Quantum Computing for Plasma Physics via Second Quantization*

Quantum computers promise to transform computational plasma physics via efficient state encoding and the potential of quantum supremacy for certain classes of problems. However, simulating plasma phenomena on quantum computers poses special challenges. The most fundamental equations of plasma physics, the Vlasov-Maxwell equations, are nonlinear and admit many instabilities, but quantum computers can only simulate linear, unitary dynamics. We address this disparity by deriving inherently quantum equations for plasma physics using a second quantization method.

In this poster, I discuss the second quantization of classical plasma physics equations, including the trivial linear two-wave interaction (shown to be equivalent to the finite-dimensional discrete quantum harmonic oscillator [1]), the homogenous quantum three-wave interaction [2] (first described in [3]), and the inhomogeneous quantum three-wave interaction. I numerically show that the unitary, quantum systems I describe limit to the behavior of the classical, nonlinear and potentially unstable equations at high dimensions [4], and I explore the potential advantages of the second quantization method over other methods for linearizing nonlinear equations for quantum computing including Koopman embedding.

[1] M. Q. May and H. Qin, ArXiV preprint (2024).

[2] M. Q. May and H. Qin, Phys. Rev. A 107, 062204 (2023).

[3] Y. Shi, H. Qin, and N. Fisch, Phys. Plamsas 28, 042104 (2021).

[4] M. Q. May and H. Qin, J. Plasma Physics, in press (2024)