Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. Many proposals for error correction in quantum computing make use of so-called stabilizer codes, which use multiqubit measurements to detect deviations from logical qubit states. Here we observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytical, numerical and experimental probes. Below a critical error rate, stabilizer measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate measurements concentrate magic. A better understanding of this behaviour in the resource theory of magic could help to identify the origins of quantum speedup and lead to methods for more efficient magic state generation.

魔法是量子态的一种属性，它可以使用简单的门操作集实现通用的容错量子计算。因此，理解魔法产生或破坏的机制是实现高效实用的容错计算的关键一步。量子计算中的许多纠错提议都利用所谓的稳定器代码，该代码使用多量子位测量来检测与逻辑量子位状态的偏差。在这里，我们观察到，受到相干误差影响的随机稳定器代码表现出魔法中的相变，我们通过分析、数值和实验探针对其进行了表征。低于临界错误率时，稳定器测量可消除电路中累积的魔力，有效防止相干错误；高于临界错误率的测量集中魔力。更好地理解魔法资源理论中的这种行为有助于识别量子加速的起源，并找到更有效的魔法状态生成方法。