Subsystem codes with spatially local generators

Sergey Bravyi · 2010 · Phys. Rev. A 83, 012320 (2011)

| 编号 QE081 | 主题 拓扑码 | 链接 arXiv:1008.1029 |

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。

We study subsystem codes whose gauge group has local generators in the 2D geometry. It is shown that there exists a family of such codes defined on lattices of size LxL with the number of logical qubits k and the minimum distance d both proportional to L. The gauge group of these codes involves only two-qubit generators of type XX and ZZ coupling nearest neighbor qubits (and some auxiliary one-qubit generators). Our proof is not constructive as it relies on a certain version of the Gilbert-Varshamov bound for classical codes. Along the way we introduce and study properties of generalized Bacon-Shor codes which might be of independent interest. Secondly, we prove that any 2D subsystem [n,k,d] code with spatially local generators obeys upper bounds kd=O(n) and d^2=O(n). The analogous upper bound proved recently for 2D stabilizer codes is kd^2=O(n). Our results thus demonstrate that subsystem codes can be more powerful than stabilizer codes under the spatial locality constraint.

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