Transitions in entanglement complexity in random quantum circuits by measurements

Random Clifford circuits doped with non Clifford gates exhibit transitions to universal entanglement spectrum statistics [1] and quantum chaotic behavior. In [2] we proved that the injection of Omega(n) non Clifford gates into a n-qubit Clifford circuit drives the transition towards the universal value of the purity fluctuations. In this paper, we show that doping a Clifford circuit with Omega(n) single qubit non Clifford measurements is both necessary and sufficient to drive the transition to universal fluctuations of the purity. (C) 2021 Elsevier B.V. All rights reserved.