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Fast quantum algorithms for Trace Distance Estimation

IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第4期70卷 2720-2733页

作者： Wang, Qisheng Zhang, Zhicheng Nagoya Univ Grad Sch Math Nagoya 4648602 Japan Univ Technol Sydney Ctr Quantum Software & Informat Ultimo NSW 2007 Australia

In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient quantum algorithms for estimating the trace distance within additive error epsilon between mixed quantum states of rank r . Specifically, we first provide a quantum algorithm using r & sdot;O (1/epsilon(2)) queries to the quantum circuits that prepare the purifications of quantum states. Then, we modify this quantum algorithm to obtain another algorithm using O (r(2)/epsilon(5)) samples of quantum states, which can be applied to quantum state certification. These algorithms have query/sample complexities that are independent of the dimension N of quantum states, and their time complexities only incur an extra O(log(N)) factor. In addition, we show that the decision version of low-rank trace distance estimation is BQP -complete.

关键词： quantum state Estimation Complexity theory quantum algorithm Time complexity Certification Task analysis quantum algorithms trace distance singular value decomposition Hadamard test

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Calculation of the moscovium ground-state energy by quantum algorithms

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INTERNATIONAL JOURNAL OF quantum CHEMISTRY 2024年第1期124卷 e27232-e27232页

作者： Zaytsev, V. A. Groshev, M. E. Maltsev, I. A. Durova, A. V. Shabaev, V. M. St Petersburg State Univ Dept Phys Univ Skaya Naberezhnaya 7-9 St Petersburg 199034 Russia Natl Res Ctr BP Konstantinov Petersburg Nucl Phys Inst Kurchatov Inst Leningrad Dist Russia

We investigate the possibility to calculate the ground-state energy of the atomic systems on a quantum computer. For this purpose we evaluate the lowest binding energy of the moscovium atom with the use of the iterative phase estimation and variational quantum eigensolver (VQE). The calculations by the VQE are performed with a disentangled unitary coupled cluster ansatz and with various types of hardware-efficient ansatze. The optimization is performed with the use of the Adam and quantum natural gradients procedures. The scalability of the ansatze and optimizers is tested by increasing the size of the basis set and the number of active electrons. The number of gates required for the iterative phase estimation and VQE is also estimated.

关键词： quantum algorithms superheavy elements

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quantum algorithms for structured prediction

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quantum MACHINE INTELLIGENCE 2022年第2期4卷 1-25页

作者： Sepehry, Behrooz Iranmanesh, Ehsan Friedlander, Michael P. Ronagh, Pooya 1QB Informat Technol 1QBit Vancouver BC Canada Univ British Columbia Vancouver BC Canada Inst Quantum Comp Waterloo ON Canada Univ Waterloo Waterloo ON Canada

We introduce two quantum algorithms for solving structured prediction problems. We first show that a stochastic gradient descent that uses the quantum minimum finding algorithm and takes its probabilistic failure into account solves the structured prediction problem with a runtime that scales with the square root of the size of the label space, and in similar to O (1/..) with respect to the precision,.., of the solution. Motivated by robust inference techniques in machine learning, we then introduce another quantum algorithm that solves a smooth approximation of the structured prediction problem with a similar quantum speedup in the size of the label space and a similar scaling in the precision parameter. In doing so, we analyze a variant of stochastic gradient descent for convex optimization in the presence of an additive error in the calculation of the gradients, and show that its convergence rate does not deteriorate if the additive errors are of the order O(v root epsilon). This algorithm uses quantum Gibbs sampling at temperature O(epsilon) as a subroutine. Based on these theoretical observations, we propose a method for using quantum Gibbs samplers to combine feedforward neural networks with probabilistic graphical models for quantum machine learning. Our numerical results using Monte Carlo simulations on an image tagging task demonstrate the benefit of the approach.

关键词： quantum algorithms Statistical learning Structured prediction Support vector machines Computational complexity Query complexity quantum minimum finding quantum Gibbs sampling Stochastic gradient descent Stochastic subgradient methods Stochastic average gradient methods Smooth approximation

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Utilizing quantum algorithms to achieve carbon neutrality in urban areas: A systematic review

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ALEXANDRIA ENGINEERING JOURNAL 2024年 108卷 911-936页

作者： Munawar, Ghifari Surendro, Kridanto Inst Teknol Bandung Sch Elect Engn & Informat Bandung 40132 Indonesia Politekn Negeri Bandung Dept Comp Engn & Informat Bandung 40559 Indonesia

