Spectral Properties and Magic Generation in $T$-doped Random Clifford
Circuits
Spectral Properties and Magic Generation in $T$-doped Random Clifford
Circuits
We study the emergence of complexity in deep random $N$-qubit $T$-gate doped Clifford circuits, as reflected in their spectral properties and in magic generation, characterized by the stabilizer R\'enyi entropy. For pure (undoped) Clifford circuits, a unique periodic orbit structure in the space of Pauli strings implies peculiar spectral correlations …