Efficient post-selection for general quantum LDPC Codes

Abstract Post-selection strategies that discard low-confidence results can significantly improve the effective fidelity of quantum computing at the cost of reduced acceptance rates, particularly useful for offline resource state generation and moderate-depth fault-tolerant circuits. Prior work has primarily relied on the “logical gap” metric, which faces fundamental limitations including computational overhead that scales exponentially with the number of logical qubits and poor generalizability beyond surface codes. We develop post-selection strategies based on computationally efficient heuristic metrics that leverage error cluster statistics from clustering-based decoders, which are applicable to arbitrary quantum low-density parity check (QLDPC) codes. We validate our method through extensive numerical simulations on surface codes, bivariate bicycle codes, and hypergraph product codes, demonstrating orders of magnitude reductions in logical error rates with moderate abort rates. For instance, applying our strategy to the [[144, 12, 12]] bivariate bicycle code achieves ~ 1000 × reduction in the logical error rate with an abort rate of only 1% at a physical error rate of 0.1%. Additionally, we integrate our approach with the sliding-window framework for real-time decoding, featuring mid-circuit abort decisions that eliminate unnecessary overheads. Notably, its performance matches or even surpasses the original strategy, while exhibiting favorable scaling in the number of rounds.