10期114卷 100404-100404页

作者： Sadegh Raeisi Michele Mosca Institute for Quantum Computing University of Waterloo Ontario N2L 3G1 Canada Department of Physics and Astronomy University of Waterloo Ontario N2L 3G1 Canada Department of Combinatorics and Optimization University of Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada Canadian Institute for Advanced Research Toronto Ontario M5G 1Z8 Canada

The purity of quantum states is a key requirement for many quantum applications. Improving the purity is limited by fundamental laws of thermodynamics. Here, we are probing the fundamental limits for a natural approach to this problem, namely, heat-bath algorithmic cooling (HBAC). The existence of the cooling limit for HBAC techniques was proved by Schulman, Mor, and Weinstein. A bound for this value was found by Elias et al. and numerical testing supported the hypothesis that their bound may be the actual limit. A proof or disproof of whether their bound was the actual limit remained open for the past decade. Here, for the first time, we prove this limit. In the context of quantum thermodynamics, this corresponds to the maximum extractable work from the quantum system. We also establish, in the case of higher dimensional reset systems, how the performance of HBAC depends on the energy spectrum of the reset system.

关键词： quantum states quantum mechanics THERMODYNAMICS quantum theory PHYSICAL & theoretical chemistry

Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era

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arXiv 2023年

作者： Kuroiwa, Kohdai Nakagawa, Yuya O. Institute for Quantum Computing University of Waterloo ONN2L 3G1 Canada Department of Combinatorics and Optimization University of Waterloo Canada Perimeter Institute for Theoretical Physics ONN2L 2Y5 Canada QunaSys Inc. Aqua Hakusan Building 9F 1-13-7 Hakusan Bunkyo Tokyo113-0001 Japan

Fault-tolerant quantum computation (FTQC) is essential to implement quantum algorithms in a noise-resilient way, and thus to enjoy advantages of quantum computers even with presence of noise. In FTQC, a quantum circuit is decomposed into universal gates that can be fault-tolerantly implemented, for example, Clifford+T gates. Here, T gate is usually regarded as an essential resource for quantum computation because its action cannot be simulated efficiently on classical computers and it is experimentally difficult to implement fault-tolerantly. Practically, it is highly likely that only a limited number of T gates are available in the near future. In this Pre-FTQC era, due to the constraint on available resources, it is vital to precisely estimate the decomposition error of a whole circuit. In this paper, we propose that the Clifford+T decomposition error for a given quantum circuit containing a large number of quantum gates can be modeled as the depolarizing noise by averaging the decomposition error for each quantum gate in the circuit, and our model provides more accurate error estimation than the naive estimation. We exemplify this by taking unitary coupled-cluster (UCC) ansatz used in the applications of quantum computers to quantum chemistry as an example. We theoretically evaluate the approximation error of UCC ansatz when decomposed into Clifford+T gates, and the numerical simulation for a wide variety of molecules verified that our model well explains the total decomposition error of the ansatz. Our results enable the precise and efficient usage of quantum resources in the early-stage applications of quantum computers and fuel further research towards what quantum computation can achieve in the upcoming future. © 2023, CC BY.

关键词： quantum computers