GPU-accelerated algorithms for many-particle continuous-time quantum walks

TL;DR

This paper introduces GPU-accelerated algorithms for simulating many-particle continuous-time quantum walks, enabling faster and scalable computations crucial for quantum technology applications.

Contribution

It presents a parallel Taylor series expansion algorithm for Hamiltonian evolution, optimized for GPU computing, outperforming traditional methods in speed and scalability.

Findings

GPU acceleration yields 8x to 20x speedup over CPU-based methods.

The Taylor-series expansion algorithm is memory-efficient and highly parallelizable.

Simulations of many interacting particles on large lattices become feasible with GPU computing.

Abstract

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.