论文标题
使用单个Ancilla和圆形连接实现一类稳定器量子误差校正代码
Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity
论文作者
论文摘要
我们描述了一类“相邻的块”稳定器量子误差校正代码，并证明可以使用单个Ancilla和圆形近邻居量子标程连接以资源有效的方式实现此类代码。我们建议对班级代码的综合征测量电路实施，并说明其针对3 Qubit重复代码的案例，Laflamme的5 Qubit代码和Shor的9 Quibit代码的工作。对于3 QUITION重复代码，Laflamme的5 Quit代码建议的方案仅使用本机两分之一CNS门的属性，这可能会减少由于较短的栅极时间而导致的不可纠正错误的量。该方案的元素可用于使用单个Ancilla的接近近纽布连接实现表面代码，如示例所示。我们使用最小体重完美的匹配方法为重复代码和LAFLAMME的5量码代码开发了有效的解码程序，以说明我们方案中的特定测量顺序。该方案可以在3 Qubit重复代码和Laflamme的5 Q Quibit Code案例中对噪声水平的分析显示出来的逻辑Qubit的保真度。我们通过使用IBM量子处理器和使用状态矢量模拟器的Laflamme的5 Quit代码来实现针对3 Q Quit代码的开发方案来补充结果。
We describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit connectivity. We propose an implementation for syndrome-measurement circuits for codes from the class and illustrate its workings for cases of 3-qubit repetition code, Laflamme's 5-qubit code, and Shor's 9-qubit code. For 3-qubit repetition code and Laflamme's 5-qubit code suggested scheme has the property that it uses only native two-qubit CNS gates, which potentially reduces the amount of non-correctable errors due to the shorter gate time. Elements of the scheme can be used to implement surface code with near-neighbour connectivity using single ancilla, as demonstrated in an example. We developed efficient decoding procedures for repetition codes and the Laflamme's 5-qubit code using a minimum weight-perfect matching approach to account for the specific order of measurements in our scheme. The analysis of noise levels for which the scheme could show improvements in the fidelity of a stored logical qubit in the 3-qubit repetition code and Laflamme's 5-qubit code cases is provided. We complement our results by realizing the developed scheme for a 3-qubit code using an IBM quantum processor and the Laflamme's 5-qubit code using the state-vector simulator.
