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 m_{2}∼t^{1/3} (with time in units of a characteristic scale t_{0}) up to the largest computed times of the order of 10^{8}. 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 1/10^{4} 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 2×10^{12}. 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.