Measuring similarity between molecules is an important part of virtual screening (VS) experiments deployed during the early stages of drug discovery. Most widely used methods for evaluating the similarity of molecules use molecular fingerprints to encode structural information. While similarity methods using fingerprint encodings are efficient, they do not consider all the relevant aspects of molecular structure. In this paper, we describe a quantum-inspired graph-based molecular similarity (GMS) method for ligand-based VS. The GMS method is formulated as a quadratic unconstrained binary optimization problem that can be solved using a quantum annealer, providing the opportunity to take advantage of this nascent and potentially groundbreaking technology. In this study, we consider various features relevant to ligand-based VS, such as pharmacophore features and three-dimensional atomic coordinates, and include them in the GMS method. We evaluate this approach on various datasets from the DUD_LIB_VS_1.0 library. Our results show that using three-dimensional atomic coordinates as features for comparison yields higher early enrichment values. In addition, we evaluate the performance of the GMS method against conventional fingerprint approaches. The results demonstrate that the GMS method outperforms fingerprint methods for most of the datasets, presenting a new alternative in ligand-based VS with the potential for future enhancement.