Transitions in entanglement complexity in random quantum circuits by measurements

• URL: http://arxiv.org/abs/2103.07481v3
• Date: Mon, 4 Oct 2021 13:24:07 GMT
• Title: Transitions in entanglement complexity in random quantum circuits by measurements
• Authors: Salvatore F.E. Oliviero, Lorenzo Leone and Alioscia Hamma
• Abstract summary: Random Clifford circuits doped with non Clifford gates exhibit transitions to universal entanglement spectrum statistics. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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