# QuAnt: Quantum Annealing with Learnt Couplings

arXiv: https://arxiv.org/abs/2210.08114 · HTML: https://mlsanity.com/paper/2210.08114/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 74 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers](https://mlsanity.com/paper/2003.11657/) (2020)
- [Quantum-enhanced machine learning](https://mlsanity.com/paper/1610.08251/) (2016)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (2019)
- [Quantum Permutation Synchronization](https://mlsanity.com/paper/2101.07755/) (2021)
- [Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems](https://mlsanity.com/paper/1911.11071/) (2019)
- [Traffic flow optimization using a quantum annealer](https://mlsanity.com/paper/1708.01625/) (2017)
- [Q-Match: Iterative Shape Matching via Quantum Annealing](https://mlsanity.com/paper/2105.02878/) (2021)
- [A practical heuristic for finding graph minors](https://mlsanity.com/paper/1406.2741/) (2014)
- [A Quantum Computational Approach to Correspondence Problems on Point Sets](https://mlsanity.com/paper/1912.12296/) (2019)
- [Adiabatic Quantum Computing for Multi Object Tracking](https://mlsanity.com/paper/2202.08837/) (2022)
- [Adiabatic Quantum Graph Matching with Permutation Matrix Constraints](https://mlsanity.com/paper/2107.04032/) (2021)
- [Quantum-soft QUBO Suppression for Accurate Object Detection](https://mlsanity.com/paper/2007.13992/) (2020)
- [Adiabatic Quantum Linear Regression](https://mlsanity.com/paper/2008.02355/) (2020)
- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [Quantum Motion Segmentation](https://mlsanity.com/paper/2203.13185/) (2022)
- [Image classification using quantum inference on the D-Wave 2X](https://mlsanity.com/paper/1905.13215/) (2019)
- [Quantum Robust Fitting](https://mlsanity.com/paper/2006.06986/) (2020)
- [Quantum Annealing Formulation for Binary Neural Networks](https://mlsanity.com/paper/2107.02751/) (2021)
- [Matching Point Sets with Quantum Circuit Learning](https://mlsanity.com/paper/2102.06697/) (2021)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)

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

- [3D-QAE: Fully Quantum Auto-Encoding of 3D Point Clouds](https://mlsanity.com/paper/2311.05604/) (2023)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Quantum Annealing for Computer Vision Minimization Problems](https://mlsanity.com/paper/2312.12848/) (2023)

## Abstract (arXiv)

Modern quantum annealers can find high-quality solutions to combinatorial optimisation objectives given as quadratic unconstrained binary optimisation (QUBO) problems. Unfortunately, obtaining suitable QUBO forms in computer vision remains challenging and currently requires problem-specific analytical derivations. Moreover, such explicit formulations impose tangible constraints on solution encodings. In stark contrast to prior work, this paper proposes to learn QUBO forms from data through gradient backpropagation instead of deriving them. As a result, the solution encodings can be chosen flexibly and compactly. Furthermore, our methodology is general and virtually independent of the specifics of the target problem type. We demonstrate the advantages of learnt QUBOs on the diverse problem types of graph matching, 2D point cloud alignment and 3D rotation estimation. Our results are competitive with the previous quantum state of the art while requiring much fewer logical and physical qubits, enabling our method to scale to larger problems. The code and the new dataset will be open-sourced.