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Sachdev-Ye-Kitaev charging advantage as a random walk on graphs

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Physical Review B 2025年第7期111卷 075138-075138页

作者： Francisco Divi Jeff Murugan Dario Rosa ICTP South American Institute for Fundamental Research Instituto de Física Teórica UNESP - Universidade Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271 01140-070 São Paulo SP Brazil Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town South Africa The National Institute for Theoretical and Computational Sciences Private Bag X1 Matieland South Africa

We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size N and the facilitation of operator delocalization by specific graph structures. A graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes.

关键词： Quantum chaos

Generation and structural characterization of Debye random media

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Physical Review E 2020年第4期102卷 043310-043310页

作者： Zheng Ma Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In their seminal paper on scattering by an inhomogeneous solid, Debye and coworkers proposed a simple exponentially decaying function for the two-point correlation function of an idealized class of two-phase random media. Such Debye random media, which have been shown to be realizable, are singularly distinct from all other models of two-phase media in that they are entirely defined by their one- and two-point correlation functions. To our knowledge, there has been no determination of other microstructural descriptors of Debye random media. In this paper, we generate Debye random media in two dimensions using an accelerated Yeong-Torquato construction algorithm. We then ascertain microstructural descriptors of the constructed media, including their surface correlation functions, pore-size distributions, lineal-path function, and chord-length probability density function. Accurate semianalytic and empirical formulas for these descriptors are devised. We compare our results for Debye random media to those of other popular models (overlapping disks and equilibrium hard disks) and find that the former model possesses a wider spectrum of hole sizes, including a substantial fraction of large holes. Our algorithm can be applied to generate other models defined by their two-point correlation functions, and their other microstructural descriptors can be determined and analyzed by the procedures laid out here.

关键词： Patterns in complex systems

One-sided GRP solver and numerical boundary conditions for compressible fluid flows

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arXiv 2021年

作者： Li, Jiequan Zhang, Qinglong Institute of Applied Physics and Computational Mathematics Beijing Center for Applied Physics and Technology Peking University China State Key Laboratory for Turbulence Research and Complex System Peking University China Department of Mathematics and Statistics Ningbo University China

In the computation of compressible fluid flows, numerical boundary conditions are always necessary for all physical variables at computational boundaries while just partial physical variables are often prescribed as physical boundary conditions. Certain extrapolation technique or ghost cells are often employed traditionally for this issue but spurious wave reflections often arise to cause numerical instability. In this paper, we associate this issue with the one-sided generalized Riemann problem (GRP) solver motivated by the accelerated piston problem in gas dynamics so that the extrapolation technique can be actually avoided. In fact, the compatibility arguments naturally requires to formulate the one-sided generalized Riemann problem and incorporate it into the numerical procedure of boundary conditions. As far as the interaction of nonlinear waves with physical boundaries, such a one-sided GRP solver shows significant effects, as numerical experiments demonstrate, on avoiding spurious wave reflections at the computational boundaries. Copyright © 2021, The Authors. All rights reserved.

关键词： Boundary conditions

On the approximability of random-hypergraph MAX-3-XORSAT problems with quantum algorithms

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arXiv 2023年

作者： Kapit, Eliot Barton, Brandon A. Feeney, Sean Grattan, George Patnaik, Pratik Sagal, Jacob Carr, Lincoln D. Oganesyan, Vadim Department of Physics Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Quantum Engineering Program Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Physics and Astronomy College of Staten Island CUNY Staten IslandNY10314 United States Physics Program and Initiative for the Theoretical Sciences The Graduate Center CUNY New YorkNY10016 United States Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New YorkNY10010 United States

A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of any guided local minimum escape method ensures both exact and approximate classical approximation hardness, but the equivalent mechanism(s) for quantum algorithms are poorly understood. For algorithms based on Hamiltonian time evolution, we explore this question through the prototypically hard MAX-3-XORSAT problem class. We conclude that the mechanisms for quantum exact and approximation hardness are fundamentally distinct. We review known results from the literature, and identify mechanisms that make conventional quantum methods (such as Adiabatic Quantum Computing) weak approximation algorithms in the worst case. We construct a family of "spectrally filtered" quantum algorithms that escape these issues, and develop analytical theories for their performance. We show that, for random hypergraphs in the approximation-hard regime, if we define the energy to be E = Nunsat - Nsat, spectrally filtered quantum optimization will return states with E ≤ qmEGS (where EGS is the ground state energy) in sub-quadratic time, where conservatively, qm 0.59. This is in contrast to qm → 0 for the hardest instances with classical searches. We test all of these claims with extensive numerical simulations. We do not claim that this approximation guarantee holds for all possible hypergraphs, though our algorithm’s mechanism can likely generalize widely. These results suggest that quantum computers are more powerful for approximate optimization than had been previously assumed. © 2023, CC BY.

