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arXiv 2022年

作者： Situ, Haozhen Lu, Tianxiang Pan, Minghua Li, Lvzhou College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China Guangxi Key Laboratory of Cryptography and Information Security Guilin University of Electronic Technology Guilin541004 China Department of Physics Tsinghua University Beijing100084 China

For the goal of strong artificial intelligence that can mimic human-level intelligence, AI systems would have the ability to adapt to ever-changing scenarios and learn new knowledge continuously without forgetting previously acquired knowledge. When a machine learning model is consecutively trained on multiple tasks that come in sequence, its performance on previously learned tasks may drop dramatically during the learning process of the newly seen task. To avoid this phenomenon termed catastrophic forgetting, continual learning, also known as lifelong learning, has been proposed and become one of the most up-to-date research areas of machine learning. As quantum machine learning blossoms in recent years, it is interesting to develop quantum continual learning. This paper focuses on the case of quantum models for quantum data where the computation model and the data to be processed are both quantum. The gradient episodic memory method is incorporated to design a quantum continual learning scheme that overcomes catastrophic forgetting and realizes knowledge backward transfer. Specifically, a sequence of quantum state classification tasks is continually learned by a variational quantum classifier whose parameters are optimized by a classical gradient-based optimizer. The gradient of the current task is projected to the closest gradient, avoiding the increase of the loss at previous tasks, but allowing the decrease. Numerical simulation results show that our scheme not only overcomes catastrophic forgetting, but also realize knowledge backward transfer, which means the classifier's performance on previous tasks is enhanced rather than compromised while learning a new task. Copyright © 2022, The Authors. All rights reserved.

关键词： Machine learning

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On the Computational Complexity of Schrödinger Operators

arXiv

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arXiv 2024年

作者： Zheng, Yufan Leng, Jiaqi Liu, Yizhou Wu, Xiaodi Department of Computer Science University of Maryland United States Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Mathematics University of Maryland United States Simons Institute for the Theory of Computing Department of Mathematics UC Berkeley United States Physics of Living Systems Department of Physics MIT United States Department of Mechanical Engineering MIT United States

We study computational problems related to the Schrödinger operator H = −∆ + V in the real space under the condition that (i) the potential function V is smooth and has its value and derivative bounded within some polynomial of n and (ii) V only consists of O(1)-body interactions. We prove that (i) simulating the dynamics generated by the Schrödinger operator implements universal quantum computation, i.e., it is BQP-hard, and (ii) estimating the ground energy of the Schrödinger operator is as hard as estimating that of local Hamiltonians with no sign problem (a.k.a. stoquastic Hamiltonians), i.e., it is StoqMA-complete. This result is particularly intriguing because the ground energy problem for general bosonic Hamiltonians is known to be QMA-hard and it is widely believed that StoqMA (Equation presented) QMA. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

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quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

arXiv

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arXiv 2023年

作者： Mukhopadhyay, Priyanka Stetina, Torin F. Wiebe, Nathan Department of Physical & Environmental Sciences University of Toronto ON Canada Simons Institute for the Theory of Computing BerkeleyCA United States Berkeley Quantum Information and Computation Center University of California Berkeley United States Department of Computer Science University of Toronto ON Canada Pacific Northwest National Laboratory RichlandWA United States Canadian Institute for Advanced Research TorontoON Canada

We provide an explicit recursive divide and conquer approach for simulating quantum dynamics and derive a discrete first quantized non-relativistic QED Hamiltonian based on the many-particle Pauli Fierz Hamiltonian. We apply this recursive divide and conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide and conquer algorithm, using lowest order Trotterization, scales for fixed grid spacing as Õ(ΛN2η2t2/ϵ) for grid size N, η particles, simulation time t, field cutoff Λ and error ϵ. Our qubitization algorithm scales as Õ(N(η + N)(η + Λ2)tlog(1/ϵ)). This shows that even a naïve partitioning and low-order splitting formula can yield, through our divide and conquer formalism, superior scaling to qubitization for large Λ. We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons, and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit level techniques for gate optimization including a new way of implementing a group of multi-controlled-X gates that can be used for better analysis of circuit cost. © 2023, CC BY.

关键词： Hamiltonians

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Distributed exact quantum algorithms for Bernstein-Vazirani and search problems

arXiv

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arXiv 2023年

作者： Zhou, Xu Qiu, Daowen Luo, Le 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 Guangzhou510006 China School of Physics and Astronomy Sun Yat-sen University Zhuhai519082 China QUDOOR Technologies Inc. Zhuhai519099 China

Distributed quantum computation has gained extensive attention since small-qubit quantum computers seem to be built more practically in the noisy intermediate-scale quantum (NISQ) era. In this paper, we give a distributed Bernstein-Vazirani algorithm (DBVA) with t computing nodes, and a distributed exact Grover’s algorithm (DEGA) that solve the search problem with only one target item in the unordered databases. Though the designing techniques are simple in the light of BV algorithm, Grover’s algorithm, the improved Grover’s algorithm by Long, and the distributed Grover’s algorithm by Qiu et al, in comparison to BV algorithm, the circuit depth of DBVA is not greater than 2max(n0,n1,··· ,nt−1) + 3 instead of 2n + 3, and the circuit depth of DEGA is 8(n mod 2) + 9, which is less than the circuit depth of Grover’s algorithm, (formula presented). In particular, we provide situations of our DBVA and DEGA on Mindquantum (a quantum software) to validate the correctness and practicability of our methods. By simulating the algorithms running in the depolarized channel, it further illustrates that distributed quantum algorithm has superiority of resisting noise. Copyright © 2023, The Authors. All rights reserved.

