A hybrid computing system for solving a computational problem includes a digital processor, a quantum processor having qubits and coupling devices that together define a working graph of the quantum processor, and at least one nontransitory processor-readable medium communicatively coupleable to the digital processor which stores at least one of processor-executable instructions or data. The digital processor receives a computational problem, and programs the quantum processor with a first set of bias fields and a first set of coupling strengths. The quantum processor generates samples as potential solutions to an approximation of the problem. The digital processor updates the approximation by determining a second set of bias fields based at least in part on the first set of bias fields and a first set of mean fields that are based at least in part on the first set of samples and coupling strengths of one or more virtual coupling devices.