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arXiv · 2603.21499

Optimal Compilation of Syndrome Extraction Circuits for General Quantum LDPC Codes

Kai Zhang·Dingchao Gao·Zhaohui Yang·Runshi Zhou·Fangming Liu·Zhengfeng Ji·Jianxin Chen
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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.

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Kai Zhang, Dingchao Gao, Zhaohui Yang, Runshi Zhou, Fangming Liu, Zhengfeng Ji, Jianxin Chen. 2026-03-23. Optimal Compilation of Syndrome Extraction Circuits for General Quantum LDPC Codes. https://arxiv.org/abs/2603.21499

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