Abstract: Quantum computing promises to accelerate simulations of finite-dimensional, linear, unitary systems, but the most basic equations of plasma physics, the Vlasov–Maxwell equations are infinite-dimensional, nonlinear, and symplectic. Each of these three differences poses nontrivial problems for the hope of a quantum advantage in plasma physics. We address them through the structure preserving method of second quantization applied to increasingly sophisticated systems: the quantum harmonic oscillator, the nonlinear three-wave interaction, and the Vlasov–Poisson system. We describe a new derivation of the finite-dimensional discrete quantum harmonic oscillator, which natively furnishes dimension ladder operators, allowing for dynamic resolution adjustment of quantum simulations of the oscillator. Next, we review work on the quantization of the nonlinear three-wave interaction, including analytical and numerical studies of the three wave instability and nonlinear oscillation. Finally, the talk will conclude with a discussion of recent results and ongoing research on the second quantized Vlasov–Poisson system and the possibility of its efficient quantum simulation.
