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Strategies for simulating the time evolution of Hamiltonian lattice field theories

Physical Review A 2025年第2期111卷 022419-022419页

作者： Siddharth Hariprakash Neel S. Modi Michael Kreshchuk Christopher F. Kane Christian W. Bauer Center for Theoretical Physics and Department of Physics University of California Berkeley California 94720 USA Physics Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA National Energy Research Scientific Computing Center (NERSC) Lawrence Berkeley National Laboratory Berkeley California 94720 USA Phasecraft Inc. Washington DC 20001 USA Department of Physics University of Arizona Tucson Arizona 85719 USA

Simulating the time evolution of quantum field theories given some Hamiltonian H requires developing algorithms for implementing the unitary operator e−iHt. A variety of techniques exist that accomplish this task, with the most common technique used so far being Trotterization, which is a special case of the application of a product formula. However, other techniques exist that promise better asymptotic scaling in certain parameters of the theory being simulated, the most efficient of which are based on the concept of block encoding. In this work we study the performance of such algorithms in simulating lattice field theories. We derive and compare the asymptotic gate complexities of several commonly used simulation techniques in application to Hamiltonian lattice field theories. Using the scalar φ̂4 theory as a test, we also perform numerical studies and compare the gate costs required by product formulas and signal-processing-based techniques to simulate time evolution. For the latter, we use the linear combination of unitaries (LCU) construction augmented with the quantum Fourier transform circuit to switch between the field and momentum eigenbases, which leads to immediate order-of-magnitude improvement in the cost of preparing the block encoding. This paper also includes a pedagogical review of the techniques used, in particular product formulas, LCU, qubitization, quantum signal processing, as well as the technique for simulating geometrically-local Hamiltonians developed by Haah, Hastings, Kothari, and Low.

关键词： Hamiltonians

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Polyp image segmentation based on improved planet optimization algorithm using reptile search algorithm

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Neural computing and Applications 2025年第8期37卷 6327-6349页

作者： Abd Elaziz, Mohamed Al-qaness, Mohammed A. A. Al-Betar, Mohammed Azmi Ewees, Ahmed A. Department of Mathematics Faculty of Science Zagazig University Zagazig Egypt College of Physics and Electronic Information Engineering Zhejiang Normal University Jinhua321004 China Zhejiang Institute of Optoelectronics Jinhua321004 China Faculty of Computer Science and Engineering Galala University Suze435611 Egypt Ajman University Ajman346 United Arab Emirates College of Computing and Information Technology University of Bisha Bisha Saudi Arabia Department of Computer Damietta University Damietta Egypt Hourani Center for Applied Scientific Research Al-Ahliyya Amman University Amman Jordan

To recognize the potential for colon polyps to develop into cancer over time, early diagnosis is crucial for preventative healthcare. Timely identification significantly improves the prognosis and treatment outcomes for colorectal cancer patients. Image segmentation is crucial in medical image analysis for accurate diagnosis and treatment planning. Therefore, in this study, we present an alternative multilevel thresholding polyp segmentation method (MPOA) to enhance the segmentation of polyp images. The proposed method is based on enhancing the planet optimization algorithm (POA) by integrating operators from the reptile search algorithm (RSA). The evaluation of the developed MPOA is tested with different polyp images and compared with other image segmentation approaches. The results highlight the superior capability of MPOA, as evidenced by various performance measures in effectively segmenting polyp images. Furthermore, metrics such as peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and fitness values demonstrate that MPOA outperforms the basic version of POA and other methods. The evaluation outcomes underscore the significant impact of RSA in enhancing the performance of POA for the segmentation of polyp images. © The Author(s) 2025.

