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Simple and High-Precision Hamiltonian Simulation by Compensating Trotter Error with Linear Combination of Unitary Operations

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PRX quantum 2025年第1期6卷 010359-010359页

作者： Pei Zeng Jinzhao Sun Liang Jiang Qi Zhao Pritzker School of Molecular Engineering The University of Chicago Illinois 60637 USA Clarendon Laboratory University of Oxford Parks Road Oxford OX1 3PU United Kingdom Blackett Laboratory Imperial College London London SW7 2AZ United Kingdom QICI Quantum Information and Computation Initiative Department of Computer Science School of Computing and Data Science The University of Hong Kong Pokfulam Road Hong Kong

Trotter and linear combination of unitary (LCU) operations are two popular Hamiltonian simulation methods. The Trotter method is easy to implement and enjoys good system-size dependence endowed by commutator scaling, while the LCU method admits high-accuracy simulation with a smaller gate cost. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates after the Kth-order Trotter formula, we realize a better time scaling than 2Kth-order Trotter. Our first algorithm exponentially improves the accuracy scaling of the Kth-order Trotter formula. For a generic Hamiltonian, the estimated gate counts of the first algorithm can be 2 orders of magnitude smaller than the best analytical bound of fourth-order Trotter formula. In the second algorithm, we consider the detailed structure of Hamiltonians and construct LCU for Trotter errors with commutator scaling. Consequently, for lattice Hamiltonians, the algorithm enjoys almost linear system-size dependence and quadratically improves the accuracy of the Kth-order Trotter. For the lattice system, the second algorithm can achieve 3 to 4 orders of magnitude higher accuracy with the same gate costs as the optimal Trotter algorithm. These algorithms provide an easy-to-implement approach to achieve a low-cost and high-precision Hamiltonian simulation.

关键词： Size distribution

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Random node reinforcement and K-core structure of complex networks

arXiv

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arXiv 2022年

作者： Ma, Rui Hu, Yanqing Zhao, Jin-Hua Guangdong Provincial Key Laboratory of Nuclear Science Institute of Quantum Matter South China Normal University Guangzhou510006 China Guangdong-Hong Kong Joint Laboratory of Quantum Matter Southern Nuclear Science Computing Center South China Normal University Guangzhou510006 China Department of Statistics and Data Science College of Science Southern University of Science and Technology Shenzhen518055 China School of Data Science and Engineering South China Normal University Shanwei516622 China

To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an optimal reinforcement solution. Yet there still lacks a systematic evaluation on how node reinforcement affects network structure at a mesoscopic level upon failures. Here we study this problem through the lens of K-cores of networks. Based on an analytical percolation framework, we first show that, on uncorrelated random graphs, with a critical size of reinforced nodes, an abrupt emergence of K-cores is smoothed out to a continuous one, and a detailed phase diagram is derived. We then show that, with a cost-benefit analysis on random reinforcement, for proper weight factors in cost functions with constant and increasing marginal costs, a gain function shows a unimodality, thus we can analytically find an optimal reinforcement fraction by locating the maximal gain. In all, our framework offers a gain-oriented analytical perspective to designing robust interconnected systems. Copyright © 2022, The Authors. All rights reserved.

关键词： Reinforcement

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

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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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Distinguishing unitary gates on the IBM quantum processor

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science China(Information sciences) 2019年第7期62卷 210-216页

作者： Shusen LIU Yinan LI Runyao DUAN School of Data and Computer Science Sun Yat-sen University Centre for Quantum Software and Information Faculty of Engineering and Information TechnologyUniversity of Technology Sydney Centrum Wiskunde & Informatica and Research Center for Quantum Software Institute for Quantum Computing

An unknown unitary gate, which is secretly chosen from several known ones, can always be distinguished perfectly. In this paper, we implement such a task on IBM's quantum processor. More precisely,we experimentally demonstrate the discrimination of two qubit unitary gates, the identity gate and the 2/3π-phase shift gate, using two discrimination schemes — the parallel scheme and the sequential scheme. We program these two schemes on the ibmqx4, a 5-qubit superconducting quantum processor via IBM cloud,with the help of the QSI modules. We report that both discrimination schemes achieve success probabilities at least 85%.

关键词： quantum experiment IBM quantum computer software-aided quantum experiment sequential schemes for unitary discrimination parallel schemes for unitary discrimination

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Loophole-free test of macroscopic realism via high-order correlations of measurement

arXiv

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arXiv 2024年

作者： Wang, Ping Chen, Chong Liao, Hao Vorobyov, Vadim V. Wrachtrup, Jörg Liu, Ren-Bao College of Education for the Future Beijing Normal University Zhuhai519087 China Department of Physics The Chinese University of Hong Kong New Territories Shatin Hong Kong Centre for Quantum Coherence The Chinese University of Hong Kong New Territories Shatin Hong Kong The Hong Kong Institute of Quantum Information Science and Technology The Chinese University of Hong Kong New Territories Shatin Hong Kong National Engineering Laboratory on Big Data System Computing Technology Guangdong Province Engineering Center of China-made High Performance Data Computing System College of Computer Science and Software Engineering Shenzhen University Shenzhen518060 China 3rd Institute of Physics Research Center SCoPE and IQST University of Stuttgart Stuttgart70569 Germany New Cornerstone Science Laboratory The Chinese University of Hong Kong New Territories Shatin Hong Kong