In the face of climate change, urban areas, as major sources of greenhouse gas (GHG) emissions, are pivotal in mitigation efforts. Cities worldwide are striving to achieve carbon neutrality, aligning with the Sustainable Development Goals (SDGs). quantum computing (QC), with its ability to leverage qubits and surpass the limitations of classical computing, presents a promising avenue for optimizing processes in energy, transportation, and climate change mitigation. This study conducts a systematic literature review following Kitchenham's framework, analyzing 96 out of 3397 articles from four major academic databases. The review focuses on the implementation of quantum algorithms, including pure quantum algorithms (PQA), hybrid quantum-classical algorithms (HQC), and quantum-inspired classical algorithms (QIC), with 40 distinct methods such as quantum Annealing (QA), quantum-inspired Particle Swarm Optimization (QiPSO), and quantum Approximate Optimization Algorithm (QAOA). The analysis identifies key application domains: algorithmic tasks, types of implications, GHG emission sectors, and quantum methods, highlighting allocation and routing tasks as dominant themes. Notably, the transportation and energy sectors, along with the QA method, feature prominently. Furthermore, a detailed nexus analysis reveals significant interconnections between algorithmic tasks, quantum methods, and their practical implications, particularly in energy efficiency and resource allocation. The findings underscore the growing role of quantum algorithms in reducing urban GHG emissions and advancing toward carbon neutrality, showcasing QC's potential in supporting sustainable cities and effective climate action. (c) 2017 Elsevier Inc. All rights reserved.

关键词： quantum algorithms carbon-neutrality GHG emissions sustainable city review

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Efficient quantum algorithms for some instances of the semidirect discrete logarithm problem

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DESIGNS CODES AND CRYPTOGRAPHY 2024年第10期92卷 2825-2843页

作者： Imran, Muhammad Ivanyos, Gabor Budapest Univ Technol & Econ Dept Algebra & Geometry Egry Jozsef U 1 H-1111 Budapest Hungary HUN REN Inst Comp Sci & Control Kende U 13-17 H-1111 Budapest Hungary

The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup G (sic) End(G) for a finite semigroup G. Given g is an element of G, sigma is an element of End(G), and h = Pi(t-1)(i=0) sigma(i) (g) for some integer t, the SDLP(G, sigma), for g and h, asks to determine t. As Shor's algorithm crucially depends on commutativity, it is believed not to be applicable to the SDLP. For generic semigroups, the best known algorithm for the SDLP is based on Kuperberg's subexponential time quantum algorithm. Still, the problem plays a central role in the security of certain proposed cryptosystems in the family of semidirect product key exchange. This includes a recently proposed signature protocol called SPDH-Sign. In this paper, we show that the SDLP is even easier in some important special cases. Specifically, for a finite group G, we describe quantum algorithms for the SDLP in G (sic) Aut(G) for the following two classes of instances: the first one is when G is solvable and the second is when G is amatrix group and a power of sigma with a polynomially small exponent is an inner automorphism of G. We further extend the results to groups composed of factors from these classes. Aconsequence is that SPDH-Sign and similar cryptosystems whose security assumption is based on the presumed hardness of the SDLP in the cases described above are insecure against quantum attacks. The quantum ingredients we rely on are not new: these are Shor's factoring and discrete logarithm algorithms and well-known generalizations.

关键词： Semidirect discrete logarithm problem quantum algorithms quantum cryptanalysis

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New quantum algorithms for Computing quantum Entropies and Distances

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IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第8期70卷 5653-5680页

作者： Wang, Qisheng Guan, Ji Liu, Junyi Zhang, Zhicheng Ying, Mingsheng Tsinghua Univ Dept Comp Sci & Technol Beijing 100084 Peoples R China Nagoya Univ Grad Sch Math Nagoya 4648602 Japan Chinese Acad Sci Key Lab Syst Software Beijing 100190 Peoples R China Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing 100190 Peoples R China Univ Maryland Joint Ctr Quantum Informat & Comp Sci College Pk MD 20742 USA Univ Technol Sydney Ctr Quantum Soft ware & Informat Sydney NSW 2007 Australia

We propose a series of quantum algorithms forcomputing a wide range of quantum entropies and distances,including the von Neumann entropy, quantum R & eacute;nyi entropy,trace distance, and fidelity. The proposed algorithms significantlyoutperform the prior best (and even quantum) ones in thelow-rank case, some of which achieve exponential *** particular, forN-dimensional quantum states of rankr, ourproposed quantum algorithms for computing the von Neumannentropy, trace distance and fidelity within additive error epsilon havetime complexity of O(r/epsilon(2)), O(r(5)/epsilon(6))and O(r(6.5)/epsilon(7.5)),respectively. By contrast, prior quantum algorithms for the vonNeumann entropy and trace distance usually have time complex-ity ohm (N), and the prior best one for fidelity has time complexity O(r(12.5)/epsilon(13.5)). The key idea of our quantum algorithms isto extend block-encoding from unitary operators in previouswork to quantum states (i.e., density operators). It is realized bydeveloping several convenient techniques to manipulate quantumstates and extract information from them. The advantage of ourtechniques over the existing methods is that no restrictions ondensity operators are required;in sharp contrast, the previousmethods usually require a lower bound on the minimal non-zeroeigenvalue of density operators

关键词： quantum state quantum algorithm Entropy quantum computing Complexity theory Computational modeling Time complexity quantum algorithms quantum entropy trace distance quantum fidelity

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Resilience-runtime tradeoff relations for quantum algorithms

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REPORTS ON PROGRESS IN PHYSICS 2025年第3期88卷 037601-037601页

作者： Pedro Garcia-Pintos, Luis O'Leary, Tom Biswas, Tanmoy Bringewatt, Jacob Cincio, Lukasz Brady, Lucas T. Liu, Yi-Kai Los Alamos Natl Lab Theoret Div T4 Los Alamos NM 87545 USA Univ Oxford Clarendon Lab Parks Rd Oxford OX1 3PU England Univ Maryland Joint Ctr Quantum Informat & Comp Sci College Pk MD 20742 USA Univ Maryland Joint Quantum Inst College Pk MD 20742 USA Harvard Univ Dept Phys Cambridge MA 02138 USA NASA Ames Res Ctr Quantum Artificial Intelligence Lab Moffett Field CA 94035 USA Natl Inst Stand & Technol Appl & Computat Math Div Gaithersburg MD 20899 USA

A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer's potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize the resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm's number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.

