检索结果-内蒙古大学图书馆

SSRN 2023年

作者： He, Zhimin Deng, Maijie Zheng, Shenggen Li, Lvzhou Situ, Haozhen School of Electronic and Information Engineering Foshan University Foshan528000 China School of Mechatronic Engineering and Automation Foshan University Foshan528000 China Peng Cheng Laboratory Shenzhen518055 China Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China

quantum Architecture Search (QAS) is a promising approach for designing quantum circuits specifically tailored for variational quantum algorithms (VQAs). However, existing QAS algorithms require calculating the ground-truth performances of a substantial number of quantum circuits during the search process, rendering them computationally demanding and limiting their applicability to large-scale quantum circuits. Recently, a predictor-based QAS has been proposed to address this challenge by estimating circuit performance directly based on their structures using a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is highly time-consuming to obtain a substantial number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS that trains a predictor by self-supervised learning. Specifically, we first pre-train a graph encoder using a well-designed pretext task on a large number of unlabeled quantum circuits, aiming to generate meaningful representations of quantum circuits. Subsequently, the downstream predictor is trained on a small set of quantum circuits' representations and their corresponding labels. Once the encoder is trained, it becomes applicable to various downstream tasks. To effectively encode spatial topology information and avoid huge dimensions of feature vectors for large-scale quantum circuits, we propose a graph-based encoding scheme for quantum circuits. Simulation results on QAS for variational quantum eigensolver and quantum state classification demonstrate that GSQAS outperforms the state-of-the-art predictor-based QAS, yielding superior performance with fewer labeled circuits. © 2023, The Authors. All rights rese

关键词： Timing circuits

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quantum-Informed Recursive Optimization Algorithms

arXiv

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arXiv 2023年

作者： Finžgar, Jernej Rudi Kerschbaumer, Aron Schuetz, Martin J.A. Mendl, Christian B. Katzgraber, Helmut G. BMW AG Munich Germany Technical University Munich School of CIT Department of Computer Science Garching Germany Amazon Quantum Solutions Lab SeattleWA United States AWS Center for Quantum Computing PasadenaCA United States Technical University of Munich Institute for Advanced Study Garching Germany

We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific classical reduction steps that recursively simplify the problem. These reduction steps address the limitations of the quantum component (e.g., locality) and ensure solution feasibility in constrained optimization problems. Additionally, we use backtracking techniques to further improve the performance of the algorithm without increasing the requirements on the quantum hardware. We showcase the capabilities of our approach by informing QIRO with correlations from classical simulations of shallow circuits of the quantum approximate optimization algorithm (QAOA), solving instances of maximum independent set and maximum satisfiability problems with hundreds of variables. We also demonstrate how QIRO can be deployed on a neutral atom quantum processor to find large independent sets of graphs. In summary, our scheme achieves results comparable to classical heuristics even with relatively weak quantum resources. Furthermore, enhancing the quality of these quantum resources improves the performance of the algorithms. Notably, the modular nature of QIRO offers various avenues for modifications, positioning our work as a template for a broader class of hybrid quantum-classical algorithms for combinatorial optimization. Copyright © 2023, The Authors. All rights reserved.

关键词： Combinatorial optimization

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GSQAS: Graph Self-supervised quantum Architecture Search

arXiv

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arXiv 2023年

quantum Architecture Search (QAS) is a promising approach to designing quantum circuits for variational quantum algorithms (VQAs). However, existing QAS algorithms require to evaluate a large number of quantum circuits during the search process, which makes them computationally demanding and limits their applications to large-scale quantum circuits. Recently, predictor-based QAS has been proposed to alleviate this problem by directly estimating the performances of circuits according to their structures with a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is very time-consuming to obtain a large number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS, which trains a predictor based on self-supervised learning. Specifically, we first pre-train a graph encoder on a large number of unlabeled quantum circuits using a well-designed pretext task in order to generate meaningful representations of circuits. Then the downstream predictor is trained on a small number of quantum circuits’ representations and their labels. Once the encoder is trained, it can apply to different downstream tasks. In order to better encode the spatial topology information and avoid the huge dimension of feature vectors for large-scale quantum circuits, we design a scheme to encode quantum circuits as graphs. Simulation results on searching circuit structures for variational quantum eigensolver and quantum state classification show that GSQAS outperforms the state-of-the-art predictor-based QAS, achieving better performance with fewer labeled circuits. Copyright © 2023, The Authors. All rights reserved.

关键词： Encoding (symbols)

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A Multilevel Approach for Solving Large-Scale QUBO Problems with Noisy Hybrid quantum Approximate Optimization

A Multilevel Approach for Solving Large-Scale QUBO Problems ...

