QUANTUM PROCESSOR-BASED SYSTEMS, METHODS AND APPARATUS FOR SOLVING PROBLEMS AS LOGIC CIRCUITS

Systems, methods and apparatus for factoring numbers are provided. The factoring may be accomplished by creating a factor graph, mapping the factor graph onto an analog processor, initializing the analog processor to an initial state, evolving the analog processor to a final state, and receiving an output from the analog processor, the output comprising a set of factors of the number. The factoring may be accomplished by generating a logic circuit representation of the factoring problem, such as a multiplication circuit, encoding the logic circuit representation as a discrete optimization problem, and solving the discrete optimization problem using a quantum processor. Output(s) of the logic circuit representation may be clamped such that the solving involves effectively executing the logic circuit representation in reverse to determine input(s) that corresponds to the clamped output(s).