Quantifying information scrambling via classical shadow tomography on programmable quantum simulators

We develop techniques to probe the dynamics of quantum information and implement them experimentally on an IBM superconducting quantum processor. Our protocols adapt shadow tomography for the study of time -evolution channels rather than of quantum states and rely only on single-qubit operations and measurements. We identify two unambiguous signatures of quantum information scrambling, neither of which can be mimicked by dissipative processes, and relate these to many-body teleportation. By realizing quantum chaotic dynamics in experiment, we measure both signatures and support our results with numerical simulations of the quantum system. We additionally investigate operator growth under this dynamics and observe behavior characteristic of quantum chaos. As our methods require only a single quantum state at a time, they can be readily applied on a wide variety of quantum simulators.