Machine Learning Regression for Operator Dynamics
This work addresses a computational bottleneck for researchers in quantum physics, specifically for simulating long-time dynamics in one-dimensional quantum spin models, and is incremental as it builds on existing matrix product state methods.
The authors tackled the computational cost of extending expectation value calculations for quantum many-body systems to long time intervals by using a multi-layer perceptron for regression on short-time matrix product state data, achieving significant computational cost reduction while maintaining high accuracy.
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.