# Multi-block ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers

arXiv: https://arxiv.org/abs/2001.02069 · HTML: https://mlsanity.com/paper/2001.02069/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2020.

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

- [Efficient MILP Decomposition in Quantum Computing for ReLU Network Robustness](https://mlsanity.com/paper/2305.00472/) (2023)
- [Variational Quantum Eigensolver with Constraints (VQEC): Solving Constrained Optimization Problems via VQE](https://mlsanity.com/paper/2311.08502/) (2023)
- [A Quantum Fuzzy-based Approach for Real-Time Detection of Solar Coronal Holes](https://mlsanity.com/paper/2403.18347/) (2024)

## Abstract (arXiv)

Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved using, e.g., the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We present a decomposition-based approach to extend the applicability of current approaches to "quadratic plus convex" mixed binary optimization (MBO) problems, so as to solve a broad class of real-world optimization problems. In the MBO framework, we show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms), and continuous constrained convex subproblems (that can be solved cheaply with classical optimization solvers). The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit, an open-source quantum computing software development framework.