Probes of chaos in quantum systems approach Haar distribution moments under T-doped circuits and chaotic GUE ensembles but deviate under non-chaotic GDE ensembles.
X i Π⊗2 i ⊗ψ (1−η) ⊗ψ (η) # = dTr h ψ(1−η) i Tr h ψ(η) i = d(G199) for the Haar case, while for the Clifford case one gets: ⃗I Q η,4 I = Tr
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Probes of chaos over the Clifford group and approach to Haar values
Probes of chaos in quantum systems approach Haar distribution moments under T-doped circuits and chaotic GUE ensembles but deviate under non-chaotic GDE ensembles.