A hybrid quantum solver for the Lorenz system

Abstract

We develop a hybrid classical-quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved using the Variational Quantum Linear Solver (VQLS) algorithm. We present numerical results comparing the hybrid method with the classical approach for solving the Lorenz system. The simulation results demonstrate that the VQLS method can effectively compute solutions comparable to classical methods. The method is easily extended to solving similar nonlinear differential equations.

Figures (9)

• Figure 1: The trajectory was generated using the method described in Subsection \ref{['sec:method']} on a classical computer.
• Figure 2: Blue: the starting point is $(1e-16,1e-16,1e-16)$. Red: the starting point is $(1e-16,-1e-16,1e-16)$ and the parameters are $(13.92655741, 10, 8/3)$. The two trajectories generated using the method in Section \ref{['sec:method']} differ widely.
• Figure 3: The starting point is $(1,1,1)$.
• Figure 4: Five layer Ansatz used in the VQLS algorithm.
• Figure 6: The relationship between the condition number of matrix $A$ and the value of $h$.