Phase transition in Stabilizer Entropy and efficient purity estimation
arXiv:2302.07895 · doi:10.1103/PhysRevA.109.032403
Abstract
Stabilizer Entropy (SE) quantifies the spread of a state in the basis of Pauli operators. It is a computationally tractable measure of non-stabilizerness and thus a useful resource for quantum computation. SE can be moved around a quantum system, effectively purifying a subsystem from its complex features. We show that there is a phase transition in the residual subsystem SE as a function of the density of non-Clifford resources. This phase transition has important operational consequences: it marks the onset of a subsystem purity estimation protocol that requires many queries to a circuit containing non-Clifford gates that prepares the state from a stabilizer state. Then, for , it estimates the purity with polynomial resources and, for highly entangled states, attains an exponential speed-up over the known state-of-the-art algorithms.
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