Finding the Dynamics of an Integrable Quantum Many-Body System via Machine Learning

Aug 5, 2026

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Study of the Gaudin magnet (central-spin model) dynamics using machine-learning techniques addresses the difficulty of obtaining closed-form analytic time evolution despite the model’s integrability and many conserved quantities. The work represents each variational eigenstate with a restricted Boltzmann machine and uses variational Monte Carlo to accurately capture the ground state and low-lying excitations. From these states, the non-perturbative dynamic transverse spin susceptibility is extracted, enabling linear-response characterization of a central spin driven by a time-varying transverse field in a spin bath. Efficient susceptibility descriptions support improved qubit characterization and quantum control.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

AccessFree to download

Introduction

Quantum many-body dynamics and simulation challenges

Variational Monte Carlo and neural-network quantum states

Gaudin magnet motivation and goals

arXiv :2307 .03310v1 [ quant-ph] 6 Jul 2023 Finding the Dynamics of an Integrable Quantum Many-Body System via Machine Learning Victor Wei, 1, 2, 3, 􀀃 Alev Or􀀌, 1, 2, 3, y Felix Fehse, 1, z and W. A. Coish 1, x 1 Department of Physics, McGill University, Montreal, QC, Canada 2 Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada 3 Department of Physics and Astronomy, University of Waterloo, ON, Canada (Dated: July 10, 2023) We study the dynamics of the Gaudin magnet (\central-spin model") using machine-learning methods. This model is of practical importance, e.g., for studying non-Markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivity. The Gaudin magnet is also integrable, admitting many conserved quantities: For N spins, the model Hamiltonian can be written as the sum of N independent commuting operators. Despite this high degree of symmetry, a general closed-form analytic solution for the dynamics of this many-body problem remains elusive. Machine-learning methods may be well suited to exploiting the high degree of symmetry in integrable problems, even when an explicit analytic solution is not obvious. Motivated in part by this intuition, we use a neural-network representation (restricted Boltzmann machine) for each variational eigenstate of the model Hamiltonian. We then obtain accurate representations of the ground state and of the low-lying excited states of the Gaudin-magnet Hamiltonian through a variational Monte Carlo calculation. From the low-lying eigenstates, we 􀀌nd the non-perturbative dynamic transverse spin susceptibility, describing the linear response of a central spin to a time-varying transverse magnetic 􀀌eld in the presence of a spin bath. Having an e􀀎cient description of this susceptibility opens the door to improved characterization and quantum control procedures for qubits interacting with an environment of quantum two-level systems. These systems include electron-spin and hole-spin qubits interacting with environmental nuclear spins via hyper􀀌ne interactions or qubits with charge or 􀀍ux degrees of freedom interacting with coherent charge or paramagnetic impurities. I. INTRODUCTION Predicting the dynamics of quantum many-body systems is crucial for understanding many important physical phenomena. For example, the dynamics of the FermiHubbard model can advance our understanding of superconductivity and quantum magnetism in correlated materials [1, 2] . However, brute-force numerical approaches such as exact diagonalization on a classical computer have an exponential cost in time and/or memory and can therefore only be used to simulate small quantum systems. To tackle the problem of quantum many-body simulation, a large-scale fault-tolerant quantum computer could be used to e􀀎ciently run quantum simulations with predictable bounded errors [3, 4] . The hardware challenge behind building a useful quantum computer is, however, signi􀀌cant. General-purpose quantum simulation on a quantum computer may not be feasible until far in the future. Despite the limitations of classical computers in simulating quantum systems, there are nevertheless many classical algorithms that are e􀀋ective in special cases. A notable example is the variational Monte Carlo (VMC) method, which 􀀌nds an approximate ground state upon 􀀃 [yanfei.wei@mail.mcgill.ca](yanfei.wei@mail.mcgill.ca)[y](y alev.or)[ alev.or](y alev.or)􀀌@uwaterloo.ca [z](z felix.fehse@mail.mcgill.ca)[ felix.fehse@mail.mcgill.ca](z felix.fehse@mail.mcgill.ca)[ ](z felix.fehse@mail.mcgill.ca)[x](x william.coish@mcgill.ca)[ william.coish@mcgill.ca](x william.coish@mcgill.ca) A1 S0 B AN S 1 A2 S2 Ak . . . . . . Sk SN FIG. 1. Diagrammatic representation of the Gaudin magnet, where Sk are the individual spin-1/2 operators, Ak is the coupling between the kth spin and the central spin, and B is the extern

FAQs

What practical impact could this efficient susceptibility description have?

It enables improved characterization and quantum control procedures for qubits interacting with environmental two-level systems, including spin qubits coupled to nuclear spins and qubits with charge or flux degrees of freedom coupled to impurities.

Aug 5, 2026

Upload by Himbo