Second quantization of the nonlinear Vlasov–Poisson system for quantum computation

Abstract

Abstract Current quantum algorithms for plasma physics require linearized systems, and quantum algorithms for nonlinear systems are highly system-specific. Second quantization, which is system-agnostic, has the exceptional capacity to render many systems suitable for quantum computation, i.e. finite-dimensional, linear, and unitary. We show how the Fourier mode-truncated Schrödinger–Poisson representation of the Vlasov–Poisson system can be second quantized into a finite-dimensional Hamiltonian system. With three- and five-mode examples, the second quantized system is shown to reproduce corresponding nonlinear dynamics in the Schrödinger–Poisson system in the simulated time intervals. Parallel integration of wide distributions of initial conditions of the Vlasov–Poisson system has the potential to be efficiently computable using the proposed second quantized model on a quantum computer.