Autoregressive pairwise Graphical Models efficiently find ground state representations of stoquastic Hamiltonians

TL;DR

This paper introduces Autoregressive Graphical Models (AGMs) as an efficient approach for approximating ground states of stoquastic Hamiltonians, demonstrating their effectiveness and faster convergence compared to more complex models.

Contribution

The paper presents a novel AGM framework that emphasizes pairwise interactions, showing that simple linear models outperform complex ones in certain quantum ground state approximations.

Findings

AGMs with pairwise energy functions effectively model ground states.

Simple linear AGMs outperform complex models in resource-limited settings.

AGMs show faster convergence on frustrated Hamiltonians.

Abstract

We introduce Autoregressive Graphical Models (AGMs) as an Ansatz for modeling the ground states of stoquastic Hamiltonians. Exact learning of these models for smaller systems show the dominance of the pairwise terms in the autoregressive decomposition, which informs our modeling choices when the Ansatz is used to find representations for ground states of larger systems. We find that simple AGMs with pairwise energy functions trained using first-order stochastic gradient methods often outperform more complex non-linear models trained using the more expensive stochastic reconfiguration method. We also test our models on Hamiltonians with frustration and observe that the simpler linear model used here shows faster convergence to the variational minimum in a resource-limited setting.