引用

IEEE Conference on High Performance Extreme computing (HPEC)

作者： Filip B. Maciejewski Bao G. Bach Maxime Dupont P. Aaron Lott Bhuvanesh Sundar David E. Bernal Neira Ilya Safro Davide Venturelli Quantum Artificial Intelligence Laboratory (QuAIL) NASA Ames Research Center CA USA USRA Research Institute for Advanced Computer Science (RIACS) CA USA Department of Computer and Information Sciences University of Delaware Newark DE USA Rigetti Computing Berkeley CA Davidson School of Chemical Engineering Purdue University West Lafayette IN USA

ISBN: (数字)9798350387131

ISBN: (纸本)9798350387148

quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the existing quantum processing units (QPUs) are of relatively small size, and canonical mappings of QUBO via the Ising model require one qubit per variable, rendering direct large-scale optimization infeasible. In classical optimization, a general strategy for addressing many large-scale problems is via multilevel/multigrid methods, where the large target problem is iteratively coarsened and the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentally test how existing QPUs perform when used as a sub-solver within such a multilevel strategy. To this aim, we combine and extend (via additional classical processing steps) the recently proposed Noise-Directed Adaptive Remapping (NDAR) and quantum Relax & Round (QRR) algorithms. We first demonstrate the effectiveness of our heuristic extensions on Rigetti's superconducting transmon device Ankaa-2. We find approximate solutions to 10 instances of fully connected 82-qubit Sherrington-Kirkpatrick graphs with random integer-valued coefficients obtaining normalized approximation ratios (ARs) in the range $\sim 0.98-1.0$ , and the same class with real-valued coefficients (ARs $\sim 0.94-1.0)$ . Then, we implement the extended NDAR and QRR algorithms as subsolvers in the multilevel algorithm for 6 large-scale graphs with at most $\sim 27,000$ variables. In practice, the QPU (with classical post-processing steps) is used to find approximate solutions to dozens of at most 82-qubit problems, which are iteratively used to construct the global solution. We observe that quantum optimization results are competitive in terms of the quality of solutions when compared to classical heuristics used as subsolvers within the multilevel approach. Reproducibility

关键词： Superconducting devices Performance evaluation quantum advantage Source coding Qubit Pipelines Approximation algorithms Rendering (computer graphics) Noise measurement Optimization

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Verifying Safety of Neural Networks from Topological Perspectives

arXiv

引用

arXiv 2023年

作者： Liang, Zhen Ren, Dejin Xue, Bai Wang, Ji Yang, Wenjing Liu, Wanwei National University of Defense Technology Institute for Quantum Information State Key Laboratory of High Performance Computing Hunan Changsha410073 China Chinese Academy of Sciences State Key Lab. of Computer Science BeijingBAI XUE China

Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment in practice. In this paper, we propose a set-boundary reachability method to investigate the safety verification problem of NNs from a topological perspective. Given an NN with an input set and a safe set, the safety verification problem is to determine whether all outputs of the NN resulting from the input set fall within the safe set. In our method, the homeomorphism property and the open map property of NNs are mainly exploited, which establish rigorous guarantees between the boundaries of the input set and the boundaries of the output set. The exploitation of these two properties facilitates reachability computations via extracting subsets of the input set rather than the entire input set, thus controlling the wrapping effect in reachability analysis and facilitating the reduction of computation burdens for safety verification. The homeomorphism property exists in some widely used NNs such as invertible residual networks (i-ResNets) and Neural ordinary differential equations (Neural ODEs), and the open map is a less strict property and easier to satisfy compared with the homeomorphism property. For NNs establishing either of these properties, our set-boundary reachability method only needs to perform reachability analysis on the boundary of the input set. Moreover, for NNs that do not feature these properties with respect to the input set, we explore subsets of the input set for establishing the local homeomorphism property and then abandon these subsets for reachability computations. Finally, some examples demonstrate the performance of the proposed *** Codes 68Q60, 68T07 Copyright © 2023, The Authors. All rights reserved.

关键词： Topology

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Sample complexity of hidden subgroup problem

arXiv

引用

arXiv 2021年

作者： Ye, Zekun Li, Lvzhou Institute of Quantum Computing and Computer Science Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-Sen University Guangzhou510006 China

