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Efficiently Verifiable Quantum Advantage on Near-Term Analog Quantum Simulators

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PRX Quantum 2025年第1期6卷 010341-010341页

作者： Zhenning Liu Dhruv Devulapalli Dominik Hangleiter Yi-Kai Liu Alicia J. Kollár Alexey V. Gorshkov Andrew M. Childs Joint Center for Quantum Information and Computer Science NIST/University of Maryland College Park Maryland 20742 USA Joint Quantum Institute NIST/University of Maryland College Park Maryland 20742 USA Department of Computer Science University of Maryland College Park Maryland 20742 USA Simons Institute for the Theory of Computing University of California at Berkeley California 94720 USA Applied and Computational Mathematics Division National Institute of Standards and Technology (NIST) Gaithersburg Maryland 20899 USA Department of Physics University of Maryland College Park Maryland 20742 USA Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 USA

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an O(λ2)-time classical computation, and the prover need only prepare O(1) samples of a history state and perform O(λ2) single-qubit measurements, for a security parameter λ. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

关键词： Quantum computers

Distinguishability-based genuine nonlocality with genuine multipartite entanglement

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arXiv 2022年

作者： Xiong, Zong-Xing Li, Mao-Sheng Zheng, Zhu-Jun Li, Lvzhou Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China School of Mathematics South China University of Technology Guangzhou510640 China

A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This form of multipartite nonlocality, although more naturally arising than the recently popular "strong nonlocality" in the context of local distinguishability, receives much less attention. In this work, we study the distinguishability-based genuine nonlocality of a typical type of genuine multipartite entangled states — the d-dimensional GHZ states, featuring systems with local dimension not limited to 2. In the three-partite case, we find the existence of small genuinely nonlocal sets consisting of these states: we show that the cardinality can at least scale down to linear in the local dimension d, with the linear factor l = 1. Specifically, the method we use is semidefinite program and the GHZ states to construct these sets are special ones which we call "GHZ-lattices". This result might arguably suggest a significant gap between the strength of strong nonlocality and the distinguishability-based genuine nonlocality. Moreover, we put forward the notion of (s, n)-threshold distinguishability and utilizing a similar method, we successfully construct (2, 3)-threshold sets consisting of GHZ states in three-partite systems. © 2022, CC BY.

关键词： Quantum entanglement

On algebraic properties of power monoids of numerical monoids

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arXiv 2022年

作者： Bienvenu, Pierre-Yves Geroldinger, Alfred Graz University of Technology NAWI Graz Institute of Analysis and Number Theory Kopernikusgasse 24/2 Graz8010 Austria University of Graz NAWI Graz Institute for Mathematics and Scientific Computing Heinrichstraße 36 Graz8010 Austria

Let S ⊂ N0 be a numerical monoid and let Pfin(S), resp. Pfin,0(S), denote the power monoid, resp. the restricted power monoid, of S, that is the set of all finite nonempty subsets of S, resp. the set of all finite nonempty subsets of S containing 0, with set addition as operation. The arithmetic of power monoids received some attention in recent literature. We complement these investigations by studying algebraic properties of power monoids, such as their prime spectrum. Moreover, we show that almost all elements of Pfin,0(S) are irreducible (i.e., they are not proper sumsets). Copyright © 2022, The Authors. All rights reserved.

关键词： Algebra

Approaching multifractal complexity in decentralized cryptocurrency trading

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arXiv 2024年

作者： Wątorek, Marcin Królczyk, Marcin Kwapień, Jaroslaw Stanisz, Tomasz Drozdz, Stanislaw Faculty of Computer Science and Telecommunications Cracow University of Technology Kraków31-155 Poland Complex Systems Theory Department Institute of Nuclear Physics Polish Academy of Sciences Kraków31-342 Poland Adapt Centre School of Computing Dublin City University DublinD09 Y074 Ireland

Multifractality is a concept that helps compactly grasping the most essential features of the financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded on the centralized exchanges. A new element that adds complexity to cryptocurrency markets is the possibility of decentralized trading. Based on the extracted tick-by-tick transaction data from the Universal Router contract of the Uniswap decentralized exchange, from June 6, 2023, to June 30, 2024, the present study using Multifractal Detrended Fluctuation Analysis (MFDFA) shows that even though liquidity on these new exchanges is still much lower compared to centralized exchanges convincing traces of multifractality are already emerging on this new trading as well. The resulting multifractal spectra are however strongly left-side asymmetric which indicates that this multifractality comes primarily from large fluctuations and small ones are more of the uncorrelated noise type. What is particularly interesting here is the fact that multifractality is more developed for time series representing transaction volumes than rates of return. On the level of these larger events a trace of multifractal cross-correlations between the two characteristics is also observed. Copyright © 2024, The Authors. All rights reserved.

