Quantum Information Scrambling Through a High-Complexity Operator Mapping

TL;DR

This paper introduces a novel high-complexity operator mapping that enables quantum information scrambling by embedding logical information into complex many-body correlations, with efficient sampling algorithms and observable dynamics analysis.

Contribution

It proposes an unconventional operator mapping mechanism for quantum scrambling, along with an efficient sampling algorithm and analysis of information spreading and classical diffusion emergence.

Findings

Demonstrates exponential growth of out-of-time-order correlators indicating scrambling.

Shows classical diffusion dynamics emerge at late times in the system.

Develops an efficient polynomial-cost algorithm for simulating dynamics with the mapping.

Abstract

Quantum information scrambling has attracted much attention amid the effort to reconcile the conflict between quantum-mechanical unitarity and the thermalizaiton-irreversibility in many-body systems. Here we propose an unconventional mechanism to generate quantum information scrambling through a high-complexity mapping from logical to physical degrees-of-freedom that hides the logical information into non-separable many-body-correlations. Corresponding to this mapping, we develop an algorithm to efficiently sample a Slater-determinant wavefunction and compute all physical observables in dynamics with a polynomial cost in system-size. The system shows information scrambling in the quantum many-body Hilbert space characterized by the spreading of Hamming-distance. At late time, we find emergence of classical diffusion dynamics in this quantum many-body system. We establish that the operator-mapping enabled growth in out-of-time-order-correlator exhibits exponential-scrambling behavior. The quantum information-hiding mapping approach may shed light on the understanding of fundamental connections among computational complexity, information scrambling and quantum thermalization.