Exponential speedup in measuring out-of-time-ordered correlators and gate fidelity with a single bit of quantum information

Out-of-time-ordered correlators (OTOC) are a quantifier of quantum information scrambling and chaos. We propose an efficient algorithm to measure OTOCs that provides exponential speed-up over the best known classical provided OTOC operator be estimated admits gate decomposition. also discuss scheme obtain about eigenvalue spectrum spectral density OTOCs.