The hidden subgroup problem (HSP) has been attracting much attention in quantum computing, since several well-known quantum algorithms including Shor algorithm can be described in a uniform framework as quantum methods to address different instances of it. One of the central issues about HSP is to characterize its quantum/classical complexity. For example, from the viewpoint of learning theory, sample complexity is a crucial concept. However, while the quantum sample complexity of the problem has been studied, a full characterization of the classical sample complexity of HSP seems to be absent, which will thus be the topic in this paper. HSP over a finite group is defined as follows: For a finite group G and a finite set V , given a function f : G → V and the promise that for any x, y ∈ G, f(x) = f(xy) iff y ∈ H for a subgroup H ∈ H, where H is a set of candidate subgroups of G, the goal is to identify H. Our contributions are as follows: i) For HSP, we show that the number of uniform examples necessary to learn the hidden subgroup with bounded error is at least Ω max (Hmin ∈H loglog |H|| | H G| |Hmin ∈Hr||HG|| loglog |H|| | H G| |)! , and on the other hand, O (Hmax ∈Hn sr(H), q||HG|| sr(H) o) uniform examples are sufficient, where sr(H) = max r(H) and r(H) is the rank of H. H∈H ii) By concretizing the parameters of HSP, we consider a class of restricted Abelian hidden subgroup problem (rAHSP) and obtain the upper and lower bounds for the sample complexity of rAHSP. iii) We continue to discuss a special case of rAHSP, generalized Simon’s problem (GSP), and show that the sample complexity of GSP is Θ (max n k, pk · pn-ko) . Thus we obtain a complete characterization of the sample complexity of GSP. © 2021, CC BY.

关键词： quantum computers

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Efficient algorithms to solve atom reconfiguration problems. II. Assignment-rerouting-ordering algorithm

引用

Physical Review A 2023年第2期108卷 023108-023108页

作者： Remy El Sabeh Jessica Bohm Zhiqian Ding Stephanie Maaz Naomi Nishimura Izzat El Hajj Amer E. Mouawad Alexandre Cooper Department of Computer Science American University of Beirut Beirut 1107 2020 Lebanon Institute for Quantum Computing University of Waterloo Waterloo Ontarion N2L 3G1 Canada David R. Cheriton School of Computer Science University of Waterloo Waterloo Ontario N2L 3G1 Canada AG Theoretische Informatik University of Bremen 28359 Bremen Germany

Programmable arrays of optical traps enable the assembly of configurations of single atoms to perform controlled experiments on quantum many-body systems. Finding the sequence of control operations to transform an arbitrary configuration of atoms into a predetermined one requires solving an atom reconfiguration problem quickly and efficiently. A typical approach to solving atom reconfiguration problems is to use an assignment algorithm to determine which atoms to move to which traps. This approach results in control protocols that exactly minimize the number of displacement operations; however, this approach does not optimize for the number of displaced atoms or the number of times each atom is displaced, resulting in unnecessary control operations that increase the execution time and failure rate of the control protocol. In this work we propose the assignment-rerouting-ordering (ARO) algorithm to improve the performance of assignment-based algorithms in solving atom reconfiguration problems. The ARO algorithm uses an assignment subroutine to minimize the total distance traveled by all atoms, a rerouting subroutine to reduce the number of displaced atoms, and an ordering subroutine to guarantee that each atom is displaced at most once. The ordering subroutine relies on the existence of a partial ordering of moves that can be obtained using a polynomial-time algorithm that we introduce within the formal framework of graph theory. We numerically quantify the performance of the ARO algorithm in the presence and in the absence of loss and show that it outperforms the exact, approximation, and heuristic algorithms that we use as benchmarks. Our results are useful for assembling large configurations of atoms with high success probability and fast preparation time, as well as for designing and benchmarking novel atom reconfiguration algorithms.

关键词： Atom & ion trapping & guiding Cooling & trapping Molecule trapping & guiding Optical lattices & traps quantum simulation Graph theory

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Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism

arXiv

引用

arXiv 2021年

作者： Hopkins, Samuel B. Kamath, Gautam Majid, Mahbod Simons Institute for the Theory of Computing United States Cheriton School of Computer Science University of Waterloo Canada

We give the first polynomial-time algorithm to estimate the mean of a d-variate probability distribution with bounded covariance from Õ(d) independent samples subject to pure differential privacy. Prior algorithms for this problem either incur exponential running time, require Ω(d1.5) samples, or satisfy only the weaker concentrated or approximate differential privacy conditions. In particular, all prior polynomial-time algorithms require d1+Ω(1)samples to guarantee small privacy loss with "cryptographically" high probability, 1 - 2-dΩ(1), while our algorithm retains Õ(d) sample complexity even in this stringent setting. Our main technique is a new approach to use the powerful Sum of Squares method (SoS) to design differentially private algorithms. SoS proofs to algorithms is a key theme in numerous recent works in high-dimensional algorithmic statistics - estimators which apparently require exponential running time but whose analysis can be captured by low-degree Sum of Squares proofs can be automatically turned into polynomial-time algorithms with the same provable guarantees. We demonstrate a similar proofs to private algorithms phenomenon: instances of the workhorse exponential mechanism which apparently require exponential time but which can be analyzed with low-degree SoS proofs can be automatically turned into polynomial-time differentially private algorithms. We prove a meta-theorem capturing this phenomenon, which we expect to be of broad use in private algorithm design. Our techniques also draw new connections between differentially private and robust statistics in high dimensions. In particular, viewed through our proofs-to-private-algorithms lens, several well-studied SoS proofs from recent works in algorithmic robust statistics directly yield key components of our differentially private mean estimation algorithm. Copyright © 2021, The Authors. All rights reserved.

