Quantum Simulation of the Nonlinear Vlasov-Poisson System using Repeated Measurement

We present a hybrid quantum-classical algorithm based on repeated measurement to solve the one-dimensional, nonlinear Vlasov-Poisson equations. We store the distribution function in a quantum state, discretized in both position- and velocity-space, and map the Vlasov-Poisson system to a Hamiltonian form, where the Hamiltonian matrix is a function of dynamical variables. We use expectation values to update our Hamiltonian classically, then perform standard quantum Hamiltonian simulation over a short period, using the evaluated constant Hamiltonian matrix. We analyze the solution's accuracy and scaling as influenced by the stochastic sampling rate and the degree of discretization. We consider finally extensions to higher dimensions and more complex geometries.