Nonlocal Magic Generation and Information Scrambling in Noisy Clifford Circuits

Abstract: In this work, we investigate the average information scrambling and nonlocal magic generation properties of random Clifford encoding-decoding circuits perturbed by local noise. We quantify these with the bipartite algebraic out-of-time order correlator ($\mathcal{A}$-OTOC) and average Pauli-entangling power (APEP) respectively. Using recent advances in the representation theory of the Clifford group, we compute both quantities' averages in the limit that the circuits become infinitely large. We observe that both display a ``butterfly effect" whereby noise occurring on finitely many qubits leads to macroscopic information scrambling and nonlocal magic generating power. Finally, we numerically study the relationship between the magic capacity, an operator-level magic monotone, of the noise channel and the APEP of the resulting circuit, which may provide insight for designing efficient nonlocal magic factories.