HQ-PIDT: A Hybrid Quantum Physics-Informed Decision Transformer for Resilient Distribution System Restoration Under Uncertainty

Abstract

Distribution system restoration (DSR) requires sequential switching decisions that restore loads while satisfying physical and operational constraints. Deep reinforcement learning (DRL)-based methods have shown promise for DSR, but their data-intensive training process and limited long-horizon reasoning capability can restrict their effectiveness in large-scale and complex distribution systems. Decision-transformer (DT)-based methods provide an alternative by modeling restoration as a trajectory-conditioned sequence prediction problem. However, conventional transformer attention mechanisms still face challenges in extracting stable and informative trajectory representations from noisy and time-varying system observations. To address this challenge, this paper proposes a hybrid quantum physics-informed decision transformer (HQ-PIDT) for DSR under dynamic and uncertain operational conditions. The key innovation of HQ-PIDT is a hybrid quantum fidelity-based multi-head self-attention mechanism that embeds parameterized quantum circuits into query-key-value projection and uses quantum-state fidelity to compute attention similarity. This design enables restoration contexts to be represented and compared through quantum-state-overlap-based representations while preserving the autoregressive structure of causal transformers. Evaluations on three distribution-system test feeders show that HQ-PIDT achieves more reliable optimal or near-optimal restoration outcomes than a physics-informed DT baseline and two DRL baselines under constrained, dynamic, and noisy-input scenarios.