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Adaptive shot allocation for fast convergence in variational quantum algorithms

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arXiv 2021年

作者： Gu, Andi Lowe, Angus Dub, Pavel A. Coles, Patrick J. Arrasmith, Andrew Theoretical Division Los Alamos National Laboratory Los AlamosNM87545 United States Department of Physics University of California BerkeleyCA94720 United States Department of Combinatorics and Optimization and Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Chemistry Division Los Alamos National Laboratory Los AlamosNM87545 United States

Variational quantum Algorithms (VQAs) are a promising approach for practical applications like chemistry and materials science on near-term quantum computers as they typically reduce quantum resource requirements. However, in order to implement VQAs, an efficient classical optimization strategy is required. Here we present a new stochastic gradient descent method using an adaptive number of shots at each step, called the global Coupled Adaptive Number of Shots (gCANS) method, which improves on prior art in both the number of iterations as well as the number of shots required. These improvements reduce both the time and money required to run VQAs on current cloud platforms. We analytically prove that in a convex setting gCANS achieves geometric convergence to the optimum. Further, we numerically investigate the performance of gCANS on some chemical configuration problems. We also consider finding the ground state for an Ising model with different numbers of spins to examine the scaling of the method. We find that for these problems, gCANS compares favorably to all of the other optimizers we consider. Copyright © 2021, The Authors. All rights reserved.

关键词： Ising model

Quantifying quantum speedups: Improved classical simulation from tighter magic monotones

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arXiv 2020年

作者： Seddon, James R. Regula, Bartosz Pashayan, Hakop Ouyang, Yingkai Campbell, Earl T. Department of Physics and Astronomy University College London London United Kingdom School of Physical and Mathematical Sciences Nanyang Technological University 637371 Singapore Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Centre for Engineered Quantum Systems School of Physics The University of Sydney SydneyNSW2006 Australia Department of Physics & Astronomy University of Sheffield SheffieldS3 7RH United Kingdom AWS Center for Quantum Computing PasadenaCA91125 United States

Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by establishing precise connections with a family of magic monotones. Our first simulator introduces a new class of quasiprobability distributions and connects its runtime to a generalized notion of negativity. We prove that this algorithm has significantly improved exponential scaling compared to all prior quasiprobability simulators for qubits. Our second simulator is a new variant of the stabilizer-rank simulation algorithm, extended to work with mixed states and with significantly improved runtime bounds. Our third simulator trades precision for speed by discarding negative quasiprobabilities. We connect each algorithm’s performance to a corresponding magic monotone and, by comprehensively characterizing the monotones, we obtain a precise understanding of the simulation runtime and error bounds. Our analysis reveals a deep connection between all three seemingly unrelated simulation techniques and their associated monotones. For tensor products of single-qubit states, we prove that our monotones are all equal to each other, multiplicative and efficiently computable, allowing us to make clear-cut comparisons of the simulators’ performance scaling. Furthermore, our monotones establish several asymptotic and non-asymptotic bounds on state interconversion and distillation rates. Beyond the theory of magic states, our classical simulators can be adapted to other resource theories under certain axioms, which we demonstrate through an explicit application to the theory of quantum coherence. Copyright © 2020, The Authors. All rights reserved.

关键词： Simulators

Comparison of memory thresholds for planar qudit geometries

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arXiv 2017年

作者： Marks, Jacob Jochym-O'Connor, Tomas Gheorghiu, Vlad Department of Physics Yale University New HavenCT06520 United States Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Walter Burke Institute for Theoretical Physics Institute for Quantum Information and Matter California Institute of Technology PasadenaCA91125 United States Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada

We introduce and analyze a new type of decoding algorithm called General Color Clustering (GCC), based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under a generalized bit flip error model, and is used to obtain the first memory threshold estimates for qudit 6-6-6 color codes. The proposed decoder is compared with similar decoding schemes for qudit surface codes as well as the current leading qubit decoders for both sets of codes. We find that, as with surface codes, clustering performs sub-optimally for qubit color codes, giving a threshold of 5.6% compared to the 8.0% obtained through surface projection decoding methods. However, the threshold rate increases by up to 112% for large qudit dimensions, plateauing around 11.9%. All the analysis is performed using QTop, a new open-source software for simulating and visualizing topological quantum error correcting codes. Copyright © 2017, The Authors. All rights reserved.

