# A Quantum Approach for Stochastic Constrained Binary Optimization

arXiv: https://arxiv.org/abs/2301.01443 · HTML: https://mlsanity.com/paper/2301.01443/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2023.

## Built on by (most cited first, 3 of 3)

- [Qubit-efficient Variational Quantum Algorithms for Image Segmentation](https://mlsanity.com/paper/2405.14405/) (2024)
- [Solving Conic Programs over Sparse Graphs using a Variational Quantum Approach: The Case of the AC Optimal Power Flow](https://mlsanity.com/paper/2509.00341/) (2025)
- [Variational Quantum Eigensolver with Constraints (VQEC): Solving Constrained Optimization Problems via VQE](https://mlsanity.com/paper/2311.08502/) (2023)

## Abstract (arXiv)

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.