关键词： Probability distributions

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Analytic model reveals local molecular polarizability changes induced by collective strong coupling in optical cavities

引用

Physical Review Research 2025年第1期7卷 013242-013242页

作者： Jacob Horak Dominik Sidler Thomas Schnappinger Wei-Ming Huang Michael Ruggenthaler Angel Rubio Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science Luruper Chaussee 149 22761 Hamburg Germany The Hamburg Center for Ultrafast Imaging Luruper Chaussee 149 22761 Hamburg Germany PSI Center for Scientific Computing Theory and Data 5232 Villigen PSI Switzerland Department of Physics Stockholm University AlbaNova University Center SE-106 91 Stockholm Sweden Department of Physics and Center for Quantum Information Science National Cheng Kung University Tainan 70101 Taiwan Center for Computational Quantum Physics (CCQ) The Flatiron Institute 162 Fifth Avenue New York New York 10010 USA

Despite recent numerical evidence, one of the fundamental theoretical mysteries of polaritonic chemistry is how and if collective strong coupling can induce local changes of the electronic structure to modify chemical properties. Here we present nonperturbative analytic results for a model system consisting of an ensemble of N harmonic molecules under vibrational strong coupling (VSC) that alters our present understanding of this fundamental question. By applying the cavity Born-Oppenheimer partitioning on the Pauli-Fierz Hamiltonian in dipole approximation, the dressed many-molecule problem can be solved nonperturbatively and analytically in the dilute limit, i.e., a self-consistent solution with the mean-field Hartree-product wave function becomes exact. We discover that the electronic molecular polarizabilities are modified even in the case of vanishingly small single-molecule couplings. Consequently, this nonperturbative local polarization mechanism persists even in the large-N limit. In contrast, a perturbative calculation of the polarizabilities based on the uncoupled ensemble wave function leads to a qualitatively erroneous scaling behavior with vanishing effects in the large-N limit. Nevertheless, the exact (self-consistent) polarizabilities can be determined from single-molecule strong coupling simulations instead. Our fundamental theoretical observations demonstrate that hitherto existing collective-scaling arguments are insufficient for polaritonic chemistry and they pave the way for refined single- (or few-)molecule strong-coupling ab initio simulations of chemical systems under collective strong coupling.

关键词： Hamiltonians

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Security boundaries of an optical power limiter for protecting quantum key distribution systems

arXiv

引用

arXiv 2023年

作者： Peng, Qingquan Gao, Binwu Zaitsev, Konstantin Wang, Dongyang Ding, Jiangfang Liu, Yingwen Liao, Qin Guo, Ying Huang, Anqi Wu, Junjie Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China School of Automation Central South University Changsha410083 China China Greatwall Research Institute China Greatwall Technology Group Co. Ltd. Shenzhen518057 China Russian Quantum Center Skolkovo Moscow121205 Russia NTI Center for Quantum Communications National University of Science and Technology MISiS Moscow119049 Russia Vigo Quantum Communication Center University of Vigo Vigo Spain Escuela de Ingeniería de Telecomunicación Department of Signal Theory and Communications University of Vigo Vigo Spain atlanTTic Research Center University of Vigo Vigo Spain College of Computer Science and Electronic Engineering Hunan University Changsha410082 China School of Computer Science Beijing University of Posts and Telecommunications Beijing100876 China

Unauthorized light injection has always been a vital threat to the practical security of a quantum key distribution (QKD) system. An optical power limiter (OPL) based on the thermo-optical defocusing effect has been proposed and implemented, limiting the injected hacking light. As a hardware countermeasure, the performance of the OPL under various light-injection attacks shall be tested to clarify the security boundary before being widely deployed. To investigate the OPL’s security boundary in quantum cryptography, we comprehensively test and analyse the behavior of OPL under continuous-wave (c.w.) light-injection attacks and pulse illumination attacks with pulses’ repetition rate at 0.5-Hz, 40-MHz, and 1-GHz. The testing results illuminate the security boundary of the OPL, which allows one to properly employ the OPL in the use cases. The methodology of testing and analysis proposed here is applicable to other power-limitation components in a QKD system. Copyright © 2023, The Authors. All rights reserved.

关键词： Pulse repetition rate

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