Lokta-Volterra simulation on quantum computers

Simulating non-linearity with a quantum computer is a longstanding goal, with significant efforts from both the plasma computational physics community and the quantum computing community. Identifying which non-linearities can be simulated by a quantum computer is crucial for developing new computational tools for plasma physics simulations and understanding the capabilities of quantum computers. The Koopman-von Neumann (KvN) mapping proposes a straightforward method to address some non-linear PDEs through phase space simulation. The advantage of this scheme lies in the fact that, in many cases, the quantum numerical scheme requires only the Quantum Fourier Transform and diagonal operators that are efficiently implementable on quantum computers. In this work, we present a general and efficient algorithm to simulate the Lokta-Volterra system using the KvN mapping. The Lotka-Volterra system: a predator-prey model originally developed to understand population dynamics. In plasma physics, predator-prey models such as the Kim-Diamond model are used to investigate shear-flow-driven turbulence. In the absence of external sources or damping, the Kim-Diamond model reduces exactly to the Lokta-Volterra equations. Consequently, this work is a step toward simulating nonlinear plasma physics phenomena on quantum computers.