Topological subsystem bivariate bicycle codes with four-qubit check operators

Zijian Liang and Yu-An Chen · 2026 · arXiv

| 编号 QE164 | 主题 qLDPC 码 | 链接 arXiv:2605.04151 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

High-rate bivariate bicycle (BB) codes are promising low-overhead quantum memories, but their stabilizer checks typically have weight $6$ or higher, making syndrome extraction challenging. We introduce subsystem bivariate bicycle (SBB) codes, a translation-invariant CSS subsystem construction that realizes BB-code logical structure using local weight-$4$ gauge measurements. Their stabilizer syndromes are inferred by multiplying the corresponding gauge outcomes. We further show that nonlocal stabilizers in translation-invariant CSS subsystem codes can be detected using a determinantal-ideal criterion based on the gauge-operator commutation matrix. When this criterion excludes nonlocal stabilizers, a finite-depth Clifford circuit decouples gauge qubits and identifies the protected subsystem with a corresponding BB stabilizer code. An SBB code is topological, meaning that it has no nontrivial local logical operators, if and only if the corresponding BB code is topological. A finite search yields low-overhead examples including $[[27,6,3]]$, $[[75,10,5]]$, and $[[108,12,6]]$; the latter encodes six times more logical qubits than a subsystem surface code at the same block length and dis

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