PropHunt: Automated Optimization of Quantum Syndrome Measurement Circuits

Fault-Tolerant Quantum Computing (FTQC) relies on Quantum Error Correction (QEC) codes to reach error rates necessary for large scale quantum applications. At a physical level, QEC codes perform parity checks on data qubits, producing syndrome information, through Syndrome Measurement (SM) circuits. These circuits define a code's logical error rate and must be run repeatedly throughout the entire program. The performance of SM circuits is therefore critical to the success of a FTQC system. While ultimately implemented as physical circuits, SM circuits have challenges that are not addressed by existing circuit optimization tools. Importantly, inside SM circuits themselves errors are expected to occur, and how errors propagate through SM circuits directly impacts which errors are detectable and correctable, defining the code's logical error rate. This is not modeled in NISQ-era tools, which instead optimize for targets such as gate depth or gate count to mitigate the chance that any error occurs. This gap leaves key questions unanswered about the expected real-world effectiveness of QEC codes. In this work we address this gap and present PropHunt, an automated tool for optimizing SM circuits for CSS codes. We evaluate PropHunt on a suite of relevant QEC codes and demonstrate PropHunt's ability to iteratively improve performance and recover existing hand-designed circuits automatically. We also propose a near-term QEC application, Hook-ZNE, which leverages PropHunt's fine-grained control over logical error rate to improve Zero-Noise Extrapolation (ZNE), a promising error mitigation strategy.