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.
Let us show the calculation of one component of the vectors ⃗I H 3,C2 , ⃗I Q 3,C2, as the one for ⃗I H 3,CD , ⃗I Q 3,CD goes in the same way
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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.