Beyond Circuit Connections: A Non-Message Passing Graph Transformer Approach for Quantum Error Mitigation

Despite the progress in quantum computing, one major bottleneck against the practical utility is its susceptibility to noise, which frequently occurs in current quantum systems. Existing quantum error mitigation (QEM) methods either lack generality to noise and circuit types or fail to capture the global dependencies of entire systems in addition to circuit structure. In this work, we first propose a unique circuit-to-graph encoding scheme with qubit-wise noisy measurement aggregated. Then, we introduce GTranQEM, a non-message passing graph transformer designed to mitigate errors in expected circuit measurement outcomes effectively. GTranQEM are equipped with a quantum-specific positional encoding, a structure matrix as attention bias guiding nonlocal aggregation, and a virtual quantum-representative node to further grasp graph representations, which guarantees to model the long-range entanglement. Experimental evaluations demonstrate that GTranQEM outperforms state-of-the-art QEM methods on both random and structured quantum circuits across noise types and scales among diverse settings. Recent advances in machine learning-based QEM methods have shown improved efficiency (Liao et al., 2024) and insensitivity to both circuit structure and noise types (Kim et al., 2020) . However, most of them fail to effectively encode the structural information of quantum circuits, such as the * Correspondence author, † Equal contribution. Work was in part supported by NSFC 62222607.