Systems and methods that employ interactions between quantum computing systems and digital computing systems are described. For an iterative method, a quantum computing system may be designed, operated, and/or adapted to provide a rate of convergence that is greater than the rate of convergence of a digital supercomputer. When the digital supercomputer is iteratively used to evaluate an objective function at a cost incurred of C per iteration, the quantum computing system may be used to provide the input parameter(s) to the objective function and quickly converge on the input parameter(s) that optimize the objective function. Thus, a quantum computing system may be used to minimize the total cost incurred CT for consumption of digital supercomputer resources when a digital supercomputer is iteratively employed to evaluate an objective function.