Phase transition in magic with random quantum circuits

Abstract

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. Coherent noise affecting a random error correcting code is now shown to produce a transition between phases that accumulate and destroy magic.