关键词： quantum theory

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Fault-tolerant compiling of classically hard IQP circuits on hypercubes

arXiv

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arXiv 2024年

作者： Hangleiter, Dominik Kalinowski, Marcin Bluvstein, Dolev Cain, Madelyn Maskara, Nishad Gao, Xun Kubica, Aleksander Lukin, Mikhail D. Gullans, Michael J. Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD20742 United States Simons Insitute for the Theory of Computing University of California at Berkeley BerkeleyCA94720 United States Department of Physics Harvard University CambridgeMA02138 United States JILA Department of Physics University of Colorado BoulderCO80309 United States AWS Center for Quantum Computing PasadenaCA91125 United States California Institute of Technology PasadenaCA91125 United States

Realizing computationally complex quantum circuits in the presence of noise and imperfections is a challenging task. While fault-tolerant quantum computing provides a route to reducing noise, it requires a large overhead for generic algorithms. Here, we develop and analyze a hardware-efficient, fault-tolerant approach to realizing complex sampling circuits. We co-design the circuits with the appropriate quantum error correcting codes for efficient implementation in a reconfigurable neutral atom array architecture, constituting what we call a fault-tolerant compilation of the sampling algorithm. Specifically, we consider a family of [[2D, D, 2]] quantum error detecting codes whose transversal and permutation gate set can realize arbitrary degree-D instantaneous quantum polynomial (IQP) circuits. Using native operations of the code and the atom array hardware, we compile a fault-tolerant and fast-scrambling family of such IQP circuits in a hypercube geometry, realized recently in the experiments by Bluvstein et al. [Nature 626, 7997 (2024)]. We develop a theory of second-moment properties of degree-D IQP circuits for analyzing hardness and verification of random sampling by mapping to a statistical mechanics model. We provide strong evidence that sampling from these hypercube IQP circuits is classically hard to simulate even at relatively low depths. We analyze the linear cross-entropy benchmark (XEB) in comparison to the average fidelity and, depending on the local noise rate, find two different asymptotic regimes. To realize a fully scalable approach, we first show that Bell sampling from degree-4 IQP circuits is classically intractable and can be efficiently validated. We further devise new families of [[O(dD), D, d]] color codes of increasing distance d, permitting exponential error suppression for transversal IQP sampling. Our results highlight fault-tolerant compiling as a powerful tool in co-designing algorithms with specific error-correcting codes and realisti

关键词： Digital arithmetic

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Characterizing entanglement using quantum discord over state extensions

引用

Physical Review A 2022年第1期105卷 012426-012426页

作者： Chunhe Xiong Sunho Kim Daowen Qiu Asutosh Kumar Junde Wu Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou 510006 China Interdisciplinary Center for Quantum Information Department of Physics Zhejiang University Hangzhou 310027 China School of Computer and Computing Science Zhejiang University City College Hangzhou 310015 China School of Mathematical Sciences Harbin Engineering University Harbin 150001 China Instituto de Telecomunicaçőes Departamento de Matemática Instituto Superior Técnico Avenida Rovisco Pais 1 1049-001 Lisbon Portugal P. G. Department of Physics Gaya College Magadh University Rampur Gaya 823001 India Harish-Chandra Research Institute HBNI Chhatnag Road Jhunsi Allahabad 211019 India Vaidic and Modern Physics Research Centre Bhagal Bhim Bhinmal Jalore 343029 India School of Mathematical Sciences Zhejiang University Hangzhou 310027 China

We propose a framework to characterize entanglement with quantum discord, both asymmetric and symmetric, over state extensions. In particular, we show that the minimal Bures distance of discord over state extensions is equivalent to the Bures distance of entanglement. This equivalence places quantum discord in a more primitive position than entanglement conceptually in the sense that entanglement can be interpreted as an irreducible part of discord over all state extensions. Based on this equivalence, we also offer an operational meaning of the Bures distance of entanglement by connecting it to quantum state discrimination. Moreover, for the relative entropy part, we prove that the entanglement measure introduced by Devi and Rajagopal [A. R. U. Devi and A. K. Rajagopal, Phys. Rev. Lett. 100, 140502 (2008)] is actually equivalent to the relative entropy of entanglement. We also provide several quantifications of entanglement based on discord measures.

