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Thermodynamics of quantum Switch Information Capacity Activation

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Physical Review Letters 2022年第23期129卷 230604-230604页

作者： Xiangjing Liu Daniel Ebler Oscar Dahlsten Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and Technology Shenzhen 518055 China Theory Lab Central Research Institute 2012 Labs Huawei Technology Co. Ltd. Hong Kong Science Park Hong Kong SAR Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong SAR

We address a new setting where the second law is under question: thermalizations in a quantum superposition of causal orders, enacted by the so-called quantum switch. This superposition has been shown to be associated with an increase in the communication capacity of the channels, yielding an apparent violation of the data-processing inequality and a possibility to separate hot from cold. We analyze the thermodynamics of this information capacity increasing process. We show how the information capacity increase is compatible with thermodynamics. We show that there may indeed be an information capacity increase for consecutive thermalizations obeying the first and second laws of thermodynamics if these are placed in an indefinite order and moreover that only a significantly bounded increase is possible. The increase comes at the cost of consuming a thermodynamic resource, the free energy of coherence associated with the switch.

关键词： quantum channels quantum information theory quantum thermodynamics Resource theories

QDCNN: quantum Deep Learning for Enhancing Safety and Reliability in Autonomous Transportation Systems

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arXiv 2025年

作者： Meghanath, Ashtakala Das, Subham Behera, Bikash K. Khan, Muhammad Attique Al-Kuwari, Saif Farouk, Ahmed Department of Physics Indian Institute of Science Education and Research Thiruvananthapuram India Pvt. Ltd. WB Mohanpur741246 India Department of AI College of Computer Engineering and Science Prince Mohammad Bin Fahd University Al Khobar Saudi Arabia Qatar Center for Quantum Computing College of Science and Engineering Hamad Bin Khalifa University Doha Qatar Department of Computer Science Faculty of Computers and Artificial Intelligence Hurghada University Hurghada Egypt

In transportation cyber-physical systems (CPS), ensuring safety and reliability in real-time decision-making is essential for successfully deploying autonomous vehicles and intelligent transportation networks. However, these systems face significant challenges, such as computational complexity and the ability to handle ambiguous inputs like shadows in complex environments. This paper introduces a quantum Deep Convolutional Neural Network (QDCNN) designed to enhance the safety and reliability of CPS in transportation by leveraging quantum algorithms. At the core of QDCNN is the UU† method, which is utilized to improve shadow detection through a propagation algorithm that trains the centroid value with preprocessing and postprocessing operations to classify shadow regions in images accurately. The proposed QDCNN is evaluated on three datasets on normal conditions and one road affected by rain to test its robustness. It outperforms existing methods in terms of computational efficiency, achieving a shadow detection time of just 0.0049352 seconds, faster than classical algorithms like intensity-based thresholding (0.03 seconds), chromaticity-based shadow detection (1.47 seconds), and local binary pattern techniques (2.05 seconds). This remarkable speed, superior accuracy, and noise resilience demonstrate QDCNN’s —key factors for safe navigation in autonomous transportation in real-time. This research demonstrates the potential of quantum-enhanced models in addressing critical limitations of classical methods, contributing to more dependable and robust autonomous transportation systems within the CPS framework. © 2025, CC BY.

关键词： Convolutional neural networks

quantum game theory and the complexity of approximating quantum Nash equilibria

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arXiv 2021年

作者： Bostanci, John Watrous, John Computer Science Department Columbia University United States Institute for Quantum Computing School of Computer Science University of Waterloo Canada

This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that the computational problem of finding an approximate Nash equilibrium in a broad class of quantum games is, like the analogous problem for classical games, included in (and therefore complete for) the complexity class PPAD. Our main technical contribution, which facilitates this inclusion, is an extension of prior methods in computational game theory to strategy spaces that are characterized by semidefinite programs. © 2021, CC BY-SA.

