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

Siddhartha Srivastava, Veera Sundararaghavan

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 in- volved 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.