Algorithms for variational Monte Carlo calculations of fermion projected entangled pair states in the swap gates formulation and the detailed balance of tensor network sequential sampling

TL;DR

This paper develops algorithms for variational Monte Carlo calculations of fermion PEPS using swap gates and proves the detailed balance condition for sequential tensor network sampling, advancing computational methods for quantum many-body systems.

Contribution

It introduces algorithms for fermion PEPS VMC in the swap gates formulation and establishes the detailed balance of tensor network sequential sampling.

Findings

Algorithms for fermion PEPS VMC derived and explained.

Proof of detailed balance for tensor network sequential sampling.

Enhancement of computational techniques for quantum many-body ground states.

Abstract

In recent years, the variational Monte Carlo (VMC) calculations of projected entangled pair states (PEPS) has emerged as a competitive method for computing the ground states of many-body quantum systems. This method is particularly important for fermion systems where sign problems are abundant. We derive and explain the algorithms for the VMC calculations of fermion PEPS in the swap gates formulation. As a separate key result, we prove the detailed balance of sequential sampling of tensor networks.