Test of macroscopic realism (MR) is key to understanding the foundation of quantum mechanics. Due to the existence of the non-invasive measurability loophole and other interpretation loopholes, however, such test remains an open question. Here we propose a general inequality based on high-order correlations of measurements for a loophole-free test of MR at the weak signal limit. Importantly, the inequality is established using the statistics of raw data recorded by classical devices, without requiring a specific model for the measurement process, so its violation would falsify MR without the interpretation loophole. The non-invasive measurability loophole is also closed, since the weak signal limit can be verified solely by measurement data (using the relative scaling behaviors of different orders of correlations). We demonstrate that the inequality can be broken by a quantum spin model. The inequality proposed here provides an unambiguous test of the MR principle and is also useful to characterizing quantum coherence. Copyright © 2024, The Authors. All rights reserved.

关键词： quantum theory

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Towards quantum Federated Learning

arXiv

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arXiv 2023年

作者： Ren, Chao Yan, Rudai Zhu, Huihui Yu, Han Xu, Minrui Shen, Yuan Xu, Yan Xiao, Ming Dong, Zhao Yang Skoglund, Mikael Niyato, Dusit Kwek, Leong Chuan School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Sweden School of Electrical and Electronic Engineering Nanyang Technological University Singapore College of Computing and Data Science Nanyang Technological University Singapore Division of Information Science and Engineering KTH Royal Institute of Technology Sweden City University of Hong Kong China Center for Quantum Technologies National University of Singapore Singapore Nanyang Technological University Singapore

quantum Federated Learning (QFL) is an emerging interdisciplinary field that merges the principles of quantum computing (QC) and Federated Learning (FL), with the goal of leveraging quantum technologies to enhance privacy, security, and efficiency in the learning process. Currently, there is no comprehensive survey for this interdisciplinary field. This review offers a thorough, holistic examination of QFL. We aim to provide a comprehensive understanding of the principles, techniques, and emerging applications of QFL. We discuss the current state of research in this rapidly evolving field, identify challenges and opportunities associated with integrating these technologies, and outline future directions and open research questions. We propose a unique taxonomy of QFL techniques, categorized according to their characteristics and the quantum techniques employed. As the field of QFL continues to progress, we can anticipate further breakthroughs and applications across various industries, driving innovation and addressing challenges related to data privacy, security, and resource optimization. This review serves as a first-of-its-kind comprehensive guide for researchers and practitioners interested in understanding and advancing the field of QFL. Copyright © 2023, The Authors. All rights reserved.

关键词： Federated learning

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JERALD: high-fidelity dark matter, stellar mass and neutral hydrogen maps from fast N-body simulations

arXiv

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arXiv 2025年

作者： Rigo, Mauro Trotta, Roberto Viel, Matteo Theoretical and Scientific Data Science SISSA Via Bonomea 265 Trieste34136 Italy INFN National Institute for Nuclear Physics Via Valerio 2 Trieste34127 Italy ICSC Centro Nazionale di Ricerca in High Performance Computing Big Data e Quantum Computing Via Magnanelli 2 Bologna Italy Astrophysics Group Physics Department Blackett Lab Imperial College London Prince Consort Road LondonSW7 2AZ United Kingdom INAF Osservatorio Astronomico di Trieste Via G. B. Tiepolo 11 TriesteI-34143 Italy

We present a new code and approach, JERALD—JAX Enhanced Resolution Approximate Lagrangian Dynamics—, that improves on and extends the Lagrangian Deep Learning method of Dai & Seljak (2021), producing high-resolution dark matter, stellar mass and neutral hydrogen maps from lower-resolution approximate N-body simulations. The model is trained using the Sherwood-Relics simulation suite (for a fixed cosmology), specifically designed for the intergalactic medium and the neutral hydrogen distribution in the cosmic web. The output is tested in the redshift range from z = 5 to z = 0 and the generalization properties of the learned mapping is demonstrated. JERALD produces maps with dark matter, stellar and neutral hydrogen power spectra in excellent agreement with full-hydrodynamic simulations with 8× higher resolution, at large and intermediate scales;in particular, JERALD’s neutral hydrogen power spectra agree with their higher-resolution full-hydrodynamic counterparts within 90% up to k 1 hMpc−1 and within 70% up to k 10 hMpc−1. JERALD provides a fast, accurate and physically motivated approach that we plan to embed in a statistical inference pipeline, such as Simulation-Based Inference, to constrain dark matter properties from large- to intermediate-scale structure observables. Copyright © 2025, The Authors. All rights reserved.

