Machine Learning Regression for Operator Dynamics

TL;DR

This paper introduces a machine learning regression approach using MLPs to efficiently compute long-time expectation values in quantum many-body systems, reducing computational costs while maintaining accuracy.

Contribution

It presents a novel method combining MPS calculations with neural network regression to extend quantum operator dynamics to long times efficiently.

Findings

Significant reduction in computational cost for long-time dynamics.

High accuracy maintained in expectation value predictions.

Applicable to quantum spin models in one dimension.

Abstract

Determining the dynamics of the expectation values for operators acting on a quantum many-body (QMB) system is a challenging task. Matrix product states (MPS) have traditionally been the "go-to" models for these systems because calculating expectation values in this representation can be done with relative simplicity and high accuracy. However, such calculations can become computationally costly when extended to long times. Here, we present a solution for efficiently extending the computation of expectation values to long time intervals. We utilize a multi-layer perceptron (MLP) model as a tool for regression on MPS expectation values calculated within the regime of short time intervals. With this model, the computational cost of generating long-time dynamics is significantly reduced, while maintaining a high accuracy. These results are demonstrated with operators relevant to quantum spin models in one spatial dimension.