Distance-preserving stabilizer measurements in hypergraph product codes

Abstract

Unlike the surface code, quantum low-density parity-check (QLDPC) codes can have a finite encoding rate, potentially lowering the error correction overhead. However, finite-rate QLDPC codes have nonlocal stabilizers, making it difficult to design stabilizer measurement circuits that are low-depth and do not decrease the effective distance. Here, we demonstrate that a popular family of finite-rate QLDPC codes, hypergraph product codes, has the convenient property of distance-robustness: any stabilizer measurement circuit preserves the effective distance. In particular, we prove the depth-optimal circuit in [Tremblay et al, PRL 129, 050504 (2022)] is also optimal in terms of effective distance.

5 pages plus references, comments welcome

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Cited by in corpus (6)

• Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates
• Adaptive Syndrome Extraction
• Single-shot preparation of hypergraph product codes via dimension jump
• On the energy barrier of hypergraph product codes
• QUITS: A modular Qldpc code circUIT Simulator
• Effective Distance of Higher Dimensional HGPs and Weight-Reduced Quantum LDPC Codes