Wave Packet Spreading with Disordered Nonlinear Discrete-Time Quantum Walks

Abstract

We use a novel unitary map toolbox - discrete-time quantum walks originally designed for quantum computing - to implement ultrafast computer simulations of extremely slow dynamics in a nonlinear and disordered medium. Previous reports on wave packet spreading in Gross-Pitaevskii lattices observed subdiffusion with the second moment m2∼t1/3 (with time in units of a characteristic scale t0) up to the largest computed times of the order of 108. A fundamental and controversially debated question - whether this process can continue ad infinitum, or has to slow down - stands unresolved. Current experimental devices are not capable to even reach 1/104 of the reported computational horizons. With our toolbox, we outperform previous computational results and observe that the universal subdiffusion persists over an additional four decades reaching astronomic times 2×1012. Such a dramatic extension of previous computational horizons suggests that subdiffusion is universal, and that the toolbox can be efficiently used to assess other hard computational many-body problems. © 2019 American Physical Society.