关键词： Diseases

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Surrogate modeling of gravitational waves microlensed by spherically symmetric potentials

arXiv

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arXiv 2025年

作者： Deka, Uddeepta Prabhu, Gopalkrishna Shaikh, Md Arif Kapadia, Shasvath J. Varma, Vijay Field, Scott E. International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore560089 India Inter-University Centre for Astronomy and Astrophysics Post Bag 4 Ganeshkhind Pune411007 India Department of Physics Vivekananda Satavarshiki Mahavidyalaya Vidyasagar University West Bengal Manikpara721513 India Department of Physics and Astronomy Seoul National University Seoul08826 Korea Republic of Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

The anticipated observation of the gravitational microlensing of gravitational waves (GWs) promises to shed light on a host of astrophysical and cosmological questions. However, extracting the parameters of the lens from the modulated GWs requires accurate modeling of the lensing amplification factor, accounting for wave-optics effects. Analytic solutions to the lens equation have not been found to date, except for a handful of simplistic lens models. While numerical solutions to this equation have been developed, the time and computational resources required to evaluate the amplification factor numerically make large-scale parameter estimation of the lens (and source) parameters prohibitive. On the other hand, surrogate modeling of GWs has proven to be a powerful tool to accurately, and rapidly, produce GW templates at arbitrary points in parameter space, interpolating from a finite set of available waveforms at discrete parameter values. In this work, we demonstrate that surrogate modeling can also effectively be applied to the evaluation of the time-domain microlensing amplification factor eF(t), for arbitrary lens configurations. We show this by constructing eF(t) for two lens models, viz. point-mass lens, and singular isothermal sphere. We benchmark the evaluation times, and accuracy, of the surrogate microlensed templates, and show that indeed surrogate modeling is a powerful tool to make large-scale parameter estimation in the context of microlensed GWs practicable. © 2025, CC BY.

关键词： Time domain analysis

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A semi-adaptive finite difference method for simulating two-sided fractional convection-diffusion quenching problems

arXiv

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arXiv 2025年

作者： Dong, Rumin Zhu, Lin Sheng, Qin Zhao, Bingxin School of Mathematics and Statistics Ningxia Key Laboratory of Interdisciplinary Mechanics and Scientific Computing Ningxia Basic Science Research Center of Mathematics Ningxia University Yinchuan750021 China Department of Mathematics Center for Astrophysics Space Physics and Engineering Research Baylor University WacoTX76798-7328 United States

This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in conjunction with standard and shifted Grünwald formulas. The advective term is handled utilizing a straightforward Euler formula, resulting in a semi-discretized system of nonlinear ordinary differential equations. The conservativeness of the proposed scheme is rigorously proved and validated through simulation experiments. The study is further advanced to a fully discretized, semi-adaptive finite difference method. Detailed analysis is implemented for the monotonicity, positivity and stability of the scheme. Investigations are carried out to assess the potential impacts of the fractional order on quenching location, quenching time, and critical length. The computational results are thoroughly discussed and analyzed, providing a more comprehensive understanding of the quenching phenomena modeled through two-sided fractional order convection-diffusion problems. Copyright © 2025, The Authors. All rights reserved.

关键词： Ordinary differential equations

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Quantifying anatomically-based in-silico electrocardiogram variability for cardiac digital twins

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Computers in Biology and Medicine 2025年 189卷 109930-109930页

作者： Zappon, Elena Gsell, Matthias A.F. Gillette, Karli Plank, Gernot Division of Biophysics and Medical Physics Gottfried Schatz Research Center Medical University of Graz Graz Austria Scientific Computing and Imaging Institute University of Utah SLC UT United States Department of Biomedical Engineering University of Utah SLC UT United States BioTechMed-Graz Graz Austria

