Feasibility study to quantify the potential of using quantum algorithms to simulate MHD effects in liquid metals

This work addresses the computational challenge of simulating the magnetohydrodynamic equations of liquid metals such as Li or LiPb, which are used as coolants and sources of neutron multipliers and tritium breeding in nuclear fusion reactors. This project is a feasibility study into the use of quantum algorithms for simulating the magnetohydrodynamics of liquid metals, which are used as coolants and sources of tritium in nuclear fusion reactors. The fusion industry requires accurate predictions of liquid metal dynamics under high intensity magnetic fields.

Simulating liquid metal flows within fusion reactors presents some specific challenges, due to the presence of phenomena such as turbulences induced by the magnetic fields present. In the case of tritium breeding in fusion reactors, this will directly influence the diffusion of tritium into the fuel cycle. It is also essential that liquid metals operate at high flow rates under these conditions. Accurate simulation of the magnetohydrodynamics of liquid metals could pave the way for more realistic simulation of liquid metals and computer-aided design of future fusion reactors.

Modelling turbulences accurately with traditional finite difference methods requires very fine grids to achieve a high enough resolution, with accurate solutions quickly becoming computationally intractable using classical computers. Quantum computers present a new computational paradigm which has the potential speed up computational tasks such as solving certain partial differential equations (PDEs). Quantum computing algorithms for solving PDEs have shown promise in modelling scenarios which require extremely high resolutions, such as turbulence.

This project aims to assess the feasibility of applying quantum algorithms for simulating liquid metal flows. Currently proposed quantum algorithms for solving nonlinear PDEs are formulated in an abstract way, which cannot readily be implemented. Those algorithms typically address simpler PDEs than the MHD equations. A specific novelty of the proposed idea is the inclusion of the Lorentz force term present in the PDE, which has not been considered in quantum algorithms before and is essential to accurately modelling liquid metals in fusion reactors. This project will also investigate the resources required for running such algorithms on future fault-tolerant quantum devices and attempt to provide a framework for estimating the resources of these nonlinear PDEs. Successful deployment of these algorithms in the future could address the challenges of high-resolution simulation of liquid metals, accelerate engineering cycles for new reactors and potentially reduce the massive costs associated with experimental testing.