In the dilute limit of a Brownian all-to-all circuit, the renormalized OTOC grows at the unperturbed chaos rate at early times and saturates to a value set by r/(1+kappa), showing no localization phase transition.
Quantum scrambling with classical shadows
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abstract
Quantum dynamics is of fundamental interest and has implications in quantum information processing. The four-point out-of-time-ordered correlator (OTOC) is traditionally used to quantify quantum information scrambling under many-body dynamics. Due to the OTOC's unusual time ordering, its measurement is challenging. We propose higher-point OTOCs to reveal early-time scrambling behavior, and present protocols to measure any higher-point OTOC using the shadow estimation method. The protocols circumvent the need for time-reversal evolution and ancillary control. They can be implemented in near-term quantum devices with single-qubit readout.
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Scrambling Dynamics with Imperfections in a Solvable Model
In the dilute limit of a Brownian all-to-all circuit, the renormalized OTOC grows at the unperturbed chaos rate at early times and saturates to a value set by r/(1+kappa), showing no localization phase transition.