Recent years have seen significant advances in quantum/quantum-inspired
technologies capable of approximately searching for the ground state of Ising
spin Hamiltonians. The promise of leveraging such technologies to accelerate
the solution of difficult optimization problems has spurred an increased
interest in exploring methods to integrate Ising problems as part of their
solution process, with existing approaches ranging from direct transcription to
hybrid quantum-classical approaches rooted in existing optimization algorithms.
While it is widely acknowledged that quantum computers should augment classical
computers, rather than replace them entirely, comparatively little attention
has been directed toward deriving analytical characterizations of their
interactions. In this paper, we present a formal analysis of hybrid algorithms
in the context of solving mixed-binary quadratic programs (MBQP) via Ising
solvers. We show the exactness of a convex copositive reformulation of MBQPs,
allowing the resulting reformulation to inherit the straightforward analysis of
convex optimization. We propose to solve this reformulation with a hybrid
quantum-classical cutting-plane algorithm. Using existing complexity results
for convex cutting-plane algorithms, we deduce that the classical portion of
this hybrid framework is guaranteed to be polynomial time. This suggests that
when applied to NP-hard problems, the complexity of the solution is shifted
onto the subroutine handled by the Ising solver