关键词： Decentralized finance

Dense Outputs from Quantum Simulations

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SSRN

SSRN 2023年

作者： Liu, Jin-Peng Lin, Lin Department of Mathematics University of California Berkeley United States Simons Institute for the Theory of Computing University of California Berkeley United States Center for Theoretical Physics Massachusetts Institute of Technology Cambridge United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States Challenge Institute for Quantum Computation University of California Berkeley Berkeley United States

The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time $T$ and error tolerance $\epsilon$. Our results demonstrate that the linearization approach can nearly achieve optimal complexity $\mathcal{O}(T/\epsilon)$ for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning. © 2023, The Authors. All rights reserved.

关键词： Linearization

Dense outputs from quantum simulations

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arXiv 2023年

The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and spectroscopic computation. We present a range of algorithms designed to operate on both early and fully fault-tolerant quantum platforms. These methodologies draw upon techniques like amplitude estimation, Hamiltonian simulation, quantum linear Ordinary Differential Equation (ODE) solvers, and quantum Carleman linearization. We provide a comprehensive complexity analysis with respect to the evolution time T and error tolerance ǫ. Our results demonstrate that the linearization approach can nearly achieve optimal complexity O(T/ǫ) for a certain type of low-rank dense outputs. Moreover, we provide a linearization of the dense output problem that yields an exact and finite-dimensional closure which encompasses the original states. This formulation is related to the Koopman Invariant Subspace theory and may be of independent interest in nonlinear control and scientific machine learning. Copyright © 2023, The Authors. All rights reserved.

关键词： Linearization

Quantum Depth in the Random Oracle Model

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arXiv 2022年

作者： Arora, Atul Singh Coladangelo, Andrea Coudron, Matthew Gheorghiu, Alexandru Singh, Uttam Waldner, Hendrik Institute for Quantum Information and Matter California Institute of Technology Department of Computing and Mathematical Sciences California Institute of Technology United States University of California Berkeley Simons Institute The Theory of Computing United States Department of Computer Science University of Maryland United States Department of Computer Science and Engineering Chalmers University of Technology Institute for Theoretical Studies ETH Zürich Switzerland Center for Theoretical Physics Polish Academy of Sciences Poland Department of Computer Science University of Maryland Max Planck Institute for Security and Privacy United States

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle: (a) BPPQNCBPP ≠ BQP. This refutes Jozsa's conjecture [Joz05] in the random oracle model. As a result, this gives the first instantiatable separation between the classes by replacing the oracle with a cryptographic hash function, yielding a resolution to one of Aaronson's ten semi-grand challenges in quantum computing [Aar05]. (b) BPPQNC ⊆ QNCBPP and QNCBPP ⊆ BPPQNC. This shows that there is a subtle interplay between classical computation and shallow quantum computation. In fact, for the second separation, we establish that, for some problems, the ability to perform adaptive measurements in a single shallow quantum circuit, is more useful than the ability to perform polynomially many shallow quantum circuits without adaptive measurements. (c) There exists a 2-message proof of quantum depth protocol. Such a protocol allows a classical verifier to efficiently certify that a prover must be performing a computation of some minimum quantum depth. Our proof of quantum depth can be instantiated using the recent proof of quantumness construction by Yamakawa and Zhandry [YZ22]. Copyright © 2022, The Authors. All rights reserved.

