Phase transition in magic with random quantum circuits

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.