关键词： quantum optics

Hamiltonian Simulation with Random Inputs

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Physical Review Letters 2022年第27期129卷 270502-270502页

作者： Qi Zhao You Zhou Alexander F. Shaw Tongyang Li Andrew M. Childs Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA QICI Quantum Information and Computation Initiative Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong Key Laboratory for Information Science of Electromagnetic Waves (Ministry of Education) Fudan University Shanghai 200433 China Nanyang Quantum Hub School of Physical and Mathematical Sciences Nanyang Technological University 637371 Singapore Center on Frontiers of Computing Studies Peking University Beijing 100871 China School of Computer Science Peking University Beijing 100871 China Center for Theoretical Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Computer Science and Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 USA

The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic. To address this, we develop a theory of average-case performance of Hamiltonian simulation with random initial states. We relate the average-case error to the Frobenius norm of the multiplicative error and give upper bounds for the product formula (PF) and truncated Taylor series methods. As applications, we estimate average-case error for the digital Hamiltonian simulation of general lattice Hamiltonians and k-local Hamiltonians. In particular, for the nearest-neighbor Heisenberg chain with n spins, the error is quadratically reduced from O(n) in the worst case to O(n) on average for both the PF method and the Taylor series method. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models. We also apply our results to error analysis in the simulation of quantum scrambling.

关键词： quantum algorithms quantum computation quantum simulation

On Differentially Private String Distances

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arXiv 2024年

作者： Hu, Jerry Yao-Chieh Liu, Erzhi Liu, Han Song, Zhao Zhang, Lichen Ensemble AI San FranciscoCA United States Center for Foundation Models and Generative AI Department of Computer Science Northwestern University EvanstonIL United States Center for Foundation Models and Generative AI Department of Computer Science Department of Statistics and Data Science Northwestern University EvanstonIL United States Simons Institute for the Theory of Computing UC Berkeley BerkeleyCA United States Department of Mathematics & Computer Science and Artificial Intelligence Laboratory MIT CambridgeMA United States

Given a database of bit strings A1, . . ., Am ∈ {0, 1}n, a fundamental data structure task is to estimate the distances between a given query B ∈ {0, 1}n with all the strings in the database. In addition, one might further want to ensure the integrity of the database by releasing these distance statistics in a secure manner. In this work, we propose differentially private (DP) data structures for this type of tasks, with a focus on Hamming and edit distance. On top of the strong privacy guarantees, our data structures are also time- and space-efficient. In particular, our data structure is ǫ-DP against any sequence of queries of arbitrary length, and for any query B such that the maximum distance to any string in the database is at most k, we output m distance estimates. Moreover, • For Hamming distance, our data structure answers any query in Oe(mk + n) time and each estimate deviates from the true distance by at most Oe(k/eǫ/ log k);• For edit distance, our data structure answers any query in Oe(mk2 + n) time and each estimate deviates from the true distance by at most Oe(k/eǫ/(log k log n)). For moderate k, both data structures support sublinear query operations. We obtain these results via a novel adaptation of the randomized response technique as a bit flipping procedure, applied to the sketched strings. © 2024, CC BY-NC-SA.

关键词： Structured Query Language

Time-energy uncertainty relation for noisy quantum metrology

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Time-energy uncertainty relation for noisy quantum metrology

Conference on quantum Information and Measurement, ICQI 2021

作者： Faist, Philippe Woods, Mischa P. Albert, Victor V. Renes, Joseph M. Eisert, Jens Preskill, John Dahlem Center for Complex Quantum Systems Freie Universität Berlin Germany Institute for Theoretical Physics ETH Zürich Switzerland National Institute of Standards and Technology United States Joint Center for Quantum Information and Computer Science University of Maryland United States Institute for Quantum Information and Matter Caltech United States Walter Burke Institute for Theoretical Physics Caltech United States AWS Center for Quantum Computing Caltech Pasadena United States

We derive a fundamental trade-off relating the accuracy loss of a quantum clock due to a noise channel to the information about the energy of the clock that leaks to the environment. © Optica Publishing Group 202... 详细信息

