The growing quantity of public and private data sets focused on small molecules screened against biological targets or whole organisms provides a wealth of drug discovery relevant data. This is matched by the availability of machine learning algorithms such as Support Vector Machines (SVM) and Deep Neural Networks (DNN) that are computationally expensive to perform on very large data sets with thousands of molecular descriptors. Quantum computer (QC) algorithms have been proposed to offer an approach to accelerate quantum machine learning over classical computer (CC) algorithms, however with significant limitations. In the case of cheminformatics, which is widely used in drug discovery, one of the challenges to overcome is the need for compression of large numbers of molecular descriptors for use on a QC. Here, we show how to achieve compression with data sets using hundreds of molecules (SARS-CoV-2) to hundreds of thousands of molecules (whole cell screening data sets for plague and M. tuberculosis) with SVM and the data reuploading classifier (a DNN equivalent algorithm) on a QC benchmarked against CC and hybrid approaches. This study illustrates the steps needed in order to be "quantum computer ready" in order to apply quantum computing to drug discovery and to provide the foundation on which to build this field.