Quantum and Quantum-inspired Methods forde novoDiscovery of Altered Cancer Pathways

The combinatorial calculations for de novo discovery of altered pathways in cancer cohorts involve both coverage (i.e. recurrence) and mutual exclusivity, and solving mutual exclusivity problems is NP-hard for classical computers. Advances in quantum computing systems and our classical, quantum-inspired algorithm GAMA (Graver Aug-mented Multi-seed Algorithm) motivated us to revisit methods for identifying altered pathways. Using different types of quantum and classical algorithms, we report novel formulations of the problem that are tailored to these new computational models. Our formulations require fewer binary variables than available methods, and offer a tuning parameter that allows a trade-off between coverage and exclusivity; varying this parameter returns a variety of solutions. We illustrate our formulations and methods with TCGA mutation data for Acute Myeloid Leukemia (AML). Both the D-Wave quantum annealing solver and the classical GAMA solver returned altered pathways that are known to be important in AML, with different tuning parameter values returning alternative altered pathways. Our reduced-variable algorithm and QUBO problem for-mulations demonstrate how quantum annealing-based binary optimization solvers can be used now in cancer genomics.