Nonstabilizerness of Permutationally Invariant Systems

Abstract

Typical measures of nonstabilizerness of a system of $N$ qubits require computing $4^N$ expectation values, one for each Pauli string in the Pauli group, over a state of dimension $2^N$. For permutationally invariant systems, this exponential overhead can be reduced to just $O(N^3)$ expectation values on a state with a dimension $O(N)$. We exploit this simplification to study the nonstabilizerness phase transitions of systems with hundreds of qubits.

6 + 4 pages, 4 + 6 figures

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• Non-Stabilizerness of Sachdev-Ye-Kitaev Model
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Nonstabilizerness of a Boundary Time Crystal
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• The non-stabilizerness of fermionic Gaussian states
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• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
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• Van Hove singularities in stabilizer entropy densities