A Review of Molecular Representations in Quantum Machine Learning

This review synthesizes state-of-the-art quantum machine learning (QML) techniques for molecular modeling, focusing on strategies designed to overcome the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware. A central challenge is the encoding of high-dimensional chemical data, including fingerprints, graphs, and 3D geometries, onto low-qubit devices. The survey covers several key approaches, including the radical compression of molecular fingerprints for discriminative classifiers; hybrid generative models that embed quantum circuits within classical graph-based frameworks; iterative encoding of local atomic neighborhoods to process molecules of any size with fixed-size circuits; and the use of quantum annealers to sample from energy-based models by reformulating them as quadratic unconstrained binary optimization (QUBO) problems. This review categorizes these distinct methods, illuminates the common principles of hybrid design, and identifies key bottlenecks.