Parallel evaluation of quantum algorithms for computational fluid dynamics

Chia‐Liang Lin, Jenn‐Kun Kuo, Tsu-Hsu Yen

Shang Xian Matthew Lee, Melissa Kozul, Muhammad Usman +3 more

Quantum-inspired algorithms are an emerging class of algorithms for computational fluid dynamics (CFD) with potentially favourable scaling for large problems compared to classical methods. However, their applications have been limited to incompressible flows due to arithmetic limitations, which are addressed in this work. This work introduces the first true end-to-end quantum-inspired computational fluid dynamics (QICFD) solver for direct numerical simulation of the compressible Navier-Stokes equations, that is, all arithmetic operations, as well as initialisation and post-processing, are undertaken in the tensor train (TT) format. Importantly, new division and square-root algorithms using TTs enable the use of Sutherland's law for viscosity, and leverages recent improvements in TT arithmetic algorithms for reduced runtime and memory cost. The new QICFD solver is validated by comparison with the classical CFD solver HiPSTAR and by way of a challenging fluid-flow test case, the low resolution Taylor-Green Vortex (TGV) at Mach numbers of 0.8 and 0.1. The TGV test case is a transient turbulent case that is very sensitive to accumulating errors, yet our QICFD solver achieves excellent agreement with the classical CFD reference. This work demonstrates the correctness of the new TT division and square-root algorithms, and that QICFD is capable of compressible flow simulations. The new QICFD solver is also able to perform simultaneous simulations, running multiple TGV-like cases initialised differently in parallel with reduced extra cost. Finally, the demonstrated TGV test case reveals additional challenges of QICFD as well as highlight the need for future advances to make TT methods viable for industrially-relevant conditions.

Jeffrey Yepez

Giulio Malinverno, Javier Blasco Alberto, Pradeep Kanchan

This article aims to assess a quantum annealing algorithm proposed for the evaluation of the performance of refrigerant ejectors used in aircrafts environmental control systems to mix two streams at different pressures and temperatures, through the formalization of Society of Automotive Engineers (SAE) 1168/6 method in the quadratic unconstrained binary optimization model, including the extension for compressible fluids. The assessment includes the comparison with the traditional analytical methods based on SAE 1168/6 methodology as well as computational fluid-dynamics simulations of an existing ejector. The article shows how the behavior of the ejector can be evaluated with different independent approaches, namely experimental tests, analytical iterative and quantum-based methods, and the computational fluid dynamics (CFD) numerical simulations, with the quantum algorithm achieving reasonable practical results compared with the other methods, thus the article highlights how this method can be effectively implemented to solve thermo-fluid dynamic problems given its advantages and besides its intrinsic limitations.

Chuang-Chao Ye, Ning-Bo An, Teng-Yang Ma +5 more

Recent advancements in quantum computing provide opportunities to address the challenges of computational resource limitations in computational fluid dynamics (CFD). This work presents a hybrid quantum-classical CFD framework that leverages quantum linear algorithms to practical flow simulations. By transforming nonlinear fluid dynamics problems into linear systems, the framework employs quantum linear algorithms to compute solutions, effectively integrating quantum and classical computing approaches. Furthermore, this framework employs subspace methods to map the original large-scale linear systems to small ones solved by quantum linear algorithms, thereby enabling the solution of large-scale problems using the currently limited quantum resources. We applied the famous Harrow–Hassidim–Lloyd (HHL) algorithm and variational quantum linear solver to simulate complex flows, including unsteady flows around a cylinder, simulation of an aircraft with turbulence model, and combustion flows. The performance and quantum resource consumption of these algorithms were evaluated in practical flow scenarios, demonstrating their effectiveness with an average relative error lower than 0.001%. We conducted quantum resource and convergence analyses to adapt this framework for use with near-term quantum computers. Our framework supports simulations of up to 9.4 × 106 grid cells, marking a significant advancement from previous quantum approaches limited to simple flows. This paper not only offers a way for employing quantum linear algorithms in solving complex flow problems but also provides insights into optimizing quantum algorithms for CFD applications, pushing forward the practical utilization of quantum CFD.

Nathan Wiebe