Quantum scrambling with classical shadows

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.

Probing many-body quantum chaos with quantum simulators

“…The goal of the present work is to develop measurement protocols for SFF and pSFF in quantum spin models of arbitrary dimension, as realized for instance with trapped ions [4,6], Rydberg atoms [7] and superconducting qubits [8]. We extend the randomized measurement toolbox [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51], which infers SFF and pSFF from statistical correlations of local random operations applied at different times in a single experiment. This ability to measure pSFF and SFF in a quantum simulation experiment provides a unified and broadly applicable testbed of many-body quantum chaotic behavior, and can be readily implemented in existing experimental platforms [11,17,18,52].…”

Importance sampling of randomized measurements for probing entanglement

“…Measuring the properties of many-body states, and in particular quantifying entanglement for increasing system sizes is a key challenge in assessing and utilizing the power of large-scale quantum computers [1] and simulators [2,3]. The recent development of randomized measurements provides us with a general toolbox to measure in a state-agnostic way physical quantities associated with entanglement [4][5][6][7][8][9][10][11][12][13][14], scrambling [15][16][17], topological order [18,19], and in cross-device quantum verification [20]. Randomized measurements are particularly well suited to present experimental settings, requiring only (random) single qubit rotations and site-resolved measurements.…”