  The classical variational autoregressive network is extended to the Euclidean
path integral representation of quantum partition function. An essential
challenge is adapting the sequential process of sample generation by an
autoregressive network to a nonlocal constraint due to the periodic boundary
condition in path integral. An add-on oracle is devised for this purpose, which
accurately identifies and stalls unviable configurations as soon as they occur.
The oracle leads to rejection-free sampling conforming to the periodic boundary
condition. As a demonstration, the oracle-guided autoregressive network is
applied to obtain variational solutions of quantum spin chains at finite
temperatures with relatively large system sizes and numbers of time slicing,
which enable efficient computation of thermodynamic quantities.
