Quantum Calculation for Two-Stream Instability and Advection Test of Vlasov-Maxwell Equations: Numerical Evaluation of Hamiltonian Simulation

Abstract

The Vlasov-Maxwell equations provide kinetic simulations of collisionless plasmas, but numerically solving them on classical computers is often impractical. This is due to the computational resource constraints imposed by the time evolution in the 6-dimensional phase space, which requires broad spatial and temporal scales. In this study, we develop a quantum-classical hybrid Vlasov-Maxwell solver. Specifically, the Vlasov solver implements the Hamiltonian simulation based on Quantum Singular Value Transformation (QSVT), coupled with a classical Maxwell solver. We perform numerical simulation of a 1D advection test and a 1D1V two-stream instability test on the Qiskit-Aer-GPU quantum circuit emulator with an A100 GPU. The computational complexity of our quantum algorithm can potentially be reduced from the classical $O(N^6{T}^2)$ to $O(\text{poly}(\log (N),N,T))$ for the $N$ grid system and simulation time $T$. Furthermore, the numerical analysis reveals that our quantum algorithm is robust under larger time steps compared with classical algorithms with the constraint of Courant-Friedrichs-Lewy (CFL) condition.

24 pages, 11 figures

References in corpus (12)

• Quantum algorithm for solving linear systems of equations
• Universal computation by quantum walk
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Architectures for a quantum random access memory
• Quantum algorithm and circuit design solving the Poisson equation
• Quantum simulation of partial differential equations via Schrodingerisation: technical details
• Quantum Circuits for partial differential equations via Schrödingerisation
• Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits
• Quantum Signal Processing for simulating cold plasma waves
• An open-source modular framework for quantum computing
• A quantum algorithm for the linear Vlasov equation with collisions
• Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos

Cited by in corpus (1)

• Post-Moore Technologies for Plasma Simulation: A Community Roadmap