Title: The role of entropy in topological quantum error correction Show Chinese title

Title: 熵在拓扑量子错误纠正中的作用

Abstract: The performance of a quantum error-correction process is determined by the likelihood that a random configuration of errors introduced to the system will lead to the corruption of encoded logical information. In this work we compare two different variants of the surface code with a comparable number of qubits: the surface code defined on a square lattice and the same model on a lattice that is rotated by $\pi / 4$. This seemingly innocuous change increases the distance of the code by a factor of $\sqrt{2}$.However, as we show, this gain can come at the expense of significantly increasing the number of different failure mechanisms that are likely to occur. We use a number of different methods to explore this tradeoff over a large range of parameter space under an independent and identically distributed noise model. We rigorously analyze the leading order performance for low error rates, where the larger distance code performs best for all system sizes. Using an analytical model and Monte Carlo sampling, we find that this improvement persists for fixed sub-threshold error rates for large system size, but that the improvement vanishes close to threshold. Remarkably, intensive numerics uncover a region of system sizes and sub-threshold error rates where the square lattice surface code marginally outperforms the rotated model. Show Chinese abstract

Abstract: 量子纠错过程的性能由系统中引入的随机错误配置导致编码逻辑信息损坏的可能性决定。 在本工作中，我们比较了两种不同变体的表面码，它们具有相近的量子比特数量：定义在正方形晶格上的表面码和同一模型在旋转了$\pi / 4$的晶格上的模型。 这种看似无害的改变使代码的距离增加了$\sqrt{2}$倍。然而，正如我们所展示的，这种增益可能会以显著增加可能发生的故障机制数量为代价。 我们使用多种不同的方法，在独立且相同分布的噪声模型下，探索参数空间中的这一权衡。 我们严格分析了低错误率下的主导性能，其中距离更大的代码在所有系统尺寸下表现最好。 通过分析模型和蒙特卡洛采样，我们发现这种改进在大系统尺寸下对于固定的次阈值错误率仍然有效，但当接近阈值时，这种改进会消失。 值得注意的是，密集的数值计算揭示了一个系统尺寸和次阈值错误率的区域，在该区域中，正方形晶格表面码略微优于旋转模型。