A Review of the Current State-of-the-Art of Quantum Computing for CFD: Approaches, Advantages, and Limitations

Abstract This article is meant to review of current state-of-the-art of quantum computing applied to computational fluid dynamics and discuss possible applications of Quantum computing technologies in the area of thermofluid-dynamics. Quantum computers are devices that use quantum mechanical phenomena like superposition, entanglement and interference to perform calculations, with a theoretical high speed-up compared with traditional computing solutions, especially for computer science applications but also for engineering applications, like structural optimization, resolution of linear system and analysis of complex dynamics. Beside the consideration about the hardware implementation of these type of devices, this article propose a simplified taxonomy of the technologies that can be currently envisioned for the resolution of thermofluid dynamics problems, identifying the three main approaches, i.e., the traditional algorithmic or circuital approach (with the use of serval algorithms dedicated to the resolution of partial differential equations as well as algorithms dedicated to optimization and search), the analog approach (with the development of direct simulations given the analogy between quantum mechanical systems, like the Schrödinger flow or the Dirac Majorana formulation, and fluid problems, like the inviscid flow or the Lattice Boltzmann model), and the applications based on machine learning techniques. The article discusses practical examples which highlight the flexibility of the methods as well as their intrinsic limitations that hinder the application to many industrial problems, i.e. the simplifications requires to manage physical non-linearities, or the absence of a general purpose algorithm, indicating, beside the intrinsic properties of each method, the technology readiness level (TRL) of this type of approach and the required level of modelling.