The swap-gates fPEPS VMC algorithm is presented with benchmarks, but the proof of detailed balance for sequential sampling is incorrect.
The different ways are equivalent due to the gauge constraint Eq
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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
The swap-gates fPEPS VMC algorithm is presented with benchmarks, but the proof of detailed balance for sequential sampling is incorrect.