Triangular color codes on trivalent graphs with flag qubits
Triangular color codes on trivalent graphs with flag qubits
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DOI：
10.1088/1367-2630/ab68fd
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发表时间：
2020-02-01
影响因子：
3.3
通讯作者：
Zhu, Guanyu
中科院分区：
文献类型：
--
作者：
Chamberland, Christopher;Kubica, Aleksander;Zhu, Guanyu
色码是一种拓扑量子纠错码，支持多种有价值的容错逻辑门。尽管量子位连接受到限制，但它的二维版本（三角色码）可能很快就会用当前可用的超导硬件实现。为了指导这项实验工作，我们研究了存储阈值的三角色码对电路级去极化噪声。首先，我们适应限制解码器的三角色码的设置和现象学噪声。然后，我们提出了一个容错的稳定器测量电路的实现，其中包括标志量子位。我们展示了如何从标志量子位的信息可以使用一个有效的和可扩展的方式与限制解码器，以保持有效的距离的代码。我们用数值方法估计了三角色码的阈值为0.2%，这与其他拓扑量子码的阈值是有竞争力的。我们还证明，1-标志稳定器测量电路是足够的，以保持完整的代码的距离，这可能是用来找到更简单的症状提取电路的颜色代码。
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available superconducting hardware despite constrained qubit connectivity. To guide this experimental effort, we study the storage threshold of the triangular color code against circuit-level depolarizing noise. First, we adapt the Restriction Decoder to the setting of the triangular color code and to phenomenological noise. Then, we propose a fault-tolerant implementation of the stabilizer measurement circuits, which incorporates flag qubits. We show how information from flag qubits can be used in an efficient and scalable way with the Restriction Decoder to maintain the effective distance of the code. We numerically estimate the threshold of the triangular color code to be 0.2%, which is competitive with the thresholds of other topological quantum codes. We also prove that 1-flag stabilizer measurement circuits are sufficient to preserve the full code distance, which may be used to find simpler syndrome extraction circuits of the color code.