关键词： Color

Upper bounds on device-independent quantum key distribution rates and a revised Peres conjecture

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arXiv 2020年

作者： Leditzky, Felix Arnon-Friedman, Rotem Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada EECS Department University of California Berkeley BerkeleyCA94720 United States JILA & Center for Theory of Quantum Matter University of Colorado Boulder BoulderCO80309 United States

Device-independent quantum key distribution (DIQKD) is one of the most challenging tasks in quantum cryptography. The protocols and their security are based on the existence of Bell inequalities and the ability to violate them by measuring entangled states. We study the entanglement needed for DIQKD protocols in two different ways. Our first contribution is the derivation of upper bounds on the key rates of CHSH-based DIQKD protocols in terms of the violation of the inequality;this sets an upper limit on the possible DI key extraction rate from states with a given violation. Our upper bound improves on the previously known bound of Kaur et al. Our second contribution is the initiation of the study of the role of bound entangled states in DIQKD. We present a revised Peres conjecture stating that such states cannot be used as a resource for DIQKD. We give a first piece of evidence for the conjecture by showing that the bound entangled state found by Vertesi and Brunner, even though it can certify DI randomness, cannot be used to produce a key using protocols analogous to the well-studied CHSH-based DIQKD protocol. Copyright © 2020, The Authors. All rights reserved.

关键词： quantum cryptography

Every quantum Helps: Operational Advantage of quantum Resources beyond Convexity

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Physical Review Letters 2024年第15期132卷 150201-150201页

作者： Kohdai Kuroiwa Ryuji Takagi Gerardo Adesso Hayata Yamasaki Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics Ontario N2L 2Y5 Canada Department of Basic Science The University of Tokyo 3-8-1 Komaba Meguro-ku Tokyo 153-8902 Japan School of Mathematical Sciences and Centre for the Mathematical and Theoretical Physics of Quantum Non-Equilibrium Systems University of Nottingham University Park Nottingham NG7 2RD United Kingdom Department of Physics Graduate School of Science The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan

Identifying what quantum-mechanical properties are useful to untap a superior performance in quantum technologies is a pivotal question. quantum resource theories provide a unified framework to analyze and understand such properties, as successfully demonstrated for entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a nonconvex set of free states and their interpretation has so far remained elusive. Here we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness measure in general resource theories. First, we characterize the generalized robustness in terms of a nonlinear resource witness and reveal that any state is more advantageous than a free one in some multicopy channel discrimination task. Next, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any specification on the structure of the free states.

关键词： quantum channels quantum measurements Resource theories

Simulating 2D Effects in Lattice Gauge Theories on a quantum Computer

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PRX quantum 2021年第3期2卷 030334-030334页

作者： Danny Paulson Luca Dellantonio Jan F. Haase Alessio Celi Angus Kan Andrew Jena Christian Kokail Rick van Bijnen Karl Jansen Peter Zoller Christine A. Muschik Institute for Quantum Computing University of Waterloo Waterloo Ontario N2L 3G1 Canada Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada Institute of Theoretical Physics and IQST Universität Ulm Albert-Einstein-Allee 11 Ulm D-89069 Germany Departament de Física Universitat Autònoma de Barcelona Bellaterra E-08193 Spain Center of Quantum Physics University of Innsbruck Innsbruck A-6020 Austria Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences Innsbruck A-6020 Austria Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario N2L 3G1 Canada NIC DESY Zeuthen Platanenallee 6 Zeuthen 15738 Germany Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada

quantum computing is in its greatest upswing, with so-called noisy-intermediate-scale-quantum devices heralding the computational power to be expected in the near future. While the field is progressing toward quantum advantage, quantum computers already have the potential to tackle classically intractable problems. Here, we consider gauge theories describing fundamental-particle interactions. On the way to their full-fledged quantum simulations, the challenge of limited resources on near-term quantum devices has to be overcome. We propose an experimental quantum simulation scheme to study ground-state properties in two-dimensional quantum electrodynamics (2D QED) using existing quantum technology. Our protocols can be adapted to larger lattices and offer the perspective to connect the lattice simulation to low-energy observable quantities, e.g., the hadron spectrum, in the continuum theory. By including both dynamical matter and a nonminimal gauge-field truncation, we provide the novel opportunity to observe 2D effects on present-day quantum hardware. More specifically, we present two variational-quantum-eigensolver- (VQE) based protocols for the study of magnetic field effects and for taking an important first step toward computing the running coupling of QED. For both instances, we include variational quantum circuits for qubit-based hardware. We simulate the proposed VQE experiments classically to calculate the required measurement budget under realistic conditions. While this feasibility analysis is done for trapped ions, our approach can be directly adapted to other platforms. The techniques presented here, combined with advancements in quantum hardware, pave the way for reaching beyond the capabilities of classical simulations.

