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

Understand

Out-of-time-ordered correlators (OTOC) are a quantifier of quantum information scrambling and quantum chaos.

• We propose an efficient quantum algorithm to measure OTOCs that provides an exponential speed-up over the best known classical algorithm provided the OTOC operator to be estimated admits an efficient gate decomposition.
• We also discuss a scheme to obtain information about the eigenvalue spectrum and the spectral density of OTOCs.