Re-anchoring Quantum Monte Carlo with Tensor-Train Sketching

TL;DR

This paper introduces a new quantum Monte Carlo algorithm that integrates tensor-train sketching to improve the accuracy and efficiency of calculating ground-state energies in quantum many-body systems, especially large spin systems.

Contribution

It combines AFQMC with tensor-train methods to iteratively refine trial wavefunctions, enhancing sampling efficiency and reducing variance in energy estimates.

Findings

High accuracy for large spin systems

High fidelity in ground-state wavefunction overlap

Effective variance reduction in energy estimation

Abstract

We propose a novel algorithm for calculating the ground-state energy of quantum many-body systems by combining auxiliary-field quantum Monte Carlo (AFQMC) with tensor-train sketching. In AFQMC, a good trial wavefunction to guide the random walk is crucial for improving the sampling efficiency and controlling the sign problem. Our proposed method iterates between determining a new trial wavefunction in the form of a tensor train, derived from the current walkers, and using this updated trial wavefunction to anchor the next phase of AFQMC. Numerical results demonstrate that the algorithm is highly accurate for large spin systems. The overlap between the estimated trial wavefunction and the ground-state wavefunction also achieves high fidelity. We additionally provide a convergence analysis, highlighting how an effective trial wavefunction can reduce the variance in the AFQMC energy estimation. From a complementary perspective, our algorithm also extends the reach of tensor-train methods for studying quantum many-body systems.