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

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