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.
Highlights
Quantum scrambling describes the delocalization of quantum information in quantum chaotic systems [1,2]
We find that the eight-point of-time-ordered correlator (OTOC) reveals early-time information delocalization not present in the four-point OTOC, making it a promising candidate to probe scrambling dynamics
We provide a statistical error analysis to show that our protocols are more efficient than brute force tomography
Summary
Quantum scrambling describes the delocalization of quantum information in quantum chaotic systems [1,2]. Scrambling can be studied by probing the four-point out-of-time-ordered correlator (OTOC) [8,9,10]. This correlator can be used to quantify chaos in many-body systems ranging from a non-integrable Ising model [11] to the Dicke model [12,13,14]. A method based on statistical correlations computes the four-point OTOC in terms of experimentally friendly correlators [30]; it was demonstrated in Ref. We present protocols to measure any higher-point outof-time-ordered correlator using classical shadows [34,35], which is an efficient scheme recently proposed to predict functions of quantum states. We numerically simulate our protocols in a nonintegrable, mixedfield Ising model and show that they can be implemented by current experimental platforms containing a moderate number of qubits
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