Human cardiac Cardiac digital twins (CDTs) are digital replicas of patient hearts, designed to match clinical observations precisely. The electro-cardiogram (ECG), as the most common non-invasive electrophysiology (EP) measurement, has been recently successfully employed for calibrating CDT. However, ECG-based calibration methods often fail to account for the inherent uncertainties in clinical data acquisition and CDT anatomical generation workflows. As a result, discrepancies inevitably arise between the actual physical and simulated patient EP and ECG. In this study, we aim to qualitatively and quantitatively analyze the impact of these uncertainties on ECG morphology and diagnostic markers, and therefore to assess the reliability of ECG-based CDT calibration. We analyze residual beat-to-beat variability in ECG recordings obtained from three datasets, including healthy subjects and patients treated for ventricular tachycardia and atrial fibrillation. Using a biophysically detailed and anatomically accurate computational model of whole-heart EP combined with a detailed torso model calibrated to closely replicate measured ECG signals, we vary anatomical factors (heart location, orientation, size), heterogeneity in electrical conductivities in the heart and torso, and electrode placements across ECG leads to assess their qualitative impact on ECG morphology. Our study demonstrates that diagnostically relevant ECG features and overall morphology remain close to the ground through ECG independently of the investigated uncertainties. This resilience is consistent with the narrow distribution of ECG due to residual beat-to-beat variability observed in both healthy subjects and patients. Overall, our results suggest that observation uncertainties do not impede an accurate calibration of the CDT. © 2025 The Authors

关键词： Heart

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Surrogate modeling of gravitational waves microlensed by spherically symmetric potentials

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Physical Review D 2025年第10期111卷 104042-104042页

作者： Uddeepta Deka Gopalkrishna Prabhu Md Arif Shaikh Shasvath J. Kapadia Vijay Varma Scott E. Field International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore 560089 India Inter-University Centre for Astronomy and Astrophysics Post Bag 4 Ganeshkhind Pune 411007 India Department of Physics Vivekananda Satavarshiki Mahavidyalaya (affiliated to Vidyasagar University) Manikpara 721513 West Bengal India Department of Physics and Astronomy Seoul National University Seoul 08826 South Korea Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA

The anticipated observation of the gravitational microlensing of gravitational waves (GWs) promises to shed light on a host of astrophysical and cosmological questions. However, extracting the parameters of the lens from the modulated GWs requires accurate modeling of the lensing amplification factor, accounting for wave-optics effects. Analytic solutions to the lens equation have not been found to date, except for a handful of simplistic lens models. While numerical solutions to this equation have been developed, the time and computational resources required to evaluate the amplification factor numerically make large-scale parameter estimation of the lens (and source) parameters prohibitive. On the other hand, surrogate modeling of GWs has proven to be a powerful tool to accurately, and rapidly, produce GW templates at arbitrary points in parameter space, interpolating from a finite set of available waveforms at discrete parameter values. In this work, we demonstrate that surrogate modeling can also effectively be applied to the evaluation of the time-domain microlensing amplification factor F˜(t). We show this by constructing F˜(t) for two lens models, viz. point-mass lens, and singular isothermal sphere, which notably includes logarithmic divergence behavior. We find both surrogates reproduce the original lens models accurately, with mismatches ≲5×10−4 across a range of plausible microlensed binary black hole sources observed by the Einstein Telescope. This surrogate is between 5 and 103 times faster than the underlying lensing models, and can be evaluated in about 100 ms. The accuracy and efficiency attained by our surrogate models will enable practical parameter estimation analyses of microlensed GWs.

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Superconvergent Discontinuous Galerkin Method for the Scalar Teukolsky Equation on Hyperboloidal Domains: Efficient Waveform and Self-Force Computation

arXiv

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arXiv 2025年

作者： Vishal, Manas Field, Scott E. Gottlieb, Sigal Ryan, Jennifer Department of Mathematics University of Massachusetts DartmouthMA02747 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden

The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta distribution) for self-force computations. Spectrally accurate methods, such as nodal discontinuous Galerkin (DG) methods, are well suited for these tasks. Their numerical errors typically decrease as ∝ (∆x)N+1, where ∆x is the subdomain size and N is the polynomial degree of the approximation. However, certain DG schemes exhibit superconvergence, where truncation, phase, and dispersion errors can decrease as fast as ∝ (∆x)2N+1. Superconvergent numerical solvers are, by construction, extremely efficient and accurate. We theoretically demonstrate that our DG scheme for the scalar Teukolsky equation with a distributional source is superconvergent, and this property is retained when combined with the hyperboloidal layer compactification technique. This ensures that waveforms, total energy and angular-momentum fluxes, and self-force computations benefit from superconvergence. We empirically verify this behavior across a family of hyperboloidal layer compactifications with varying degrees of smoothness. Additionally, we show that self-force quantities for circular orbits, computed at the point particle’s location, also exhibit a certain degree of superconvergence. Our results underscore the potential benefits of numerical superconvergence for efficient and accurate gravitational waveform simulations based on DG methods. Copyright © 2025, The Authors. All rights reserved.

