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arXiv 2025年

作者： Aharonov, Dorit Alberton, Ori Arad, Itai Atia, Yosi Bairey, Eyal Brakerski, Zvika Cohen, Itsik Golan, Omri Gurwich, Ilya Kenneth, Oded Leviatan, Eyal Lindner, Netanel H. Melcer, Ron Aharon Meyer, Adiel Schul, Gili Shutman, Maor Qedma Quantum Computing Tel Aviv Israel The Benin School of Computer Science and Engineering Hebrew University Jerusalem Israel Centre for Quantum Technologies National University of Singapore Singapore Faculty of Mathematics and Computer Science Weizmann Institute of Science Israel Department of Physics Technion Haifa Israel

quantum error mitigation (EM) is a family of hybrid quantum-classical methods for eliminating or reducing the effect of noise and decoherence on quantum algorithms run on quantum hardware, without applying quantum error correction (EC). While EM has many benefits compared to EC, specifically that it requires no (or little) qubit overhead, this benefit comes with a painful price: EM seems to necessitate an overhead in quantum run time which grows as a (mild) exponent [1–4]. Accordingly, recent results show that EM alone cannot enable exponential quantum advantages (QAs), for an average variant of the expectation value estimation problem [5]. These works raised concerns regarding the role of EM in the road map towards QAs. We aim to demystify the discussion, and provide a clear picture of the role of EM in achieving QAs, both in the near and long term. We first propose a clear distinction between finite QA and asymptotic QA, which is crucial to the understanding of the question, and present the notion of circuit volume boost, which we claim is an adequate way to quantify the benefits of EM. Using these notions we can argue straightforwardly that EM is expected to have a significant role in achieving QAs. Specifically, that EM is likely to be the first error reduction method for useful finite QAs, before EC;that the first such QAs are expected to be achieved using EM in the very near future;and that EM is expected to maintain its important role in quantum computation even when EC will be routinely used – for as long as high-quality qubits remain a scarce resource. © 2025, CC BY.

关键词： Qubits

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Mass spectra of strange double charm pentaquarks with strangeness S=−1

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Physical Review D 2024年第5期110卷 056022页

作者： Zi-Yan Yang Qian Wang Wei Chen Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE) Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter Institute of Quantum Matter Guangdong-Hong Kong Joint Laboratory of Quantum Matter Guangdong Provincial Key Laboratory of Nuclear Science Southern Nuclear Science Computing Center Southern Center for Nuclear-Science Theory (SCNT) Institute of Modern Physics School of Physics

The observation of the Tcs¯(2900) indicates the potential existence of strange double charm pentaquarks based on the heavy antidiquark symmetry. We systematically study the mass spectra of strange double charm pentaquarks with strangeness S=−1 in both molecular and compact structures for quantum numbers JP=1/2−, 3/2−, 5/2−. By constructing the interpolating currents, the mass spectra can be extracted from the two-point correlation functions in the framework of QCD sum rule method. In the molecular picture, we find that the Ξc′+D*+, Ξc*+D*+, Ξcc*++K¯*0, and Ωcc*+ρ+ may form molecular strange double charm pentaquarks. In both pictures, the masses of the JP=1/2−,3/2− pentaquarks locate within the 4.2–4.6 GeV and 4.2–4.5 GeV regions, respectively. As all of them are above the thresholds of their strong decay channels, they behave as a broad state, making them challenging to be detected experimentally. On the other hand, the strange double charm pentaquark with JP=5/2− lies below its strong decay channel, which may be a very narrow state and easy to identify experimentally. The best observed channel is its semileptonic decay to double charm baryon. As the result, we strongly suggest experiments to search for JP=5/2− strange double charm pentaquarks first.

关键词： Multiquark bound states Nonperturbative effects in field theory quantum chromodynamics Strong interaction

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Estimation of Hamiltonian Parameters from Thermal States

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Physical Review Letters 2024年第4期133卷 040802-040802页

作者： Luis Pedro García-Pintos Kishor Bharti Jacob Bringewatt Hossein Dehghani Adam Ehrenberg Nicole Yunger Halpern Alexey V. Gorshkov Theoretical Division (T4) Joint Center for Quantum Information and Computer Science and Joint Quantum Institute Institute of High Performance Computing (IHPC) Agency for Science Technology and Research (A*STAR) 1 Fusionopolis Way # 16-16 Connexis Singapore 138632 Republic of Singapore Department of Physics Institute for Physical Science and Technology

We upper bound and lower bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term’s degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/n, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g., a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

关键词： quantum metrology quantum parameter estimation quantum sensing

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Coherent optical link phase noise control based on SPGD algorithm with optimal estimation 6

Coherent optical link phase noise control based on SPGD algo...

