  We propose a scheme for solving mixed-integer programming problems in which
the optimization problem is translated to a ground-state preparation problem on
a set of bosonic quantum field modes (qumodes). We perform numerical
demonstrations by simulating a circuit-based optical quantum computer with each
individual qumode prepared in a Gaussian state. We simulate an adiabatic
evolution from an initial mixing Hamiltonian, written in terms of the momentum
operators of the qumodes, to a final Hamiltonian which is a polynomial of the
position and boson number operators. In these demonstrations, we solve a
variety of small non-convex optimization problems in integer programming,
continuous non-convex optimization, and mixed-integer programming.
