# Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing

arXiv: https://arxiv.org/abs/2307.06542 · HTML: https://mlsanity.com/paper/2307.06542/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 27 references that are in the map.
- First posted on arXiv 13 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Toward Robustness against Label Noise in Training Deep Discriminative Neural Networks](https://mlsanity.com/paper/1706.00038/) (2017)
- [Application of Quantum Annealing to Training of Deep Neural Networks](https://mlsanity.com/paper/1510.06356/) (2015)
- [A Review Paper: Noise Models in Digital Image Processing](https://mlsanity.com/paper/1505.03489/) (2015)
- [Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q](https://mlsanity.com/paper/2005.03247/) (2020)
- [Boltzmann Machines and Denoising Autoencoders for Image Denoising](https://mlsanity.com/paper/1301.3468/) (2013)

## Built on by (most cited first, 2 of 2)

- [Image Denoising with Machine Learning: A Novel Approach to Improve Quantum Image Processing Quality and Reliability](https://mlsanity.com/paper/2402.11645/) (2024)
- [QuantumQUBO Agent: Automating Quadratic Unconstrained Binary Optimization (QUBO) Formulation Generation from Natural Language](https://mlsanity.com/paper/2609.10629/) (2026)

## Abstract (arXiv)

We investigate a framework for binary image denoising via restricted Boltzmann machines (RBMs) that introduces a denoising objective in quadratic unconstrained binary optimization (QUBO) form and is well-suited for quantum annealing. The denoising objective is attained by balancing the distribution learned by a trained RBM with a penalty term for derivations from the noisy image. We derive the statistically optimal choice of the penalty parameter assuming the target distribution has been well-approximated, and further suggest an empirically supported modification to make the method robust to that idealistic assumption. We also show under additional assumptions that the denoised images attained by our method are, in expectation, strictly closer to the noise-free images than the noisy images are. While we frame the model as an image denoising model, it can be applied to any binary data. As the QUBO formulation is well-suited for implementation on quantum annealers, we test the model on a D-Wave Advantage machine, and also test on data too large for current quantum annealers by approximating QUBO solutions through classical heuristics.