Optimal Compilation of Syndrome Extraction Circuits for General Quantum LDPC Codes

2026-03-22

AI Summary

This work addresses the critical bottleneck of lacking a general, depth-optimal compilation method for stabilizer extraction circuits in quantum low-density parity-check (qLDPC) codes by proposing the Auto-Stabilizer-Check (ASC) framework. ASC leverages the sparsity of the parity-check matrix and the commutativity between X- and Z-type stabilizers, employing an SMT solver to iteratively optimize and schedule measurements, thereby automatically generating depth-optimal syndrome extraction circuits for arbitrary qLDPC codes. It represents the first automated approach capable of producing depth-optimal circuits for general qLDPC codes and resolves an open question posed by IBM regarding the existence of depth-6 circuits for bivariate bicycle codes. Experimental results demonstrate that ASC reduces circuit depth by approximately 50% and suppresses logical error rates by 7–8× on average compared to ASAP and coloring-based scheduling methods, substantially alleviating manual design overhead.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Quantum error correcting codes (QECC) are essential for constructing large-scale quantum computers that deliver faithful results. As strong competitors to the conventional surface code, quantum low-density parity-check (qLDPC) codes are emerging rapidly: they offer high encoding rates while maintaining reasonable physical-qubit connectivity requirements. Despite the existence of numerous code constructions, a notable gap persists between these designs -- some of which remain purely theoretical -- and their circuit-level deployment. In this work, we propose Auto-Stabilizer-Check (ASC), a universal compilation framework that generates depth-optimal syndrome extraction circuits for arbitrary qLDPC codes. ASC leverages the sparsity of parity-check matrices and exploits the commutativity of X and Z stabilizer measurement subroutines to search for optimal compilation schemes. By iteratively invoking an SMT solver, ASC returns a depth-optimal solution if a satisfying assignment is found, and a near-optimal solution in cases of solver timeouts. Notably, ASC provides the first definitive answer to one of IBM's open problems: for all instances of bivariate bicycle (BB) code reported in their work, our compiler certifies that no depth-6 syndrome extraction circuit exists. Furthermore, by integrating ASC with an end-to-end evaluation framework -- one that assesses different compilation settings under a circuit-level noise model -- ASC reduces circuit depth by approximately 50% and achieves an average 7x-8x suppression of the logical error rate for general qLDPC codes, compared with as-soon-as-possible (ASAP) and coloration-based scheduling. ASC thus substantially reduces manual design overhead and demonstrates its strong potential to serve as a key component in accelerating hardware deployment of qLDPC codes.

Problem

• quantum LDPC codes
• syndrome extraction
• circuit compilation
• quantum error correction
• circuit depth optimization

Innovation

• quantum LDPC codes
• syndrome extraction
• circuit compilation
• SMT solver
• logical error rate