  We outline how auxiliary-field quantum Monte Carlo (AFQMC) can leverage
graphical processing units (GPUs) to accelerate the simulation of solid state
sytems. By exploiting conservation of crystal momentum in the one- and
two-electron integrals we show how to efficiently formulate the algorithm to
best utilize current GPU architectures. We provide a detailed description of
different optimization strategies and profile our implementation relative to
standard approaches, demonstrating a factor of 40 speed up over a CPU
implementation. With this increase in computational power we demonstrate the
ability of AFQMC to systematically converge solid state calculations with
respect to basis set and system size by computing the cohesive energy of Carbon
in the diamond structure to within 0.02 eV of the experimental result.
