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Variational Monte Carlo with neural network quantum states for a Yang-Mills matrix model

Norbert Bodendorfer1, Onur Oktay2, Vaibhav Gautam3, Masanori Hanada3, and Enrico Rinaldi4,5,6

  • 1University of Regensburg, Institute of Theoretical Physics Universitätsstrasse 31, D-93053 Regensburg, Germany
  • 2Department of Physics, Karamanoglu Mehmetbey University, 70100 Karaman, Turkey
  • 3School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
  • 4Quantinuum K.K., Otemachi Financial City Grand Cube 3F 1-9-2 Otemachi, Chiyoda-ku, Tokyo, Japan
  • 5Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) Program RIKEN, Wako, Saitama 351-0198, Japan
  • 6Center for Quantum Computing (RQC), RIKEN, Wako, Saitama 351-0198, Japan

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Phys. Rev. D 112, 046010 – Published 15 August, 2025

DOI: https://doi.org/10.1103/t8m6-zhrm

Abstract

We apply the variational Monte Carlo method based on neural network quantum states, using a neural autoregressive flow architecture as our ansatz, to determine the ground state wave function of the bosonic SU(N) Yang-Mills-type two-matrix model at strong coupling. Previous literature hinted at the inaccuracy of such an approach at strong coupling. In this work, the accuracy of the results is tested using lattice Monte Carlo simulations: we benchmark the expectation value of the energy of the ground state for system sizes N that are beyond brute-force exact diagonalization methods. We observe that the variational method with neural network states reproduces the right ground state energy when the width of the network employed in this work is sufficiently large. We confirm that the correct result is obtained for N=2 and 3, while obtaining a precise value for N=4 requires more resources than the amount available for this work.

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Phys. Rev. D 112, 046010– Published 15 August, 2025
  • Received 14 May 2025
  • Accepted 10 July 2025
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