# QUBO-based training for VQAs on Quantum Annealers

arXiv: https://arxiv.org/abs/2509.01821 · HTML: https://mlsanity.com/paper/2509.01821/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [QUBO Formulations for Training Machine Learning Models](https://mlsanity.com/paper/2008.02369/) (2020)
- [An Empirical Review of Optimization Techniques for Quantum Variational Circuits](https://mlsanity.com/paper/2202.01389/) (2022)
- [Training Neural Networks with Universal Adiabatic Quantum Computing](https://mlsanity.com/paper/2308.13028/) (2023)

## Abstract (arXiv)

Quantum annealers provide an effective framework for solving large-scale combinatorial optimization problems. This work presents a novel methodology for training Variational Quantum Algorithms (VQAs) by reformulating the parameter optimization task as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Unlike traditional gradient-based methods, our approach directly leverages the Hamiltonian of the chosen VQA ansatz and employs an adaptive, metaheuristic optimization scheme. This optimization strategy provides a rich set of configurable parameters which enables the adaptation to specific problem characteristics and available computational resources. The proposed framework is generalizable to arbitrary Hamiltonians and integrates a recursive refinement strategy to progressively approximate high-quality solutions. Experimental evaluations demonstrate the feasibility of the method and its ability to significantly reduce computational overhead compared to classical and evolutionary optimizers, while achieving comparable or superior solution quality. These findings suggest that quantum annealers can serve as a scalable alternative to classical optimizers for VQA training, particularly in scenarios affected by barren plateaus and noisy gradient estimates, and open new possibilities for hybrid quantum gate - quantum annealing - classical optimization models in near-term quantum computing.