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.