ISBN: (纸本)9781957171012

关键词： Clocks

Multi-qutrit exact synthesis

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arXiv 2024年

作者： Kalra, Amolak Ratan Saikia, Manimugdha Valluri, Dinesh Winnick, Sam Yard, Jon Institute for Quantum Computing University of Waterloo WaterlooON Canada David R. Cheriton School of Computer Science University of Waterloo WaterlooON Canada Dept. of Combinatorics & Optimization University of Waterloo WaterlooON Canada Perimeter Institute for Theoretical Physics WaterlooON Canada Department of Mathematics University of Western Ontario LondonON Canada

We present an exact synthesis algorithm for qutrit unitaries in U3n([1/3, e2πi/3]) over the Clifford+T gate set with at most one ancilla. This extends the already known result of qutrit metaplectic gates being a subset of Clifford+T gate set with one ancilla. As an intermediary step, we construct an algorithm to convert 3-level unitaries into multiply-controlled gates, analogous to Gray codes converting 2-level unitaries into multiply-controlled gates. Finally, using catalytic embeddings, we present an algorithm to exactly synthesize unitaries U3n([1/3, e2πi/9]) over the Clifford+T gate set with at most 2 ancillas. This, in particular, gives an exact synthesis algorithm of single-qutrit Clifford+D over the multi-qutrit Clifford+T gate set with at most two ancillas. Copyright © 2024, The Authors. All rights reserved.

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Genuine multifractality in time series is due to temporal correlations

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Physical Review E 2023年第3期107卷 034139-034139页

作者： Jarosław Kwapień Pawel Blasiak Stanisław Drożdż Paweł Oświęcimka Complex Systems Theory Department Institute of Nuclear Physics Polish Academy of Sciences ul. Radzikowskiego 152 31-342 Kraków Poland Institute for Quantum Studies Chapman University Orange California 92866 USA Faculty of Computer Science and Telecommunications Cracow University of Technology ul. Warszawska 24 31-155 Kraków Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Łojasiewicza 11 30-348 Kraków Poland

Based on the mathematical arguments formulated within the multifractal detrended fluctuation analysis (MFDFA) approach it is shown that, in the uncorrelated time series from the Gaussian basin of attraction, the effects resembling multifractality asymptotically disappear for positive moments when the length of time series increases. A hint is given that this applies to the negative moments as well and extends to the Lévy stable regime of fluctuations. The related effects are also illustrated and confirmed by numerical simulations. This documents that the genuine multifractality in time series may only result from the long-range temporal correlations, and the fatter distribution tails of fluctuations may broaden the width of the singularity spectrum only when such correlations are present. The frequently asked question of what makes multifractality in time series—temporal correlations or broad distribution tails—is thus ill posed. In the absence of correlations only the bifractal or monofractal cases are possible. The former corresponds to the Lévy stable regime of fluctuations while the latter to the ones belonging to the Gaussian basin of attraction in the sense of the central limit theorem.

关键词： Scaling laws of complex systems Stochastic processes & statistics

quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

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PRX quantum 2024年第1期5卷 010345-010345页

作者： Priyanka Mukhopadhyay Torin F. Stetina Nathan Wiebe Department of Physical & Environmental Sciences University of Toronto Ontario M1C 1A4 Canada Simons Institute for the Theory of Computing Berkeley California 94720 USA Berkeley Quantum Information and Computation Center University of California Berkeley California 94720-1460 USA Department of Computer Science University of Toronto Ontario M5S 2E4 Canada Pacific Northwest National Laboratory Richland Washington 99354 USA Canadian Institute for Advanced Research Toronto Ontario M5G 1M1 Canada

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O~(ΛN2η2t2/ϵ) for grid size N, η particles, simulation time t, field cutoff Λ, and error ϵ. Our qubitization algorithm scales as O~(N(η+N)(η+Λ2)tlog (1/ϵ)). This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ. We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled-X gates that can be used for better analysis of circuit cost.

关键词： quantum simulation