关键词： quantum algorithms quantum computation quantum simulation

Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories

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Physical Review A 2024年第4期109卷 042403-042403页

quantum resource theories (QRTs) provide a unified framework to analyze quantum properties as resources for achieving advantages in quantum information processing. The generalized robustness and the weight of resource have been gaining increasing attention as useful resource quantifiers. However, the existing analyses of these measures were restricted to the cases where convexity of the set of free states is assumed, and physically motivated resources do not necessarily satisfy this restriction. In this paper, we give characterizations of robustness- and weight-based measures in general QRTs without convexity restriction through two different yet related approaches. On the one hand, we characterize the generalized robustness and the weight of resource by introducing a nonlinear witness. We show a general construction of new witness observables that detect the resourcefulness of a given state from multiple copies of the state and, using these witnesses, we provide operational interpretations of the above resource measures even without any convexity assumption. On the other hand, we find that the generalized robustness and the weight of resource can also be interpreted as the worst-case maximum advantage in variants of channel-discrimination and channel-exclusion tasks, respectively, where the set of free states consists of several convex subsets corresponding to multiple restrictions. We further extend these results to QRTs for quantum channels and quantum instruments. These characterizations show that every quantum resource exhibits an advantage for the corresponding tasks, even in general QRTs without convexity assumption. Thus, we establish the usefulness of robustness-based and weight-based techniques beyond the conventional scope of convex QRTs, leading to a better understanding of the general structure of QRTs.

关键词： quantum channels quantum measurements Resource theories

Homodyne-detector-blinding attack in continuous-variable quantum key distribution

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Physical Review A 2018年第1期98卷 012312-012312页

作者： Hao Qin Rupesh Kumar Vadim Makarov Romain Alléaume Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada N2L 3G1 Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario Canada N2L 3G1 Department of Physics and Astronomy University of Waterloo Waterloo Ontario Canada N2L 3G1 CAS Quantum Network Co. Ltd. 99 Xiupu Road Shanghai 201315 People's Republic of China† Télécom ParisTech LTCI 46 Rue Barrault 75634 Paris Cedex 13 France Department of Physics University of York York YO10 5DD United Kingdom† Russian Quantum Center and MISIS University Moscow Russia

We propose an efficient strategy to attack a continuous-variable (CV) quantum key distribution (QKD) system, which we call homodyne detector blinding. This attack strategy takes advantage of a generic vulnerability of homodyne receivers: A bright light pulse sent on the signal port can lead to a saturation of the detector electronics. While detector saturation has already been proposed to attack CV QKD, the attack we study in this paper has the additional advantage of not requiring an eavesdropper to be phase locked with the homodyne receiver. We show that under certain conditions, an attacker can use a simple laser, incoherent with the homodyne receiver, to generate bright pulses and bias the excess noise to arbitrary small values, fully comprising CV QKD security. These results highlight the feasibility and the impact of the detector-blinding attack. We finally discuss how to design countermeasures in order to protect against this attack.

关键词： quantum cryptography

Non-Exponential Behaviour in Logical Randomized Benchmarking

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arXiv 2022年

作者： Ceasura, Athena Iyer, Pavithran Wallman, Joel J. Pashayan, Hakop Institute for Quantum Computing University of Waterloo ONN2L 3G1 Canada Keysight Technologies Canada KanataONK2K 2W5 Canada Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Dahlem Center for Complex Quantum Systems Freie Universität Berlin Germany

We construct a gate and time-independent noise model that results in the output of a logical randomized benchmarking protocol oscillating rather than decaying exponentially. To illustrate our idea, we first construct an example in standard randomized benchmarking where we assume the existence of "hidden" qubits, permitting a choice of representation of the Clifford group that contains multiplicities. We use the multiplicities to, with each gate application, update a hidden memory of the gate history that we use to circumvent theorems which guarantee the output decays exponentially. In our focal setting of logical randomized benchmarking, we show that the presence of machinery associated with the implementation of quantum error correction can facilitate non-exponential decay. Since, in logical randomized benchmarking, the role of the hidden qubits is assigned to the syndrome qubits used in error correction and these are strongly coupled to the logical qubits via a decoder. © 2022, CC BY.

关键词： Benchmarking