Variational Quantum Evolution Equation Solver

• URL: http://arxiv.org/abs/2204.02912v1
• Date: Wed, 6 Apr 2022 16:02:11 GMT
• Title: Variational Quantum Evolution Equation Solver
• Authors: Fong Yew Leong, Wei-Bin Ewe, Dax Enshan Koh
• Abstract summary: Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. We propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator. We present a semi-implicit scheme for solving systems of evolution equations with non-linear terms, such as the reaction-diffusion and the incompressible Navier-Stokes equations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator. The use of encoded source states informed by preceding solution vectors results in faster convergence compared to random re-initialization. Through statevector simulations of the heat equation, we demonstrate how the time complexity of our algorithm scales with the ansatz volume for gradient estimation and how the time-to-solution scales with the diffusion parameter. Our proposed algorithm extends economically to higher-order time-stepping schemes, such as the Crank-Nicolson method. We present a semi-implicit scheme for solving systems of evolution equations with non-linear terms, such as the reaction-diffusion and the incompressible Navier-Stokes equations, and demonstrate its validity by proof-of-concept results.

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