Box algorithm for the solution of differential equations on a quantum annealer

Abstract

Differential equations are ubiquitous in models of physical phenomena. Applications like steady-state analysis of heat flow and deflection in elastic bars often admit to a second order differential equation. In this paper, we discuss the use of a quantum annealer to solve such differential equations by recasting a finite element model in the form of an Ising hamiltonian. The discrete variables involved in the Ising model introduce complications when defining differential quantities, for instance, gradients involved in scientific computations of solid and fluid mechanics. To address this issue, a graph coloring based methodology is proposed which searches iteratively for solutions in a subspace of weak solutions defined over a graph, hereafter called as the 'box algorithm.' The box algorithm is demonstrated by solving a truss mechanics problem on the D-Wave quantum computer.

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• A quantum annealing-sequential quadratic programming assisted finite element simulation for non-linear and history-dependent mechanical problems
• Molecular Dynamics on Quantum Annealers
• A Formulation of Structural Design Optimization Problems for Quantum Annealing
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method
• Solving Helmholtz problems with finite elements on a quantum annealer