Parallel evaluation of quantum algorithms for computational fluid dynamics

Abstract

The development and evaluation of quantum computing algorithms for computational fluid dynamics is described. A hybrid classical/quantum hardware approach is assumed where selected computationally intensive parts of the solver are implemented as quantum circuits. The vortex-in-cell method is considered as an example where the Quantum Fourier Transform is used to build a Poisson solver. Computational aspects of simulating the required quantum circuits on a classical parallel computer are discussed including an analysis of the required data exchanges for a distributed-memory parallelization using message-passing. The effect of errors and noise in the quantum algorithm on the flow solution is analyzed and it is shown that despite inevitable noise and uncertainties, meaningful flow simulations can be performed using a hybrid classical/quantum hardware approach. An improved version of the vortex-in-cell method with increased resilience to noise is also discussed along with suggestions for future steps. The presented work is limited to a single CFD algorithm. However, building on this work, a broader range of algorithms will be considered in future work.