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Out-of-time-order correlator (OTOC), been suggested as a measure of quantuminformation scrambling in quantum many-body systems, has received enormousattention recently. The experimental measurement of OTOC is quite challenging.The existing theoretical protocols consist in implementing time-reversaloperations or using ancillary quantum systems, therefore only a few experimentshave been reported. Recently, a new protocol to detect OTOC using statisticalcorrelations between randomized measurements was put forward. In this work, wedetect the OTOCs of a kicked-Ising model using this new measurement method on a4-qubit nuclear magnetic resonance quantum simulator. In experiment, we userandom Hamiltonian evolutions to generate the random operations that arerequired by the randomized OTOC detection protocol. Our experimental resultsare in good agreement with the theoretical predictions, thus confirming thefeasibility of the protocols. Therefore, our work represents a step inexploring realistic quantum chaotic dynamics in complicated quantum systems.

Detecting scrambling via statistical correlations between randomized measurements on an NMR quantum simulator