Second Quantization Model of the Vlasov–Poisson System for Quantum Computation

Fault-tolerant quantum computers will solve many classes of problems more efficiently than classical computers can, but nonlinearities can destroy quantum advantages. To address this, we model the Vlasov–Poisson equations using a second quantized Schrodinger–Poisson system, which is structure-preserving, finite-dimensional, linear, and unitary. This quantized system can capture nonlinear physics for finite times, but it will not offer any advantage in integrating single particle trajectories. However, because the quantized system is linear, it is possible to integrate entire distributions at the same computational cost of integrating a single trajectory. We present numerical examples of parallel integration in the second quantized system, discuss the mitigation of quantum effects including interference, and showcase methods for internally determining the quality of classical correspondence.