## Quantum computing, quantum machine learning, and quantum-inspired computational methods

Can quantum algorithms revolutionise the simulation of turbulent flows? Project: https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/X017249/1 Our research vision is to create a framework and toolbox to synergise over 60 years of high-performance computing with quantum computing to revolutionise understanding, modelling, and simulation of nonlinear problems, such as turbulence. Context, research questions and overarching goal. The efficient conversion of energy in wind farms, the explosion of a supernova, and the air resistance around airplanes have a common factor: a fluid. Fluid mechanics is a major UK industrial and research strength, which is an enabling technology from transport, healthcare, marine and energy. According to numbers estimated in a 2021 paper [1], fluid mechanics is a sector that employs approximately 45,000 in th UK. Fluids of practical interest can be turbulent. Both in fundamental and applied research, numerical simulation is key to understanding, predicting and controlling turbulent flows. In fundamental research, the goal is to unveil the physical mechanisms, scales and dynamics of turbulence. In industry, the goal is to embed accurate numerical simulations of turbulence with a fast turnaround into the engineering design cycle. We are far from achieving this.Although we know an excellent model for turbulent flows (the Navier-Stokes equations), the chaotic nature of turbulence makes accurate computer simulations exceedingly expensive. For example, a state-of-the-art simulation of turbulence of a simple channel flow needs 350 billion grid points and takes 260 million computing hours. To analyse fundamental and engineering configurations, large supercomputing resources are deployed. Although the flop operations of computers roughly double every two years, we will need to wait for decades before being able to tackle a fundamental flow, such as a channel flow, at realistic flow velocities. The next generation of large exascale computers, however, will only allow for a three- to five-fold increase in the flow velocities with respect to the state-of-the-art. The question is “ how can we accurately simulate turbulent flows of practical interest with affordable computations?” Classical algorithms are reaching their limits.Key to this proposal is the observation that the numerical solution of the nonlinear equations of turbulence revolves around solving linear systems. Linear systems can be solved formidably fast by quantum algorithms. Quantum computing offers a repository of algorithms that can revolutionise computational science and turbulence simulations. This is because classical computers require computational resources that scale exponentially with the system’s degrees of freedom, whereas quantum algorithms scale only polynomially. This is also known as the quantum advantage. If the conjectures published in 2021 by Google, Microsoft, IBM, MIT, Harvard, among others, on the quantum advantage are correct, the simulation of a turbulent system can be accelerated by ten to thousand orders of magnitudes. This project will pioneer this research field. In this project, we will develop and test quantum-enhanced computational fluid dynamics (q-CFD) by exploiting the untested, but plausible, quantum advantage. This will blaze the trail for computing turbulence with a synergistic combination of classical and quantum algorithms. |