# Reliable quantum simulations of plasma and fusion physics

**Supervisors: **Animesh Datta; Tom Goffrey

**Summary: **The field of quantum computation and simulations seeks to develop efficient quantum algorithms for problems that are classically inefficient to solve and are therefore computationally expensive. Furthermore, a quantum-enhanced simulation must not only perform a hard classical simulation efficiently, but also correctly. The latter goal is particularly important as real-world quantum computers are noisy and error prone. This project will develop efficient quantum simulations for problems in plasma and fusion physics, and establish their reliability in real-world quantum computers. The project is ideal for a student interested in a close interplay of quantum computation and simulation with plasma physics.

**Background**: Plasma physics and fusion science involve some of the most computationally demanding simulations in the physical sciences. Recently, a quantum algorithm has been proposed for classical plasma physics simulations such as those of the linearised Vlasov equation with a Maxwellian background distribution - a simulation that is, in fact, classically efficient [1]. Other preliminary explorations have also been undertaken [2].

In fusion science, warm dense matter (WDM) is a strongly correlated quantum system. WDM [3] is relevant for inertial confinement fusion during the solid to plasma transition driven by intense laser pulses, as well as the cores of giant planets and small stars. While quantum algorithms have been developed for simulating strongly correlated systems in condensed matter physics, such as the 2D Hubbard model, 2D XY model [4], no such algorithm exists for WDM.

**Project**: This project will develop quantum algorithms for solving the Vlasov equation going beyond the Maxwellian assumption, a regime practically relevant in high temperature tokamaks. One initial approach could be the Harrow-Hassidim-Lloyd algorithm [5], though further novel ideas will be required.

This project will also develop quantum algorithms for the simulation of WDM. There the starting point would be to evaluate the complexity of orbital-free DFT used in WDM simulations, before developing quantum Hamiltonian simulation algorithms.

Real-world quantum computers on which the above simulations are expected to run are improving in size and performance but remain noisy. It is thus crucial to quantify the reliability of their outputs. This project will do so by developing quantum accreditation [6] methods for the developed algorithms.

[1] A. Engel, G. Smith, S. E. Parker, Physical Review A, 100, 062315, (2019)

[2] I. Y. Dodin, E. A. Startsev, Physics of Plasmas 28, 092101 (2021)

[3] B. Larder *et al., *Science Advances, 5, eaaw1634, (2019)

[4] T. S. Cubitt *et al.*, Proceedings of the National Academy of Sciences, 115, 9497, (2018)

[5] A. W. Harrow, A. Hassidim, S. Lloyd, Physical Review Letters, 103, 150502, (2009)

[6] S. Ferracin, S. T. Merkel, D. McKay, A. Datta, Physical Review A, 104, 042603, (2021)