QUANT: QUANTUM ANNEALING WITH LEARNT COU-PLINGS

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 are available at https://4dqv.mpi-inf.mpg.de/QuAnt/.

1. INTRODUCTION

Hybrid computer vision methods that can be executed partially on a quantum computer (QC) are an emerging research area (Boyda et al., 2017; Cavallaro et al., 2020; Seelbach Benkner et al., 2021; Yurtsever et al., 2022) . Compared to classical methods, they promise to solve computationally demanding (e.g., combinatorial) sub-problems faster, with improved scaling, and without relaxations that often lead to approximate solutions. Although quantum primacy has not yet been demonstrated in remotely practical usages of quantum computing, all existing quantum computer vision (QCV) methods fundamentally assume that it will be achieved in the future. Thus, solving these suitable algorithmic parts on a QC has the potential to reshape the field. However, reformulating them for execution on a QC is often non-trivial. QCV continues building up momentum, fuelled by accessible experimental quantum annealers (QA) allowing to solve practical (N P-hard) optimisation problems. Existing QCV methods using QAs rely on analytically deriving QUBOs (both QUBO matrices and solution encodings) for a specific problem type, which is challenging, especially since solutions need to be encoded as binary vectors (Li & Ghosh, 2020; Seelbach Benkner et al., 2020; 2021; Birdal et al., 2021) . This often leads to larger encodings than necessary, severely impacting scalability. Alternatively, QUBO derivations with neural networks are conceivable but have not yet been scrutinised in the QA literature. In stark contrast to the state of the art, this paper proposes, for the first time, to learn QUBO forms from data for any problem type using backpropagation (see Fig. 1 ). Our framework captures, in the weights of a neural network, the entire subset of QUBOs belonging to a problem type; a single forward pass yields the QUBO form for a given problem instance. It is thus a meta-learning approach in the context of hybrid (quantum-classical) neural network training, in which the superordinate network instantiates the parameters of the QUBO form. We find that sampling instantiated QUBOs can be a reasonable alternative to non-quantum neural baselines that regress the solution directly.

