PropHunt: Automated Optimization of Quantum Syndrome Measurement Circuits

TL;DR

This work targets the critical, under-specified problem of syndrome-measurement circuit design for quantum error correction. PropHunt automates SM-circuit optimization by framing logical errors as arising from ambiguity in decoding and then minimizing this ambiguity via a circuit-level MaxSAT approach that identifies min-weight faulty patterns and corresponding circuit changes. The method yields SM circuits that approach or match hand-designed performance for common codes and provides substantial improvements for Lifted Product and Random Quantum Tanner codes (2.5x–4x at $P=0.1\%$); it also introduces Hook-ZNE, a near-term error-mitigation technique that uses intermediate SM circuits to enable fine-grained noise scaling without increasing circuit depth. Overall, PropHunt offers a scalable, code-agnostic pathway to improve QEC efficacy and complements ZNE techniques for practical quantum devices.

Abstract

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.

Figures (16)

• Figure 1: Common performance predictors targeted in Syndrome Measurement (SM) circuit design are imperfect. Data is from different SM circuits for a $d=5$ surface code. Red (square) plots indicate lower performing SM circuits despite having equal or better performance predictor values. Blue (diamond) plots indicate higher performing SM circuits despite having equal or worse performance predictor values.
• Figure 2: A $d=3$ surface code. Blue faces are $X$-type stabilizers and red faces are $Z$-type stabilizers.
• Figure 3: (a) Example syndrome measurement circuits for measuring an X check (left) and a Z check (right). (b) CNOT error propagation rules.
• Figure 4: A circuit-level model for a noisy SM circuit. Decoding graph edges are only drawn for example errors (a) and (b).
• Figure 5: Worst case X and Z hook errors for weight 4 checks.