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Near-Term quantum computing Techniques: Variational quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation

arXiv

引用

arXiv 2022年

作者： Huang, He-Liang Xu, Xiao-Yue Guo, Chu Tian, Guojing Wei, Shi-Jie Sun, Xiaoming Bao, Wan-Su Long, Gui-Lu Henan Key Laboratory of Quantum Information and Cryptography Henan Zhengzhou450000 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China School of Computer Science and Technology University of Chinese Academy of Sciences Beijing100049 China Beijing Academy of Quantum Information Sciences Beijing100193 China Department of Physics Tsinghua University Beijing100084 China

quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen a major boost in the last decade, we are still a long way from reaching the maturity of a full-fledged quantum computer. That said, we will be in the Noisy-Intermediate Scale quantum (NISQ) era for a long time, working on dozens or even thousands of qubits quantum computing systems. An outstanding challenge, then, is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise. To address this challenge, several near-term quantum computing techniques, including variational quantum algorithms, error mitigation, quantum circuit compilation and benchmarking protocols, have been proposed to characterize and mitigate errors, and to implement algorithms with a certain resistance to noise, so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications. Besides, the development of near-term quantum devices is inseparable from the efficient classical simulation, which plays a vital role in quantum algorithm design and verification, error-tolerant verification and other applications. This review will provide a thorough introduction of these near-term quantum computing techniques, report on their progress, and finally discuss the future prospect of these techniques, which we hope will motivate researchers to undertake additional studies in this field. © 2022, CC BY.

关键词： Benchmarking

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Bright photon-pair source based on a silicon dual-Mach-Zehnder microring

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science China(Physics,Mechanics & Astronomy) 2020年第2期63卷 3-6页

作者： Chao Wu YingWen Liu XiaoWen Gu XinXin Yu YueChan Kong Yang Wang XiaoGang Qiang JunJie Wu ZhiHong Zhu XueJun Yang Ping Xu Institute for Quantum Information and State Key Laboratory of High Performance Computing College of ComputerCollege of Advanced Interdisciplinary StudiesNational University of Defense TechnologyChangsha 410073China Science and Technology on Monolithic Integrated Circuits and Modules Laboratory Nanjing Electronic Devices InstituteNanjing 210016China National Laboratory of Solid State Microstructures and School of Physics Nanjing UniversityNanjing 210093China

Single photons and photon pairs are typically generated by spontaneous parametric down conversion or quantum dots;however,spontaneous four-wave mixing(SFWM)in silicon microring resonators[1]is also an appealing source of entangled photons,offering a strong cavity-enhanced nonlinear interactions while maintaining features,such as compact,simple to fabricate,and allowing for thermal ***,silicon ring-resonators usually suffer from a trade-off between providing a high pair generation rate(PGR)and high extraction *** achieve high PGR,devices are generally operated with the signal and idler photons in the undercoupling regime and pump photons at the critical coupling point,while high extraction rates require the converted photons to be ***,the optimal conditions for achieving maximal output photon pair flux are critical coupling for the pump photons and overcoupling for the converted photons[2,3].

关键词： coupling photon converted

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Application-level Benchmarking of quantum computers using Nonlocal Game Strategies

arXiv

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arXiv 2023年

作者： Furches, Jim Chehade, Sarah Hamilton, Kathleen Wiebe, Nathan Marrero, Carlos Ortiz College of Computing Georgia Institute of Technology AtlantaGA30332 United States Physical Detection Systems and Deployment Division Pacific Northwest National Laboratory RichlandWA99354 United States Quantum Computational Science Group Oak Ridge National Laboratory Oak RidgeTN37830 United States Department of Computer Science University of Toronto ONM5S 1A1 Canada High Performance Computing Group Pacific Northwest National Laboratory RichlandWA99354 United States Canadian Institute for Advanced Research TorontoONM5G 1M1 Canada Department of Electrical & Computer Engineering North Carolina State University RaleighNC27607 United States

In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. quantum strategies allow players to optimally win some games by performing joint measurements on a shared entangled state, but computing these strategies can be challenging. We present a variational quantum algorithm to compute quantum strategies for nonlocal games by encoding the rules of a nonlocal game into a Hamiltonian. We show how this algorithm can generate a short-depth optimal quantum strategy for a graph coloring game with a quantum advantage. This quantum strategy is then evaluated on fourteen different quantum hardware platforms to demonstrate its utility as a benchmark. Finally, we discuss potential sources of errors that can explain the observed decreased performance of the executed task and derive an expression for the number of samples required to accurately estimate the win rate in the presence of noise. Copyright © 2023, The Authors. All rights reserved.

