Transitions in entanglement complexity in random quantum circuits by measurements

TL;DR

This paper demonstrates that injecting a linear number of non-Clifford measurements into Clifford circuits induces a transition to universal entanglement spectrum fluctuations, highlighting a measurement-driven route to quantum chaos.

Contribution

It establishes that non-Clifford measurements, not just gates, are sufficient to induce universal entanglement fluctuations in random quantum circuits.

Findings

Injection of O(n) non-Clifford measurements causes the transition.

Measurement doping is necessary and sufficient for universality.

Results extend understanding of measurement-induced quantum chaos.

Abstract

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 $O(n)$ 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 $O(n)$ single qubit non Clifford measurements is both necessary and sufficient to drive the transition to universal fluctuations of the purity.