关键词： Hash functions

Single-cell omics: experimental workflow, data analyses and applications

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Science China(Life Sciences) 2025年第1期68卷 5-102页

作者： Fengying Sun Haoyan Li Dongqing Sun Shaliu Fu Lei Gu Xin Shao Qinqin Wang Xin Dong Bin Duan Feiyang Xing Jun Wu Minmin Xiao Fangqing Zhao Jing-Dong J.Han Qi Liu Xiaohui Fan Chen Li Chenfei Wang Tieliu Shi Department of Clinical Laboratory the Affiliated Wuhu Hospital of East China Normal University(The Second People’s Hospital of Wuhu City)Wuhu 241000China Pharmaceutical Informatics Institute College of Pharmaceutical SciencesZhejiang UniversityHangzhou 310058China Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration(Tongji University) Ministry of EducationOrthopaedic DepartmentTongji HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji UniversityShanghai 200082China Frontier Science Center for Stem Cells School of Life Sciences and TechnologyTongji UniversityShanghai 200092China Translational Medical Center for Stem Cell Therapy and Institute for Regenerative Medicine Shanghai East HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji UniversityShanghai 200082China Research Institute of Intelligent Computing Zhejiang LabHangzhou 311121China Shanghai Research Institute for Intelligent Autonomous Systems Shanghai 201210China Center for Single-cell Omics School of Public HealthShanghai Jiao Tong University School of MedicineShanghai 200025China National Key Laboratory of Chinese Medicine Modernization Innovation Center of Yangtze River DeltaZhejiang UniversityJiaxing 314103China Center for Bioinformatics and Computational Biology Shanghai Key Laboratory of Regulatory Biologythe Institute of Biomedical Sciences and School of Life SciencesEast China Normal UniversityShanghai 200241China Beijing Institutes of Life Science Chinese Academy of SciencesBeijing 100101China Peking-Tsinghua Center for Life Sciences Academy for Advanced Interdisciplinary StudiesCenter for Quantitative Biology(CQB)Peking UniversityBeijing 100871China Zhejiang Key Laboratory of Precision Diagnosis and Therapy for Major Gynecological Diseases Women’s HospitalZhejiang University School of MedicineHangzhou 310006China Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of StatisticsEast China Normal U

Cells are the fundamental units of biological systems and exhibit unique development trajectories and molecular *** exploration of how the genomes orchestrate the formation and maintenance of each cell,and control the cellular phenotypes of various organismsis,is both captivating and *** the inception of the first single-cell RNA technology,technologies related to single-cell sequencing have experienced rapid advancements in recent *** technologies have expanded horizontally to include single-cell genome,epigenome,proteome,and metabolome,while vertically,they have progressed to integrate multiple omics data and incorporate additional information such as spatial scRNA-seq and CRISPR ***-cell omics represent a groundbreaking advancement in the biomedical field,offering profound insights into the understanding of complex diseases,including ***,we comprehensively summarize recent advances in single-cell omics technologies,with a specific focus on the methodology *** overview aims to guide researchers in selecting appropriate methods for single-cell sequencing and related data analysis.

关键词： single-cell sequencing genome epigenome proteomics metabolomics multimodal spatial transcriptomics CRISPR screening

Experimental Demonstration of Inequivalent Mutually Unbiased Bases

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Physical Review Letters 2024年第8期132卷 080202-080202页

作者： Wen-Zhe Yan Yunting Li Zhibo Hou Huangjun Zhu Guo-Yong Xiang Chuan-Feng Li Guang-Can Guo CAS Key Laboratory of Quantum Information University of Science and Technology of China Hefei 230026 People’s Republic of China CAS Center For Excellence in Quantum Information and Quantum Physics University of Science and Technology of China Hefei 230026 People’s Republic of China State Key Laboratory of Surface Physics and 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 Hefei National Laboratory University of Science and Technology of China Hefei 230088 People’s Republic of China

Quantum measurements based on mutually unbiased bases (MUBs) play crucial roles in foundational studies and quantum information processing. It is known that there exist inequivalent MUBs, but little is known about their operational distinctions, not to say experimental demonstration. In this Letter, by virtue of a simple estimation problem, we experimentally demonstrate the operational distinctions between inequivalent triples of MUBs in dimension 4 based on high-precision photonic systems. The experimental estimation fidelities coincide well with the theoretical predictions with only 0.16% average deviation, which is 25 times less than the difference (4.1%) between the maximum estimation fidelity and the minimum estimation fidelity. Our experiments clearly demonstrate that inequivalent MUBs have different information extraction capabilities and different merits for quantum information processing.

关键词： Quantum foundations Quantum information processing Quantum measurements Quantum optics