  Numerous scientific and engineering applications require numerically solving
systems of equations. Classically solving a general set of polynomial equations
requires iterative solvers, while linear equations may be solved either by
direct matrix inversion or iteratively with judicious preconditioning. However,
the convergence of iterative algorithms is highly variable and depends, in
part, on the condition number. We present a direct method for solving general
systems of polynomial equations based on quantum annealing, and we validate
this method using a system of second-order polynomial equations solved on a
commercially available quantum annealer. We then demonstrate applications for
linear regression, and discuss in more detail the scaling behavior for general
systems of linear equations with respect to problem size, condition number, and
search precision. Finally, we define an iterative annealing process and
demonstrate its efficacy in solving a linear system to a tolerance of
$10^{-8}$.
