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Second moment of Hafnians in Gaussian boson sampling

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Physical Review A 2025年第4期111卷 042412-042412页

Gaussian boson sampling is a popular method for experimental demonstrations of quantum advantage, but many subtleties remain in fully understanding its theoretical underpinnings. An important component in the theoretical arguments for approximate average-case hardness of sampling is anticoncentration, which is a second-moment property of the output probabilities. In Gaussian boson sampling these are given by hafnians of generalized circular orthogonal ensemble matrices. In a companion work by Ehrenberg et al. [Phys. Rev. Lett. 134, 140601 (2025)], we develop a graph-theoretic method to study these moments and use it to identify a transition in anticoncentration. In this work, we find a recursive expression for the second moment using these graph-theoretic techniques. While we have not been able to solve this recursion by hand, we are able to solve it numerically exactly, which we do up to Fock sector 2n=80. We further derive analytical results about the second moment. These results allow us to pinpoint the transition in anticoncentration and furthermore yield the expected linear cross-entropy benchmarking score for an ideal (error-free) device.

关键词： Graph theory

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

quantum Hermitian conjugate and encoding unnormalized matrices

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arXiv 2025年

作者： Zenchuk, Alexander I. Qi, Wentao 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 School of Mathematical Sciences Zhejiang University Hangzhou310027 China

We further develop the family of matrix-manipulation algorithms based on the encoding the matrix elements into the probability amplitudes of the pure superposition state of a certain quantum system. We introduce two extensions to these algorithms which allow (i) to perform Hermitian conjugation of matrices under consideration and (ii) to weaken the restriction to the absolute values of matrix elements unavoidably imposed by the normalization condition for a pure quantum state. Both these extensions are applied to the matrix multiplication algorithm. Controlled measurement of ancilla state is implemented to avoid the problem of small success probability in the measurement process. © 2025, CC BY.

关键词： Encoding (symbols)

Remarks on controlled measurement and quantum algorithm for calculating Hermitian conjugate

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arXiv 2025年

作者： Fel’dman, Edward B. Zenchuk, Alexander I. Qi, Wentao 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 School of Mathematical Sciences Zhejiang University Hangzhou310027 China

We present two new aspects for the recently proposed algorithms for matrix manipulating based on the special encoding the matrix elements into the superposition state of a quantum system. First aspect is the controlled measurement which allows to avoid the problem of small access probability to the required ancilla state at the final step of algorithms needed to remove the garbage of the states. Application of controlled measurement to the earlier developed algorithm is demonstrated. The second aspect is the algorithm for calculating the Hermitian conjugate of an arbitrary matrix, which supplements the algorithms proposed earlier. The appropriate circuits are presented. © 2025, CC BY.

关键词： quantum electronics

Matrix encoding method in variational quantum singular value decomposition

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arXiv 2025年

We propose the variational quantum singular value decomposition based on encoding the elements of the considered matrix into the state of a quantum system of appropriate dimension. This method doesn’t use the expansion of this matrix in terms of the unitary matrices. Conditional measurement is involved to avoid small success probability in ancilla measurement. The objective function for maximization algorithm can be obtained probabilistically via measurement of the state of a one-qubit subsystem. The circuit requires O(log N) qubits for realization of this algorithm whose depths is O(log N) as well. © 2025, CC BY.

关键词： Singular value decomposition

Scalable and fault-tolerant preparation of encoded k-uniform states

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arXiv 2025年

作者： Majidy, Shayan Hangleiter, Dominik Gullans, Michael J. Department of Physics Harvard University CambridgeMA02138 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Joint Center for Quantum Information and Computer Science University of Maryland NIST College ParkMD20742 United States

k-uniform states are valuable resources in quantum information, enabling tasks such as teleportation, error correction, and accelerated quantum simulations. The practical realization of k-uniform states, at scale, faces major obstacles: verifying k-uniformity is as difficult as measuring code distances, and devising fault-tolerant preparation protocols further adds to the complexity. To address these challenges, we present a scalable, fault-tolerant method for preparing encoded k-uniform states, and we illustrate our approach using surface and color codes. We first present a technique to determine k-uniformity of stabilizer states directly from their stabilizer tableau. We then identify a family of Clifford circuits that ensures both fault tolerance and scalability in preparing these states. Building on the encoded k-uniform states, we introduce a hybrid physical–logical strategy that retains some of the error-protection benefits of logical qubits while lowering the overhead for implementing arbitrary gates compared to fully logical algorithms. We show that this hybrid approach can outperform fully physical implementations for resource-state preparation, as demonstrated by explicit constructions of k-uniform states. Copyright © 2025, The Authors. All rights reserved.