关键词： quantum correlations in quantum information quantum discord quantum entanglement

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

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Physical Review Applied 2024年第1期21卷 014026-014026页

作者： Qingquan Peng Binwu Gao Konstantin Zaitsev Dongyang Wang Jiangfang Ding Yingwen Liu Qin Liao Ying Guo Anqi Huang Junjie Wu Institute for Quantum Information and State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha 410073 China School of Automation Central South University Changsha 410083 China China Greatwall Research Institute China Greatwall Technology Group Co. Ltd. Shenzhen 518057 China Russian Quantum Center Skolkovo Moscow 121205 Russia NTI Center for Quantum Communications National University of Science and Technology MISiS Moscow 119049 Russia Vigo Quantum Communication Center University of Vigo 36310 Vigo Spain Escuela de Ingeniería de Telecomunicación Department of Signal Theory and Communications University of Vigo 36310 Vigo Spain atlanTTic Research Center University of Vigo 36310 Vigo Spain College of Computer Science and Electronic Engineering Hunan University Changsha 410082 China School of Computer Science Beijing University of Posts and Telecommunications Beijing 100876 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 will be tested to clarify the security boundary before it is widely deployed. To investigate the security boundary of the OPL in quantum cryptography, we comprehensively test and analyze the behavior of the OPL under continuous-wave (cw) light-injection attacks and pulse-illumination attacks with pulse repetition rates of 0.5 Hz, 40 MHz, and 1 GHz. The test results illuminate the security boundary of the OPL, which allows one to properly employ the OPL in use cases. The methodology of testing and analysis proposed here is applicable to other power-limitation components in a QKD system.

关键词： Optical quantum information processing Photonics quantum communication quantum cryptography Devices

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Matrix manipulations via unitary transformations and ancilla-state measurements

arXiv

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arXiv 2023年

作者： Zenchuk, Alexander I. Qi, Wentao Kumar, Asutosh Wu, Junde Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS Moscow reg. Chernogolovka142432 Russia Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China Department of Physics Gaya College Magadh University Rampur Gaya823001 India School of Mathematical Sciences Zhejiang University Hangzhou310027 China

We propose protocols for calculating inner product, matrix addition and matrix multiplication based on multiqubit Toffoli-type and the simplest one-qubit operations and employ ancilla-measurements to remove all garbage of calculations. The depth (runtime) of addition protocol is O(1) and that of other protocols logarithmically increases with the dimensionality of the considered matrices. © 2023, CC BY-NC-ND.

关键词： Matrix algebra

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A theory of quantum differential equation solvers: limitations and fast-forwarding

arXiv

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arXiv 2022年

作者： An, Dong Liu, Jin-Peng Wang, Daochen Zhao, Qi Joint Center for Quantum Information and Computer Science University of Maryland MD20742 United States Department of Mathematics University of Maryland MD20742 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Department of Mathematics University of California BerkeleyCA94720 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States QICI Quantum Information and Computation Initiative Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong

We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the ODE is inhomogeneous. On the one hand, for generic homogeneous linear ODEs, by proving worst-case lower bounds, we show that quantum algorithms suffer from computational overheads due to two types of "non-quantumness": real part gap and non-normality of the coefficient matrix. We then show that homogeneous ODEs in the absence of both types of "non-quantumness" are equivalent to quantum dynamics, and reach the conclusion that quantum algorithms for quantum dynamics work best. We generalize our results to the inhomogeneous case and find that existing generic quantum ODE solvers cannot be substantially improved. To obtain these lower bounds, we propose a general framework for proving lower bounds on quantum algorithms that are amplifiers, meaning that they amplify the difference between a pair of input quantum states. On the other hand, we show how to fast-forward quantum algorithms for solving special classes of ODEs which leads to improved efficiency. More specifically, we obtain quadratic improvements in the evolution time T for inhomogeneous ODEs with a negative semi-definite coefficient matrix, and exponential improvements in both T and the spectral norm of the coefficient matrix for inhomogeneous ODEs with efficiently implementable eigensystems, including various spatially discretized linear evolutionary partial differential equations. We give fast-forwarding algorithms that are conceptually different from existing ones in the sense that they neither require time discretization nor solving high-dimensional linear systems. Copyright © 2022, The Authors. All rights reserved.

关键词： Ordinary differential equations

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Optimal Verification of the Bell State and Greenberger-Horne-Zeilinger States in Untrusted quantum Networks

arXiv

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arXiv 2021年

作者： Han, Yun-Guang Li, Zihao Wang, Yukun Zhu, Huangjun State Key Laboratory of Surface Physics Department of Physics Fudan University Shanghai 200433 China Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai 200433 China Center for Field Theory and Particle Physics Fudan University Shanghai 200433 China Department of Computer Science and Technology China University of Petroleum Beijing102249 China

Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted quantum network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger-Horne-Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger-Horne-Zeilinger states and for detecting genuine multipartite entanglement. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum entanglement

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