关键词： Dark Matter

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Quantifying fermionic nonlinearity of quantum circuits

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Physical Review Research 2022年第4期4卷 043100-043100页

作者： Shigeo Hakkaku Yuichiro Tashima Kosuke Mitarai Wataru Mizukami Keisuke Fujii Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Toyonaka Osaka 560-8531 Japan NTT Computer and Data Science Laboratories NTT Corporation 3-9-11 Midoricho Musashino 180-8585 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Toyonaka 560-0043 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan RIKEN Center for Quantum Computing (RQC) Hirosawa 2-1 Wako Saitama 351-0198 Japan Fujitsu Quantum Computing Joint Research Division at QIQB Osaka University 1-2 Machikaneyama Toyonaka 560-0043 Japan

Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Here we propose a measure, called fermionic nonlinearity, to quantify the classical simulatability of quantum circuits designed for simulating fermionic Hamiltonians. Specifically, we construct a Monte Carlo type classical algorithm based on the classical simulatability of fermionic linear optics, whose sampling overhead is characterized by the fermionic nonlinearity. As a demonstration of these techniques, we calculate the upper bound of the fermionic nonlinearity of a rotation gate generated by four fermionic modes under the dephasing noise. Moreover, we estimate the sampling costs of the unitary coupled cluster singles and doubles quantum circuits for hydrogen chains subject to the dephasing noise. We find that, depending on the error probability and atomic spacing, there are regions where the fermionic nonlinearity becomes very small or unity, and hence the circuits are classically simulatable. We believe that our method and results help to design quantum circuits for fermionic systems with potential quantum advantages.

关键词： quantum algorithms quantum computation quantum correlations in quantum information quantum information processing quantum simulation Resource theories

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Resolvability of classical-quantum channels

arXiv

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arXiv 2024年

作者： Hayashi, Masahito Cheng, Hao-Chung Gao, Li School of Data Science The Chinese University of Hong Kong Shenzhen Longgang District Shenzhen518172 China Graduate School of Mathematics Nagoya University Nagoya464-8602 Japan School of Mathematics and Statistics Wuhan University Wuhan430072 China Department of Electrical Engineering Graduate Institute of Communication Engineering Department of Mathematics Institute of Applied Mathematical Sciences Center for Quantum Science and Engineering National Taiwan University Taipei10617 Taiwan Physics Division National Center for Theoretical Sciences Taipei10617 Taiwan Quantum Computing Center New Taipei City236 Taiwan

Channel resolvability concerns the minimum resolution for approximating the channel output. We study the resolvability of classical-quantum channels in two settings, for the channel output generated from the worst input, and form the fixed independent and identically distributed (i.i.d.) input. The direct part of the worst-input setting is derived from sequential hypothesis testing as it involves of non-i.i.d. inputs. The strong converse of the worst-input setting is obtained via the connection to identification codes. For the fixed-input setting, while the direct part follows from the known quantum soft covering result, we exploit the recent alternative quantum Sanov theorem to solve the strong converse. © 2024, CC BY.

关键词： quantum channel

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A Comprehensive Survey on Tiny Machine Learning for Human Behavior Analysis

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IEEE Internet of Things Journal 2025年

作者： Lamaakal, Ismail Essahraui, Siham Maleh, Yassine Makkaoui, Khalid El Ouahbi, Ibrahim Bouami, Mouncef Filali El-Latif, Ahmed A. Abd Almousa, May Peng, Jialiang Sultan Moulay Slimane University Laboratory LaSTI ENSAK Khouribga Morocco Prince Sultan University EIAS Data Science Lab College of Computer and Information Sciences Center of Excellence in Quantum and Intelligent Computing Riyadh11586 Saudi Arabia Menoufia University Faculty of Science Department of Mathematics and Computer Science Shebin El-Koom32511 Egypt Princess Nourah Bint Abdulrahman University College of Computer and Information Sciences Information Technology Department Riyadh Saudi Arabia Heilongjiang University School of Data Science and Technology Harbin150080 China Nanyang Technological University School of Computer Science and Engineering Nanyang Avenue Singapore639798 Singapore

The integration of Tiny Machine Learning (TinyML) with Human Behavior Analysis (HBA) represents a significant advancement in the field of Artificial Intelligence (AI), enabling real-time, efficient, and privacy-preserving analysis on resource-constrained devices. This paper provides the first comprehensive survey exploring this integration, presenting a detailed overview of TinyML, including its definitions, key concepts and advantages. The survey proposes a systematic taxonomy of TinyML applications in HBA, categorizing state-of-the-art implementations based on their use cases and specific methodologies. Furthermore, the challenges and limitations of integrating TinyML in HBA are thoroughly discussed, including technical constraints, data quality issues, and ethical considerations. Finally, future research directions and open issues are outlined, emphasizing the potential advancements and emerging trends in this field. This survey serves as a foundational resource, guiding researchers and practitioners in harnessing the capabilities of TinyML to advance HBA. © 2014 IEEE.

关键词： Embedded systems

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