Manyparticle continuoustime 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 4th order Runge–Kutta integration. We prove that both Taylorseries expansion and Runge–Kutta algorithms are reliable and have a low computational cost, the Taylorseries 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 quadcore Intel CPUs for a 2particle system over lattices of increasing dimension, showing that the speedup provided by GPU computing, with respect to the OPENMP parallelization, lies in the range between 8x and (more than) 20x, depending on the frequency of postprocessing. GPUaccelerated 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. Program summary Program Title: cuQuWa Licensing provisions: GNU General Public License, version 3 Program Files doi: http://dx.doi.org/10.17632/vjpnjgycdj.1 Programming language: CUDA C Nature of problem: Evolution of manyparticle continuoustime quantumwalks on a multidimensional grid in a noisy environment. The submitted code is specialized for the simulation of 2particle quantumwalks with periodic boundary conditions. Solution method: Taylorseries expansion of the evolution operator. The densitymatrix is calculated by averaging multiple independent realizations of the system. External routines: cuBLAS, cuRAND Unusual features: Simulations are run exclusively on the graphic processing unit within the CUDA environment. An undocumented misbehavior in the randomnumber generation routine (cuRAND package) can corrupt the simulation of large systems, though no problems are reported for small and mediumsize systems. Compiling the code with the arch=sm_30 flag for compute capability 3.5 and above fixes this issue.
GPUaccelerated algorithms for manyparticle continuoustime quantum walks / Piccinini, Enrico; Benedetti, Claudia; Siloi, Ilaria; Paris, Matteo G. A.; Bordone, Paolo.  In: COMPUTER PHYSICS COMMUNICATIONS.  ISSN 00104655.  215:(2017), pp. 235245. [10.1016/j.cpc.2017.02.014]
GPUaccelerated algorithms for manyparticle continuoustime quantum walks
SILOI, ILARIA;BORDONE, Paolo
2017
Abstract
Manyparticle continuoustime 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 4th order Runge–Kutta integration. We prove that both Taylorseries expansion and Runge–Kutta algorithms are reliable and have a low computational cost, the Taylorseries 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 quadcore Intel CPUs for a 2particle system over lattices of increasing dimension, showing that the speedup provided by GPU computing, with respect to the OPENMP parallelization, lies in the range between 8x and (more than) 20x, depending on the frequency of postprocessing. GPUaccelerated 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. Program summary Program Title: cuQuWa Licensing provisions: GNU General Public License, version 3 Program Files doi: http://dx.doi.org/10.17632/vjpnjgycdj.1 Programming language: CUDA C Nature of problem: Evolution of manyparticle continuoustime quantumwalks on a multidimensional grid in a noisy environment. The submitted code is specialized for the simulation of 2particle quantumwalks with periodic boundary conditions. Solution method: Taylorseries expansion of the evolution operator. The densitymatrix is calculated by averaging multiple independent realizations of the system. External routines: cuBLAS, cuRAND Unusual features: Simulations are run exclusively on the graphic processing unit within the CUDA environment. An undocumented misbehavior in the randomnumber generation routine (cuRAND package) can corrupt the simulation of large systems, though no problems are reported for small and mediumsize systems. Compiling the code with the arch=sm_30 flag for compute capability 3.5 and above fixes this issue.File  Dimensione  Formato  

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