Quantum lattice-gas model for the Burgers equation

摘要: A quantum algorithm is presented for modeling the time evolution of a continuous field governed by nonlinear Burgers equation in one spatial dimension. It microscopic-scale type-II computer, large lattice small computers interconnected nearest neighbor fashion classical communication channels. formula state preparation presented. The unitary conservative gate applied to each node independently. Following operation, ensemble measurements over independent microscopic realizations are made resulting finite-difference Boltzmann at mesoscopic scale. measured values then used re-prepare and step completed. procedure preparation, application, measurement continued ad infinitum. derived as an effective theory governing behavior computer its macroscopic scale where both cell size interval become infinitesimal. numerical simulation shock formation carried out agrees with exact analytical solution.