  Solving partial differential equations using an annealing-based approach is
based on solving generalized eigenvalue problems. When a partial differential
equation is discretized, it leads to a system of linear equations (SLE).
Solving an SLE can be expressed as a general eigenvalue problem, which can be
converted into an optimization problem with the objective function being a
generalized Rayleigh quotient. The proposed algorithm allows the computation of
eigenvectors at arbitrary precision without increasing the number of variables
using an Ising machine. Simple examples solved using this method and
theoretical analysis provide a guideline for appropriate parameter settings.