关键词： Constraint satisfaction problems

Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations

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arXiv 2023年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location

Local number fluctuations in ordered and disordered phases of water across temperatures: Higher-order moments and degrees of tetrahedrality

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arXiv 2024年

作者： Klatt, Michael A. Kim, Jaeuk Gartner, Thomas E. Torquato, Salvatore Institute for AI Safety and Security Wilhelm-Runge-Str. 10 Ulm89081 Germany Institute for Material Physics in Space Köln51170 Germany Department of Physics Ludwig-Maximilians-Universität München Schellingstr. 4 Munich80799 Germany Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Department of Chemical & Biomolecular Engineering Lehigh University BethlehemPA18015 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The isothermal compressibility (i.e., the asymptotic number variance) of equilibrium liquid water as a function of temperature is minimal near ambient conditions. This anomalous non-monotonic temperature dependence is due to a balance between thermal fluctuations and the formation of tetrahedral hydrogen-bond networks. Since tetrahedrality is a many-body property, it will also influence the higher-order moments of density fluctuations, including the skewness and kurtosis. To gain a more complete picture, we examine these higher-order moments that encapsulate many-body correlations using a recently developed, advanced platform for local density fluctuations. We study an extensive set of simulated phases of water across a range of temperatures (80 K to 1600 K) with various degrees of tetrahedrality, including ice phases, equilibrium liquid water, supercritical water, and disordered nonequilibrium quenches. We find clear signatures of tetrahedrality in the higher-order moments, including the skewness and excess kurtosis, that scale for all cases with the degree of tetrahedrality. More importantly, this scaling behavior leads to non-monotonic temperature dependencies in the higher-order moments for both equilibrium and non-equilibrium phases. Specifically, at near-ambient conditions, the higher-order moments vanish most rapidly for large length scales, and the distribution quickly converges to a Gaussian in our metric. However, at non-ambient conditions, higher-order moments vanish more slowly and hence become more relevant especially for improving information-theoretic approximations of hydrophobic solubility. The temperature non-monotonicity that we observe in the full distribution across length-scales could shed light on water's nested anomalies, i.e., reveal new links between structural, dynamic, and thermodynamic anomalies. © 2024, CC BY-NC-ND.

关键词： Higher order statistics

Impact of time-correlated noise on zero-noise extrapolation

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Physical Review A 2022年第5期106卷 052406-052406页

作者： Kevin Schultz Ryan LaRose Andrea Mari Gregory Quiroz Nathan Shammah B. David Clader William J. Zeng Johns Hopkins University Applied Physics Laboratory Laurel Maryland 20723 USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing Michigan 48823 USA Unitary Fund Walnut California 91789 USA Goldman Sachs & Co New York New York 10282 USA

Zero-noise extrapolation is a quantum error mitigation technique that has typically been studied under the ideal approximation that the noise acting on a quantum device is not time correlated. In this paper, we investigate the feasibility and performance of zero-noise extrapolation in the presence of time-correlated noise. We show that, in contrast to white noise, time-correlated noise is harder to mitigate via zero-noise extrapolation because it is difficult to scale the noise level without also modifying its spectral distribution. This limitation is particularly strong if “local” gate-level methods are applied for noise scaling. However, we find that “global” noise-scaling methods, e.g., global unitary folding, can be sufficiently reliable even in the presence of time-correlated noise.

关键词： Quantum algorithms Quantum benchmarking Quantum control

Equivariant geometric convolutions for emulation of dynamical systems

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arXiv 2023年

作者： Gregory, Wilson G. Hogg, David W. Blum-Smith, Ben Arias, Maria Teresa Wong, Kaze W.K. Villar, Soledad Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD United States Center for Cosmology and Particle Physics Department of Physics New York University New YorkNY United States Max-Planck-Institut für Astronomie Heidelberg Germany Center for Computational Astrophysics Flatiron Institute New YorkNY United States Department of Mathematics Universidad Autónoma de Madrid Madrid Spain Mathematical Institute for Data Science Johns Hopkins University BaltimoreMD United States

Machine learning methods are increasingly being employed as surrogate models in place of computationally expensive and slow numerical integrators for a bevy of applications in the natural sciences. However, while the laws of physics are relationships between scalars, vectors, and tensors that hold regardless of the frame of reference or chosen coordinate system, surrogate machine learning models are not coordinate-free by default. We enforce coordinate freedom by using geometric convolutions in three model architectures: a ResNet, a Dilated ResNet, and a UNet. In numerical experiments emulating 2D compressible Navier-Stokes, we see better accuracy and improved stability compared to baseline surrogate models in almost all cases. The ease of enforcing coordinate freedom without making major changes to the model architecture provides an exciting recipe for any CNN-based method applied to an appropriate class of problems. © 2023, CC BY.

关键词： Convolution

Breakdown of Boltzmann-type Models for the Alignment of Self-propelled Rods

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arXiv 2023年

作者： Murphy, Patrick Perepelitsa, Misha Timofeyev, Ilya Lieber-Kotz, Matan Islas, Brandon Igoshin, Oleg A. Department of Bioengineering Rice University HoustonTX77005 United States Center for Theoretical Biological Physics Rice University HoustonTX77005 United States Department of Mathematics University of Houston TX77204 United States Department of Computational and Applied Mathematics Rice University HoustonTX77005 United States Department of Chemistry Rice University HoustonTX77005 United States Department of Biosciences Rice University HoustonTX77005 United States

Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann’s hypothesis of"molecular chaos", that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems. © 2023, CC BY.

关键词： Boltzmann equation