论文标题
在张量 - 网络代码中的多个逻辑Qubit的平行解码
Parallel decoding of multiple logical qubits in tensor-network codes
论文作者
论文摘要
我们考虑张量 - 网络稳定器代码，并表明他们的张量 - 网格解码器具有可以并行解码的独立逻辑量子的属性。只要错误率低于阈值，我们表明该平行解码器本质上是最佳的。作为一个应用程序，我们为最大速率全息steane（Heptagon）代码验证了这一点。对于全息代码，该张量 - 网络解码器在N（物理Qubits的数量）中被证明具有复杂性多项式有效。在这里，我们表明，通过使用并行解码方案，复杂性在k中也是线性的，即逻辑Qubits的数量。由于张量 - 网络收缩在计算上是有效的，因此这使我们能够准确收缩张量张量网络，这些网络与最多半百万量子位的代码相对应。最后，我们在去极化噪声下计算了最大速率全息steane代码为9.4％的散装阈值（与代码中心的固定距离的阈值（距代码中心的固定距离）为9.4％。
We consider tensor-network stabilizer codes and show that their tensor-network decoder has the property that independent logical qubits can be decoded in parallel. As long as the error rate is below threshold, we show that this parallel decoder is essentially optimal. As an application, we verify this for the max-rate holographic Steane (heptagon) code. For holographic codes this tensor-network decoder was shown to be efficient with complexity polynomial in n, the number of physical qubits. Here we show that, by using the parallel decoding scheme, the complexity is also linear in k, the number of logical qubits. Because the tensor-network contraction is computationally efficient, this allows us to exactly contract tensor networks corresponding to codes with up to half a million qubits. Finally, we calculate the bulk threshold (the threshold for logical qubits a fixed distance from the code centre) under depolarizing noise for the max-rate holographic Steane code to be 9.4%.