关键词： Hamiltonians

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Efficient Learning of Continuous-Variable quantum States

arXiv

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arXiv 2023年

作者： Wu, Ya-Dong Zhu, Yan Chiribella, Giulio Liu, Nana John Hopcroft Center for Computer Science Shanghai Jiao Tong University Shanghai200240 China QICI Quantum Information and Computation Initiative Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong Department of Computer Science Parks Road OxfordOX1 3QD United Kingdom Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai200240 China

The characterization of continuous-variable quantum states is crucial for applications in quantum communication, sensing, simulation and computing. However, a full characterization of multimode quantum states requires a number of experiments that grows exponentially with the number of modes. Here we propose an alternative approach where the goal is not to reconstruct the full quantum state, but rather to estimate its characteristic function at a given set of points. For multimode states with reflection symmetry, we show that the characteristic function at M points can be estimated using only O(log M) copies of the state, independently of the number of modes. When the characteristic function is known to be positive, as in the case of squeezed vacuum states, the estimation is achieved by an experimentally friendly setup using only beamsplitters and homodyne measurements. © 2023, CC BY-NC-SA.

关键词： quantum communication

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Color Glass Condensate meets High Twist Expansion

arXiv

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arXiv 2024年

作者： Fu, Yu Kang, Zhong-Bo Salazar, Farid Wang, Xin-Nian Xing, Hongxi Department of Physics Duke University DurhamNC27708 United States Institute of Particle Physics Central China Normal University Wuhan430079 China Department of Physics and Astronomy University of California Los AngelesCA90095 United States Mani L. Bhaumik Institute for Theoretical Physics University of California Los AngelesCA90095 United States Center for Frontiers in Nuclear Science Stony Brook University Stony BrookNY11794 United States Institute for Nuclear Theory University of Washington SeattleWA98195 United States Nuclear Science Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Physics Department University of California BerkeleyCA94720 United States Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter Institute of Quantum Matter South China Normal University Guangzhou510006 China Guangdong-Hong Kong Joint Laboratory of Quantum Matter Guangdong Provincial Key Laboratory of Nuclear Science Southern Nuclear Science Computing Center South China Normal University Guangzhou510006 China Institute of Modern Physics Chinese Academy of Sciences Huizhou516000 China

We establish the correspondence between two well-known frameworks for QCD multiple scattering in nuclear media: the Color Glass Condensate (CGC) and the High-Twist (HT) expansion formalism. We argue that a consistent matching between both frameworks, in their common domain of validity, is achieved by incorporating the sub-eikonal longitudinal momentum phase in the CGC formalism, which mediates the transition between coherent and incoherent scattering. We perform a detailed calculation and analysis of direct photon production in proton-nucleus scattering as a concrete example to establish the matching between HT and CGC up to twist-4, including initial- and final-state interactions, as well as their interferences. The techniques developed in this work can be adapted to other processes in electron-nucleus and proton-nucleus collisions, and they provide a potential avenue for a unified picture of dilute-dense dynamics in nuclear media. Copyright © 2024, The Authors. All rights reserved.

关键词： Expansion

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Symmetries, Graph Properties, and quantum Speedups

Symmetries, Graph Properties, and Quantum Speedups

引用

Annual IEEE Symposium on Foundations of computer science

作者： Shalev Ben-David Andrew M. Childs András Gilyén William Kretschmer Supartha Podder Daochen Wang Cheriton School of Computer Science University of Waterloo Joint Center for Quantum Information and Computer Science University of Maryland Simons Institute for the Theory of Computing University of California Berkeley University of Texas at Austin University of Ottawa University of Maryland

ISBN: (数字)9781728196213

ISBN: (纸本)9781728196220

Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups. In contrast, in the adjacency list model for bounded-degree graphs-where graph symmetry is manifested differently-we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013).

