标题： 相干误差引起的相变 显示英文标题

标题： Coherent error induced phase transition

摘要： 我们研究了受相干幺正误差影响的量子稳定子码中逻辑信息的稳定性。从一个逻辑态开始，我们应用随机幺正误差信道，并随后测量稳定子检查，从而得到与误差综合征相关的后测量态。通过检查这个综合征态及其相关的综合征分布，我们确定了逻辑态行为中的相变。低于临界误差阈值 \(p_c\) 时，综合征态保持在相同的逻辑态中，使得可以通过适当的纠错协议成功恢复码的逻辑信息。然而，在高于 \(p_c\) 时，综合征态转移到不同的逻辑态，表明高效纠错的失效。值得注意的是，此过程常常会在逻辑空间内诱导出有效的幺正旋转。这种转变伴随着综合征分布全局和局部特征的定性变化。我们将这一现象称为由相干误差引起的相变。为了说明这一转变，我们提出了两类量子纠错码模型——环面码和非局域随机稳定子码，从而揭示了量子纠错在相干误差下的设计和性能极限。 显示英文摘要

摘要： We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks, resulting in a syndrome-dependent post-measurement state. By examining both this syndrome state and the associated syndrome distribution, we identify a phase transition in the behavior of the logical state. Below a critical error threshold pc, the syndrome state remains in the same logical state, enabling successful recovery of the code's logical information via suitable error-correction protocols. Above pc, however, the syndrome state shifts to a different logical state, signaling the breakdown of efficient error correction. Notably, this process can often induce an effective unitary rotation within the logical space. This transition is accompanied by qualitative changes in both the global and local features of the syndrome distribution. We refer to this phenomenon as a coherent error induced phase transition. To illustrate this transition, we present two classes of quantum error correcting code models the toric code and non-local random stabilizer codes thereby shedding light on the design and performance limits of quantum error correction under coherent errors.