Recent advances in high-throughput genomic technologies coupled with exponential increases in computer processing and memory have allowed us to interrogate the complex aberrant molecular underpinnings of human disease from a genome-wide perspective. While the deluge of genomic information is expected to increase, a bottleneck in conventional high-performance computing is rapidly approaching. Inspired in part by recent advances in physical quantum processors, we evaluated several unconventional machine learning (ML) strategies on actual human tumor data. Here we show for the first time the efficacy of multiple annealing-based ML algorithms for classification of high-dimensional, multi-omics human cancer data from The Cancer Genome Atlas. To assess algorithm performance, we compared these classifiers to a variety of standard ML methods. Our results indicate the feasibility of using annealing-based ML to provide a competitive classification of human cancer types and associated molecular subtypes and superior performance with smaller training datasets, thus providing compelling empirical evidence for the potential future application of unconventional computing architectures in the biomedical sciences.