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6th Optics Young Scientist Summit, OYSS 2023

作者： Luo, Yihao Zhang, Jun Du, Shiyin Yan, Qiuquan Zhou, Tong Jiang, Tian College of Advanced Interdisciplinary Studies National University of Defense Technology Changsha410073 China National Innovation Institute of Defense Technology Academy of Military Sciences Pla China Beijing100071 China Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China Institute of Quantum Information Science and Technology College of Science National University of Defense Technology Changsha410073 China

ISBN: (纸本)9781510672642

The Stochastic Parallel Gradient Descent (SPGD) algorithm is a widely used model-free optimization algorithm in adaptive optical systems. However, when affected by noise, the SPGD algorithm may incorrectly estimate the gradient, resulting in a significant decrease in its performance and limitations in its application in complex environments. To address this issue, this paper introduces the optimal estimation algorithm and adds a self-checking process to the SPGD algorithm, proposing a Kal-SPGD algorithm. The feasibility of the Kal-SPGD algorithm is verified through simulation and experimentation. The experimental results show that compared with the standard SPGD, the use of the Kal-SPGD algorithm can reduce the signal amplitude variance by up to 92.15%. The Kal-SPGD algorithm provides a more favorable control technique for adaptive optical systems. © COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only.

关键词： Stochastic systems

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Faster Sampling Algorithms for Polytopes with Small Treewidth

Faster Sampling Algorithms for Polytopes with Small Treewidt...

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IEEE International Conference on Big Data

作者： Yekun Ke Xiaoyu Li Zhao Song Tianyi Zhou Department of Computer Science University of Washington Seattle WA Department of Computer Science Stevens Institute of Technology Hoboken NJ The Simons Institute for the Theory of Computing University of California Berkeley Berkeley CA Department of Computer Science University of Southern California Los Angeles CA

ISBN: (数字)9798350362480

ISBN: (纸本)9798350362497

Sampling is a fundamental problem in optimization, machine learning and theoretical computer science. A common region of interest for sampling is the polytope, which is defined by a set of linear inequalities. The algorithm that is sampling from polytopes usually requires heavy matrix algebra, including matrix multiplication, matrix inversion and matrix determinant. In this work, we show how to implement the heavy matrix algebra in the area of sampling in nearly linear time for the polytope that has small treewidth. In particular, given a polytope defined by a matrix A ∈ ℝ n×d with treewidth τ, we improve the running time of each iteration for three typical sampling algorithms for polytopes such as Dikin Walk, Soft-Threshold Dikin Walk and Vaidya Walk from O(nd 2 ) to O(nτ 2 ) by exploiting the small treewidth structures of the matrices.

关键词： computer science Costs Machine learning algorithms Machine learning Big Data Matrices Linear matrix inequalities Computational complexity Optimization

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Query Complexity of Unitary Operation Discrimination

SSRN

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SSRN 2022年

作者： Huang, Xiaowei Li, Lvzhou Institute of Quantum Computing and Computer Theory School of Computer and Engineering Sun Yat-sen University Guangzhou510006 China

Discrimination of unitary operations is fundamental in quantum computation and information. A lot of quantum algorithms including the well-known DeutschJozsa algorithm, Simon’s algorithm, and Grover’s algorithm can essentially be regarded as discriminating among individual, or sets of unitary operations (oracle operators). The problem of discriminating between two unitary operations U and V can be described as: Given X ∈ { U,V }, determine which one X is. If X is given with multiple copies, then one can design an adaptive procedure that takes multiple queries to X to output the identification result of X . In this paper, we consider the problem: How many queries are required for achieving a desired failure probability ϵ of discrimination between U and V . We prove in a uniform framework: (i) if U and V are discriminated with bound error ϵ , then the number of queries T must satisfy, and (ii) if they are discriminated with one-sided error ϵ , then there is, where Θ( W ) denotes the length of the smallest arc containing all the eigenvalues of W on the unit circle. © 2022, The Authors. All rights reserved.

关键词： quantum computers

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Efficient SGD Neural Network Training via Sublinear Activated Neuron Identification

Efficient SGD Neural Network Training via Sublinear Activate...

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IEEE International Conference on Big Data

作者： Lianke Qin Zhao Song Yuanyuan Yang Department of Computer Science University of California Santa Barbara Santa Barbara CA UC Berkeley Simons Institute for the Theory of Computing San Jose CA Department of Computer Science The University of Washington Seattle WA

ISBN: (数字)9798350362480

ISBN: (纸本)9798350362497

Deep learning has been widely used in many fields, but the model training process usually consumes massive computational resources and time. Therefore, designing an efficient neural network training method with a provable convergence guarantee is a fundamental and important research question. In this paper, we present a static half-space report data structure that consists of a fully connected two-layer neural network for shifted ReLU activation to enable activated neuron identification in sublinear time via geometric search. We also prove that our algorithm can converge in O(M 2 /ϵ 2 ) time with network size quadratic in the coefficient norm upper bound M and error term ϵ.

