论文标题
Bravyi-Bacon-s-s-s-s-s-s-s-System HyperGraph产品代码的数值研究
A Numerical Study of Bravyi-Bacon-Shor and Subsystem Hypergraph Product Codes
论文作者
论文摘要
我们对通过固定量规定的两个子系统量子代码的两个子系统量子代码进行了数值研究。第一个系列由Bravyi-Bacon-s-s-s-bbs（BBS）代码组成，该代码具有针对2维中局部局部局部量子代码的最佳代码参数。第二个家庭由培根和Cassicino \ cite {Bacon2006Quantum}的恒定速率“广义”代码组成，我们将其重新品牌为子系统超刻型产品（SHP）代码。我们表明，可以通过纠缠两个SHP代码的量规来获得任何HyperGraph产品代码。为了评估这些代码的性能，我们模拟了大小示例。对于电路噪声，$ [[21,4,3]] $ bbs代码和$ [[49,16,3]] $ SHP代码的伪thresholds分别为$ 2 \ times10^{ - 3} $和$ 8 \ times10^{ - 4} $。现象学噪声的仿真表明，大的BB和SHP代码开始超过表面代码，其物理错误速率的编码速率$ 1 \ times 10^{ - 6} $和$ 4 \ times10^{ - 4} $。
We provide a numerical investigation of two families of subsystem quantum codes that are related to hypergraph product codes by gauge-fixing. The first family consists of the Bravyi-Bacon-Shor (BBS) codes which have optimal code parameters for subsystem quantum codes local in 2-dimensions. The second family consists of the constant rate "generalized Shor" codes of Bacon and Cassicino \cite{bacon2006quantum}, which we re-brand as subsystem hypergraph product (SHP) codes. We show that any hypergraph product code can be obtained by entangling the gauge qubits of two SHP codes. To evaluate the performance of these codes, we simulate both small and large examples. For circuit noise, a $[[21,4,3]]$ BBS code and a $[[49,16,3]]$ SHP code have pseudthresholds of $2\times10^{-3}$ and $8\times10^{-4}$, respectively. Simulations for phenomenological noise show that large BBS and SHP codes start to outperform surface codes with similar encoding rate at physical error rates $1\times 10^{-6}$ and $4\times10^{-4}$, respectively.