关键词： quantum algorithms noise resilience quantum computing quantum compilation

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Metasurface for programmable quantum algorithms with classical and quantum light

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NANOPHOTONICS 2024年第6期13卷 927-936页

作者： Tanuwijaya, Randy Stefan Liang, Hong Xi, Jiawei Wong, Wai Chun Yung, Tsz Kit Tam, Wing Yim Li, Jensen Hong Kong Univ Sci & Technol Dept Phys Kowloon Clear Water Bay Hong Kong Peoples R China

Metasurfaces have recently opened up applications in the quantum regime, including quantum tomography and the generation of quantum entangled states. With their capability to store a vast amount of information by utilizing the various geometric degrees of freedom of nanostructures, metasurfaces are expected to be useful for processing quantum information. Here, we propose and experimentally demonstrate a programmable metasurface capable of performing quantum algorithms using both classical and quantum light with single photons. Our approach encodes multiple programmable quantum algorithms and operations, such as Grover's search algorithm and the quantum Fourier transform, onto the same metalens array on a metasurface. A spatial light modulator selectively excites different sets of metalenses to carry out the quantum algorithms, while the interference patterns captured by a single-photon camera are used to extract information about the output state at the selected output directions. Our programmable quantum metasurface approach holds promising potential as a cost-effective means of miniaturizing components for quantum computing and information processing.

关键词： programmable metasurface quantum information quantum optics quantum algorithms

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quantum algorithms for Charged Particle Track Reconstruction in the LUXE Experiment

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Computing and Software for Big Science 2023年第1期7卷 1-12页

作者： Crippa, Arianna Funcke, Lena Hartung, Tobias Heinemann, Beate Jansen, Karl Kropf, Annabel Kühn, Stefan Meloni, Federico Spataro, David Tüysüz, Cenk Yap, Yee Chinn Deutsches Elektronen-Synchrotron DESY Platanenallee 6 Zeuthen 15738 Germany Institut für Physik Humboldt-Universität zu Berlin Newtonstr. 15 Berlin 12489 Germany Transdisciplinary Research Area “Building Blocks of Matter and Fundamental Interactions” (TRA Matter) and Helmholtz Institute for Radiation and Nuclear Physics (HISKP) University of Bonn Nußallee 14-16 Bonn 53115 Germany Center for Theoretical Physics Co-Design Center for Quantum Advantage and NSF AI Institute for Artificial Intelligence and Fundamental Interactions Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge 02139 MA United States Northeastern University London Devon House St Katharine Docks London E1W 1LP United Kingdom Deutsches Elektronen-Synchrotron DESY Notkestr. 85 Hamburg 22607 Germany Physikalisches Institut Albert-Ludwigs-Universität Freiburg Hermann-Herder-Str. 3a Freiburg 79104 Germany Computation-Based Science and Technology Research Center The Cyprus Institute 20 Kavafi Street Nicosia 2121 Cyprus

The LUXE experiment is a new experiment in planning in Hamburg, which will study quantum electrodynamics at the strong-field frontier. LUXE intends to measure the positron production rate in this unprecedented regime using, among others, a silicon tracking detector. The large number of expected positrons traversing the sensitive detector layers results in an extremely challenging combinatorial problem, which can become computationally expensive for classical computers. This paper investigates the potential future use of gate-based quantum computers for pattern recognition in track reconstruction. Approaches based on a quadratic unconstrained binary optimisation and a quantum graph neural network are investigated in classical simulations of quantum devices and compared with a classical track reconstruction algorithm. In addition, a proof-of-principle study is performed using quantum hardware. © 2023, The Author(s).

关键词： HEP particle tracking Pattern recognition quantum algorithms Strong-field QED experiment

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Photon-native quantum algorithms

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MATERIALS FOR quantum TECHNOLOGY 2025年第2期5卷 023001-023001页

作者： Salavrakos, Alexia Maring, Nicolas Emeriau, Pierre-Emmanuel Mansfield, Shane Quandela 7 Rue Leonard de Vinci F-91300 Massy France

Photonic platforms occupy a central place in quantum technologies. They appear in quantum networks and communication, in near-term quantum advantage schemes, as well as in fault-tolerant quantum computing proposals. In this perspective article, we review the advances and challenges of this technology, and we focus on algorithms and protocols that we call photon-native, i.e. which closely follow the specificities of the hardware.

关键词： photonic quantum computing quantum algorithms quantum machine learning

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