  Many-particle continuous-time quantum walks (CTQWs) represent a resource for
several tasks in quantum technology, including quantum search algorithms and
universal quantum computation. In order to design and implement CTQWs in a
realistic scenario, one needs effective simulation tools for Hamiltonians that
take into account static noise and fluctuations in the lattice, i.e.
Hamiltonians containing stochastic terms. To this aim, we suggest a parallel
algorithm based on the Taylor series expansion of the evolution operator, and
compare its performances with those of algorithms based on the exact
diagonalization of the Hamiltonian or a 4-th order Runge-Kutta integration. We
prove that both Taylor-series expansion and Runge-Kutta algorithms are reliable
and have a low computational cost, the Taylor-series expansion showing the
additional advantage of a memory allocation not depending on the precision of
calculation. Both algorithms are also highly parallelizable within the SIMT
paradigm, and are thus suitable for GPGPU computing. In turn, we have
benchmarked 4 NVIDIA GPUs and 3 quad-core Intel CPUs for a 2-particle system
over lattices of increasing dimension, showing that the speedup providend by
GPU computing, with respect to the OPENMP parallelization, lies in the range
between 8x and (more than) 20x, depending on the frequency of post-processing.
GPU-accelerated codes thus allow one to overcome concerns about the execution
time, and make it possible simulations with many interacting particles on large
lattices, with the only limit of the memory available on the device.
