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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