A Quantum Approach for Stochastic Constrained Binary Optimization

TL;DR

This paper introduces a quantum heuristic leveraging variational quantum circuits to efficiently solve stochastic constrained binary quadratic programs, demonstrating near-optimal solutions on synthetic instances.

Contribution

It presents a novel quantum approach that incorporates constraints into VQE-based heuristics for stochastic QCQPs, extending quantum optimization capabilities.

Findings

Demonstrates near-optimal solutions on synthetic problems

Shows feasibility of quantum heuristic for constrained QCQPs

Potential to generate feasible solutions for deterministic QCQPs

Abstract

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.