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The variational autoregressive network is extended to the Euclidean pathintegral representation of quantum partition function. An essential challengeis adapting the sequential process of sample generation by an autoregressivenetwork to a nonlocal constraint due to the periodic boundary condition in pathintegral. An add-on oracle is devised for this purpose, which accuratelyidentifies and stalls unviable configurations as soon as they occur. The oracleenables rejection-free sampling conforming to the periodic boundary condition.As a demonstration, the oracle-guided autoregressive network is applied toobtain variational solutions of quantum spin chains at finite temperatures withrelatively large system sizes and numbers of time slicing, and to efficientlycompute thermodynamic quantities.

Worldline algorithm by oracle-guided variational autoregressive network