Distance-preserving stabilizer measurements in hypergraph product codes

• URL: http://arxiv.org/abs/2308.15520v2
• Date: Tue, 28 Jan 2025 00:54:19 GMT
• Title: Distance-preserving stabilizer measurements in hypergraph product codes
• Authors: Argyris Giannisis Manes, Jahan Claes,
• Abstract summary: We show that a family of finite-rate QLDPC codes, hypergraph product codes, has the convenient property of distance-robustness.<n>In particular, we prove the depth-optimal circuit in [Tremblay et al, PRL 129, 050504 (2022) is also optimal in terms of effective distance.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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