[Paper Review] QuAnt: Quantum Annealing with Learnt Couplings

Marcel Seelbach Benkner, Maximilian Krahn+4 more|arXiv (Cornell University)|Oct 13, 2022

Advanced Neural Network Applications4 citations

TL;DR

This paper introduces QuAnt, a meta-learning framework that automatically learns QUBO formulations for combinatorial optimization problems in computer vision via gradient backpropagation, bypassing complex analytical derivations. By training a neural network to regress problem-specific QUBO matrices, QuAnt enables efficient quantum annealing with significantly reduced qubit requirements, achieving competitive performance on graph matching, point cloud registration, and 3D rotation estimation—outperforming prior quantum methods in noisy settings.

ABSTRACT

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.

Motivation & Objective

• To eliminate the need for problem-specific analytical derivations of QUBO formulations in quantum computer vision.
• To enable flexible, compact solution encodings by learning QUBO matrices from data instead of deriving them.
• To develop a general, scalable framework applicable across diverse computer vision problems without redesigning QUBO structures.
• To demonstrate that learned QUBOs can outperform classical baselines and prior quantum methods, especially under noisy conditions.
• To enable integration of quantum annealers as differentiable layers in neural networks through a contrastive loss.

Proposed method

• A multi-layer perceptron (MLP) regresses the QUBO matrix A from a problem instance vector p, enabling end-to-end training.
• The framework uses a contrastive loss to enable backpropagation through the non-differentiable quantum annealing process, avoiding direct gradient computation through the solver.
• Quantum annealing is used to find the minimizer x* of the QUBO defined by A, which serves as the predicted solution.
• The method is solver-agnostic and compatible with quantum annealing, simulated annealing, or exhaustive search during training and inference.
• A meta-learning setup trains the MLP to generalize across problem instances of the same type, with the QUBO matrix implicitly encoded in the network weights.
• Minor embeddings are used to map dense QUBOs to the hardware constraints of current D-Wave quantum annealers, minimizing qubit overhead.

Experimental results

Research questions

• RQ1 Can QUBO formulations for computer vision problems be learned from data using backpropagation instead of analytical derivation?
• RQ2 Does a learned QUBO approach outperform direct regression of solutions in terms of solution quality and robustness?
• RQ3 Can the framework generalize across diverse problem types such as graph matching, point cloud registration, and rotation estimation?
• RQ4 How does the method scale in terms of logical and physical qubit usage compared to prior quantum computer vision methods?
• RQ5 To what extent does the learned QUBO approach maintain performance under noisy input conditions, such as incorrect correspondences or corrupted point clouds?

Key findings

• QuAnt outperforms the classical Procrustes method in rotation estimation even with 1% incorrect correspondences, and its advantage grows with increasing noise levels.
• In graph matching with 20% incorrect correspondences, QuAnt maintains a mean error of 3.7 and median of 3.0, significantly outperforming the baseline and classical methods.
• For 2D point set registration under 20% uniform noise, QuAnt achieves a mean error of 10.3 and median of 5.4, outperforming general baselines and approaching the performance of AQM, an upper bound.
• The method requires only 9 logical and 14 physical qubits for a 9-node QUBO, demonstrating high qubit efficiency compared to prior work.
• Ablation studies show that removing either the unique solution loss or the MLP loss leads to significantly degraded performance, confirming the importance of both components.
• QuAnt generalizes well across problem types, achieving competitive results on graph matching, 2D and 3D alignment, and rotation estimation without retraining for each task.