关键词： Galerkin methods

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Exact block encoding of imaginary time evolution with universal quantum neural networks

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Physical Review research 2025年第1期7卷 013306-013306页

作者： Ermal Rrapaj Evan Rule National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA RIKEN iTHEMS Wako Saitama 351-0198 Japan Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function Ansatz is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the Ansatz yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

关键词： Stochastic systems

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Surrogate model for gravitational wave signals from comparable and large-mass-ratio black hole binaries

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Physical Review D 2020年第8期101卷 081502(R)-081502(R)页

作者： Nur E. M. Rifat Scott E. Field Gaurav Khanna Vijay Varma Department of Physics and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Mathematics and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Theoretical Astrophysics California Institute of Technology Pasadena California 91125 USA

Gravitational wave signals from compact astrophysical sources such as those observed by LIGO and Virgo require a high-accuracy, theory-based waveform model for the analysis of the recorded signal. Current inspiral-merger-ringdown models are calibrated only up to moderate mass ratios, thereby limiting their applicability to signals from high-mass-ratio binary systems. We present EMRISur1dq1e4, a reduced-order surrogate model for gravitational waveforms of 13 500 M in duration and including several harmonic modes for nonspinning black hole binary systems with mass ratios varying from 3 to 10000, thus vastly expanding the parameter range beyond the current models. This surrogate model is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) both for large-mass-ratio and comparable mass-ratio binaries. We observe that the gravitational waveforms generated through a simple application of ppBHPT to the comparable mass-ratio cases agree surprisingly well with those from full numerical relativity after a rescaling of the ppBHPT’s total mass parameter. This observation and the EMRISur1dq1e4 surrogate model will enable data analysis studies in the high-mass-ratio regime, including potential intermediate-mass-ratio signals from LIGO/Virgo and extreme-mass-ratio events of interest to the future space-based observatory LISA.

关键词： Classical black holes General relativity equations & solutions Gravitational wave sources

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Testing eccentric corrections to the radiation-reaction force in the test-mass limit of effective-one-body models

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Physical Review D 2025年第4期111卷 044036-044036页

作者： Guglielmo Faggioli Maarten van de Meent Alessandra Buonanno Aldo Gamboa Mohammed Khalil Gaurav Khanna Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 Potsdam 14476 Germany Niels Bohr International Academy Niels Bohr Institute Blegdamsvej 17 2100 Copenhagen Denmark Department of Physics University of Maryland College Park Maryland 20742 USA Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo Ontario N2L 2Y5 Canada Department of Physics and Center for Computational Research University of Rhode Island Kingston Rhode Island 02881 USA Department of Physics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Data Science Research University of Massachusetts Dartmouth Massachusetts 02747 USA

In this work, we test an effective-one-body radiation-reaction force for eccentric planar orbits of a test mass in a Kerr background, which contains third-order post-Newtonian (PN) nonspinning and second-order PN spin contributions. We compare the analytical fluxes connected to two different resummations of this force, truncated at different PN orders in the eccentric sector, with the numerical fluxes computed through the use of frequency- and time-domain Teukolsky-equation codes. We find that the different PN truncations of the radiation-reaction force show the expected scaling in the weak gravitational-field regime, and we observe a fractional difference with the numerical fluxes that is <5%, for orbits characterized by eccentricity 0≤e≤0.7, central black-hole spin −0.99M≤a≤0.99M and fixed orbital-averaged quantity x=⟨MΩ⟩2/3=0.06, corresponding to the mildly strong-field regime with semilatera recta 9M

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