Quantum information scrambling through a high-complexity operator mapping

Quantum information scrambling has attracted much attention amid the effort to reconcile the conflict between quantum-mechanical unitarity and the thermalization 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 nonseparable many-body correlations. Corresponding to this mapping, we develop an algorithm to efficiently sample a Slater-determinant wave function 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 an 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.