AlphaSyndrome: Tackling the Syndrome Measurement Circuit Scheduling Problem for QEC Codes

TL;DR

AlphaSyndrome tackles the syndrome measurement scheduling problem for commuting-stabilizer QEC codes by casting it as a decoder-conditioned optimization problem and solving it with Monte Carlo Tree Search. The method explicitly accounts for hook-error propagation and decoder performance, demonstrating up to ~$96\%$ reduction in logical error rate over depth-optimized baselines and matching Google’s surface-code schedules on rotated codes. It also reveals tradeoffs between schedule depth and reliability, showing substantial space-time reductions through shorter code distances while maintaining or improving reliability. The work provides a general, data-driven framework that adapts to different codes, decoders, and noise models, with broad implications for practical fault-tolerant quantum computing.

Abstract

Quantum error correction (QEC) is essential for scalable quantum computing, yet repeated syndrome-measurement cycles dominate its spacetime and hardware cost. Although stabilizers commute and admit many valid execution orders, different schedules induce distinct error-propagation paths under realistic noise, leading to large variations in logical error rate. Outside of surface codes, effective syndrome-measurement scheduling remains largely unexplored. We present AlphaSyndrome, an automated synthesis framework for scheduling syndrome-measurement circuits in general commuting-stabilizer codes under minimal assumptions: mutually commuting stabilizers and a heuristic decoder. AlphaSyndrome formulates scheduling as an optimization problem that shapes error propagation to (i) avoid patterns close to logical operators and (ii) remain within the decoder's correctable region. The framework uses Monte Carlo Tree Search (MCTS) to explore ordering and parallelism, guided by code structure and decoder feedback. Across diverse code families, sizes, and decoders, AlphaSyndrome reduces logical error rates by 80.6% on average (up to 96.2%) relative to depth-optimal baselines, matches Google's hand-crafted surface-code schedules, and outperforms IBM's schedule for the Bivariate Bicycle code.

Figures (15)

• Figure 1: (a) Two different schedules of the same $ZZZZ$ syndrome measurement circuit. (b) The logical error rates of two different syndrome measurement circuit schedules. The numbers in the surface code patches represent the time steps when the corresponding Pauli check between the corresponding data qubit and ancilla qubit is executed.
• Figure 2: Example of logical $X$ and $Z$ operations on (a) $[[25,1,5]]$ rotated surface code and (b) $[[19,1,5]]$ hexagonal color code, each polygon is an $X$ and $Z$ stabilizer. Two $Z_L$s on the rotated surface code are equivalent by multipling the starred stabilizers.
• Figure 3: Error correction process of a QECC. (1) syndrome measurement, and (2) decoder and correction.
• Figure 4: Two different Pauli checks: $Z$ check and $X$ check, and how error propagation during a Pauli-$X\text{ or }Z$ check. Notice the Hadamard gate (yellow) changes an error between being $X$ and $Z$.
• Figure 5: Four phases of MCTS. (a) Selection. (b) Expansion. (c) Simulation. (d) Backpropagation.