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. We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytic, numeric and experimental probes. Below a critical error rate, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate syndrome measurements concentrate magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup and pave pathways for more efficient magic state generation. We introduce a new measure—the basis-minimized measurement entropy—and also employ the second stabilizer Rényi entropy to quantify magic. We evaluate these measures via classical simulations, analytical calculations, and experiments on IonQ’s Aria trapped-ion quantum computer. The magic phase transition is revealed through finite-size scaling collapses of these observables.

Pradeep Niroula, Christopher David White, Qingfeng Wang, Sonika Johri, Daiwei Zhu, Christopher Monroe, Crystal Noel, Michael J. Gullans