关键词： Color codes

Blind calibration of a quantum computer

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arXiv 2025年

作者： Jeanette, Liam M. Wilkens, Jadwiga Roth, Ingo Than, Anton Green, Alaina M. Hangleiter, Dominik Linke, Norbert M. Joint Quantum Institute University of Maryland College ParkMD20742 United States Duke Quantum Center Duke University DurhamNC27701 United States Institute for Integrated Circuits Johannes Kepler University Linz Linz4040 Austria Quantum Research Center Technology Innovation Institute Abu Dhabi United Arab Emirates Simons Institute for the Theory of Computing University of California at Berkeley BerkeleyCA94720 United States Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD20742 United States

quantum system calibration is limited by the ability to characterize a quantum state under unknown device errors. We develop an accurate calibration protocol that is blind to the precise preparation of a specific quantum state. It extracts device errors from simple tomographic data only, and does not require bespoke experiments for a priori specified error mechanisms. Using a trapped-ion quantum computer, we experimentally demonstrate the accuracy of the method by recovering intentional miscalibrations. We then use blind calibration to estimate the native calibration parameters of the experimental system. The recovered calibrations are close to directly measured values and perform similarly in predicting state properties. © 2025, CC BY.

关键词： quantum computers

quantum speedup and limitations on matroid property problems

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Frontiers of computer Science 2024年第4期18卷 189-196页

作者： Xiaowei HUANG Jingquan LUO Lvzhou LI Institute of Quantum Computing and Computer Theory School of Computer Science and EngineeringSun Yat-sen UniversityGuangzhou 510006China

Matroid theory has been developed to be a mature branch of mathematics and has extensive applications in combinatorial optimization,algorithm design and so *** the other hand,quantum computing has attracted much attention and has been shown to surpass classical computing on solving some computational ***,crossover studies of the two fields seem to be missing in the *** paper initiates the study of quantum algorithms for matroid property *** is shown that quadratic quantum speedup is possible for the calculation problem of finding the girth or the number of circuits(bases,flats,hyperplanes)of a matroid,and for the decision problem of deciding whether a matroid is uniform or Eulerian,by giving a uniform lower boundΩ■on the query complexity of all these *** the other hand,for the uniform matroid decision problem,an asymptotically optimal quantum algorithm is proposed which achieves the lower bound,and for the girth problem,an almost optimal quantum algorithm is given with query complexityO■.In addition,for the paving matroid decision problem,a lower boundΩ■on the query complexity is obtained,and an O■ quantum algorithm is presented.

关键词： quantum computing matroid quantum algorithm quantum query complexity

quantum Hamiltonian Descent for Non-smooth Optimization

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arXiv 2025年

作者： Leng, Jiaqi Zheng, Yufan Jia, Zhiyuan Fan, Lei Zhao, Chaoyue Peng, Yuxiang Wu, Xiaodi Simons Institute for the Theory of Computing University of California Berkeley United States Department of Mathematics University of California Berkeley United States Department of Computer Science University of Maryland College Park United States Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Applied Mathematics University of Washington United States Department of Engineering Technology University of Houston United States Department of Electrical and Computer Engineering University of Houston United States Department of Industrial and Systems Engineering University of Washington United States Artephi Computing Inc United States

Non-smooth optimization models play a fundamental role in various disciplines, including engineering, science, management, and finance. However, classical algorithms for solving such models often struggle with convergence speed, scalability, and parameter tuning, particularly in high-dimensional and non-convex settings. In this paper, we explore how quantum mechanics can be leveraged to overcome these limitations. Specifically, we investigate the theoretical properties of the quantum Hamiltonian Descent (QHD) algorithm for non-smooth optimization in both continuous and discrete time. First, we propose continuous-time variants of the general QHD algorithm and establish their global convergence and convergence rate for non-smooth convex and strongly convex problems through a novel Lyapunov function design. Furthermore, we prove the finite-time global convergence of continuous-time QHD for non-smooth non-convex problems under mild conditions (i.e., locally Lipschitz). In addition, we propose discrete-time QHD, a fully digitized implementation of QHD via operator splitting (i.e., product formula). We find that discrete-time QHD exhibits similar convergence properties even with large time steps. Finally, numerical experiments validate our theoretical findings and demonstrate the computational advantages of QHD over classical non-smooth non-convex optimization algorithms. Copyright © 2025, The Authors. All rights reserved.

关键词： Continuous time systems