关键词： Testing Complexity theory Computational modeling quantum algorithm computer science Symmetric matrices Boolean functions

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Minimizing quantum Rényi Divergences via Mirror Descent with Polyak Step Size

arXiv

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arXiv 2021年

作者： You, Jun-Kai Cheng, Hao-Chung Li, Yen-Huan Department of Computer Science and Information Engineering National Taiwan University Taiwan Department of Mathematics National Taiwan University Taiwan Department of Electrical Engineering Graduate Institute of Communication Engineering National Taiwan University Taiwan Quantum Computing Centre Center for Quantum Science and Engineering National Taiwan University Taiwan

quantum information quantities play a substantial role in characterizing operational quantities in various quantum information-theoretic problems. We consider the numerical computation of four quantum information quantities: Petz-Augustin information, sandwiched Augustin information, conditional sandwiched Rényi entropy, and sandwiched Rényi information. To compute these quantities requires minimizing some order-α quantum Rényi divergences over the set of quantum states. Whereas the optimization problems are obviously convex, they violate standard bounded gradient/Hessian conditions in literature, so existing convex optimization methods and their convergence guarantees do not directly apply. In this paper, we propose a new class of convex optimization methods called mirror descent with the Polyak step size. We prove their convergence under a weak condition, showing that they provably converge for minimizing quantum Rényi divergences. Numerical experiment results show that entropic mirror descent with the Polyak step size converges fast in minimizing quantum Rényi divergences. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum optics

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quantum algorithm for dyck language with multiple types of brackets

arXiv

引用

arXiv 2021年

作者： Khadiev, Kamil Kravchenko, Dmitry Kazan Federal University Kazan Russia Kazan E. K. Zavoisky Physical-Technical Institute Kazan Russia Center for Quantum Computer Science Faculty of Computing University of Latvia Riga Latvia

We consider the recognition problem of the Dyck Language generalized for multiple types of brackets. We provide an algorithm with quantum query complexity O(√n(log n)0.5k), where n is the length of input and k is the maximal nesting depth of brackets. Additionally, we show the lower bound for this problem which is O(√nck) for some constant c. Interestingly, classical algorithms solving the Dyck Language for multiple types of brackets substantially differ form the algorithm solving the original Dyck language. At the same time, quantum algorithms for solving both kinds of the Dyck language are of similar nature and requirements. © 2021, CC BY.

关键词： quantum theory

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Genuine multifractality in time series is due to temporal correlations

arXiv

引用

arXiv 2022年

作者： Kwapień, Jaroslaw Blasiak, Pawel Drozdz, Stanislaw Oświȩcimka, Pawel Complex Systems Theory Department Institute of Nuclear Physics Polish Academy of Sciences ul. Radzikowskiego 152 Kraków31-342 Poland Institute for Quantum Studies Chapman University OrangeCA92866 United States Faculty of Computer Science and Telecommunications Cracow University of Technology ul. Warszawska 24 Kraków31-155 Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland

Based on the mathematical arguments formulated within the Multifractal Detrended Fluctuation Analysis (MFDFA) approach it is shown that in the uncorrelated time series from the Gaussian basin of attraction the effects resembling multifractality asymptotically disappear for positive moments when the length of time series increases. A hint is given that this applies to the negative moments as well and extends to the Lévy stable regime of fluctuations. The related effects are also illustrated and confirmed by numerical simulations. This documents that the genuine multifractality in time series may only result from the long-range temporal correlations and the fatter distribution tails of fluctuations may broaden the width of singularity spectrum only when such correlations are present. The frequently asked question of what makes multifractality in time series - temporal correlations or broad distribution tails - is thus ill posed. In the absence of correlations only the bifractal or monofractal cases are possible. The former corresponds to the Lévy stable regime of fluctuations while the latter to the ones belonging to the Gaussian basin of attraction in the sense of the Central Limit Theorem. Copyright © 2022, The Authors. All rights reserved.

关键词： Time series

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Distributed quantum algorithm for Simon's problem

arXiv

引用

arXiv 2022年

作者： Tan, Jiawei Xiao, Ligang Qiu, Daowen Luo, Le Mateus, Paulo Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China The Guangdong Key Laboratory of Information Security Technology Sun Yat-Sen University 510006 China QUDOOR Technologies Inc. Guangzhou China School of Physics and Astronomy Sun Yat-Sen University Zhuhai519082 China Instituto de Telecomunicações Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais Lisbon1049-001 Portugal

Limited by today's physical devices, quantum circuits are usually noisy and difficult to be designed deeply. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In this paper, we study the Simon's problem in distributed scenarios and design a distributed quantum algorithm to solve the problem. The algorithm proposed by us has the advantage of exponential acceleration compared with the classical distributed computing, and has the advantage of square acceleration compared with the best distributed quantum algorithm proposed before. In particular, the previous distributed quantum algorithm for Simon's problem can not be extended to the case of more than two computing nodes (i.e. two subproblems), but our distributed quantum algorithm can be extended to the case of multiple computing nodes (i.e. multiple subproblems) as well. Copyright © 2022, The Authors. All rights reserved.

关键词： computer architecture

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