  Analytical and practical evidence indicates the advantage of quantum
computing solutions over classical alternatives. Quantum-based heuristics
relying on the variational quantum eigensolver (VQE) and the quantum
approximate optimization algorithm (QAOA) have been shown numerically to
generate high-quality solutions to hard combinatorial problems, yet
incorporating constraints to such problems has been elusive. To this end, this
work puts forth a quantum heuristic to cope with stochastic binary
quadratically constrained quadratic programs (QCQP). Identifying the strength
of quantum circuits to efficiently generate samples from probability
distributions that are otherwise hard to sample from, the variational quantum
circuit is trained to generate binary-valued vectors to approximately solve the
aforesaid stochastic program. The method builds upon dual decomposition and
entails solving a sequence of judiciously modified standard VQE tasks. Tests on
several synthetic problem instances using a quantum simulator corroborate the
near-optimality and feasibility of the method, and its potential to generate
feasible solutions for the deterministic QCQP too.
