Transitions in entanglement complexity in random quantum circuits by measurements

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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• Interplay of entanglement structures and stabilizer entropy in spin models
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
• Non-Clifford Cost of Random Unitaries
• Rise and fall of nonstabilizerness via random measurements
• Invested and Potential Magic Resources in Measurement-Based Quantum Computation