Quantum annealers as analog or quantum processors can find paths in problem graphs embedded in a hardware graph of the processor, for example finding valid paths, shortest paths or longest paths. A set of input, for example nucleic acid reads, can be used to set up a graph with edges between nodes denoting overlap (i.e., common base pairs) between the reads with constraints applied to perform sequence alignment or sequencing of a nucleic acid (e.g., DNA) strand or sequence, finding a solution that has a ground state energy. At least a portion of the described approaches can be applied to other problems, for instance resource allocations problems, e.g., job scheduling problems, traveling salesperson problems, and other NP-complete problems.