关键词： Training Deep learning Upper bound Computational modeling Neurons Data structures Kernel Biological neural networks Optimization Convergence

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Derandomization of quantum algorithm for triangle finding

arXiv

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arXiv 2023年

作者： Li, Guanzhong Li, Lvzhou Institute of Quantum Computing and Software School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China

Derandomization is the process of taking a randomized algorithm and turning it into a deterministic algorithm, which has attracted great attention in classical computing. In quantum computing, it is challenging and intriguing to derandomize quantum algorithms, due to the inherent randomness of quantum mechanics. The significance of derandomizing quantum algorithms lies not only in theoretically proving that the success probability can essentially be 1 without sacrificing quantum speedups, but also in experimentally improving the success rate when the algorithm is implemented on a real quantum computer. In this paper, we focus on derandomizing quanmtum algorithms for the triangle sum problem (including the famous triangle finding problem as a special case), which asks to find a triangle in an edge-weighted graph with n vertices, such that its edges sum up to a given weight. We show that when the graph is promised to contain at most one target triangle, there exists a deterministic quantum algorithm that either finds the triangle if it exists or outputs "no triangle" if none exists. It makes O(n9/7) queries to the edge weight matrix oracle, and thus has the same complexity with the state-of-art bounded-error quantum algorithm. To achieve this derandomization, we make full use several techniques: nested quantum walks with quantum data structure, deterministic quantum search with adjustable parameters, and dimensional reduction of quantum walk search on Johnson graph. © 2023, CC BY.

关键词： quantum theory

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On Statistical Rates and Provably Efficient Criteria of Latent Diffusion Transformers (DiTs) 38

On Statistical Rates and Provably Efficient Criteria of Late...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Hu, Jerry Yao-Chieh Wu, Weimin Li, Zhuoru Pi, Sophia Song, Zhao Liu, Han Center for Foundation Models and Generative AI Northwestern University EvanstonIL60208 United States Department of Computer Science Northwestern University EvanstonIL60208 United States Department of Statistics and Data Science Northwestern University EvanstonIL60208 United States Simons Institute for the Theory of Computing UC Berkeley BerkeleyCA94720 United States

We investigate the statistical and computational limits of latent Diffusion Transformers (DiTs) under the low-dimensional linear latent space assumption. Statistically, we study the universal approximation and sample complexity of the DiTs score function, as well as the distribution recovery property of the initial data. Specifically, under mild data assumptions, we derive an approximation error bound for the score network of latent DiTs, which is sub-linear in the latent space dimension. Additionally, we derive the corresponding sample complexity bound and show that the data distribution generated from the estimated score function converges toward a proximate area of the original one. Computationally, we characterize the hardness of both forward inference and backward computation of latent DiTs, assuming the Strong Exponential Time Hypothesis (SETH). For forward inference, we identify efficient criteria for all possible latent DiTs inference algorithms and showcase our theory by pushing the efficiency toward almost-linear time inference. For backward computation, we leverage the low-rank structure within the gradient computation of DiTs training for possible algorithmic speedup. Specifically, we show that such speedup achieves almost-linear time latent DiTs training by casting the DiTs gradient as a series of chained low-rank approximations with bounded error. Under the low-dimensional assumption, we show that the statistical rates and the computational efficiency are all dominated by the dimension of the subspace, suggesting that latent DiTs have the potential to bypass the challenges associated with the high dimensionality of initial data. © 2024 Neural information processing systems foundation. All rights reserved.

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quantum and Classical Query Complexities for Determining Connectedness of Matroids

SSRN

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SSRN 2023年

作者： Huang, Xiaowei Feng, Shiguang Li, Lvzhou Institute of Quantum Computing and and Software School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China

Connectivity is a fundamental structural property of matroids, and has been studied algorithmically over 50 years. To the best of our knowledge, the classical query complexity lower bound and the quantum complexity for this problem have not been considered. Thus, in this paper we are devoted to addressing these issues, and our contributions are threefold as follows:(i) First, we prove that the randomized query complexity of determining whether a matroid is connected is $\Omega(n^2)$ and thus the algorithm proposed by Cunningham is optimal in classical computing. (ii) Second, we present a quantum algorithm with $O(n^{3/2})$ queries, which exhibits provable quantum speedups over classical ones.(iii) Third, we prove that any quantum algorithm requires $\Omega(n)$ queries, which indicates that quantum algorithms can achieve at most a quadratic speedup over classical ones. Therefore, we have a relatively comprehensive understanding of the potential of quantum computing in determining the connectedness of matroids. © 2023, The Authors. All rights reserved.

关键词： quantum theory

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