A method of operation in a hybrid problem solving system that comprises both a quantum processor and a digital computer to at least approximately solve a problem, the quantum processor and the digital computer communicatively coupled to one another and the quantum processor operated as a sample generator providing samples from a probability distribution over the states of the quantum processor, the method comprising: constructing a model of the problem via the digital computer, wherein the problem includes an at least approximate minimization of an objective function and the model captures at least one statistical commonality with the objective function; generating samples from the probability distribution via the quantum processor, wherein each sample corresponds to a respective state of the quantum processor, wherein a shape of the probability distribution depends on a configuration of a number of programmable parameters for the quantum processor, and wherein a number of low-energy states of the quantum processor respectively correspond to a number of high probability samples of the probability distribution; processing the samples via the digital computer, wherein processing each sample via the digital computer includes inputting the respective state into the objective function and determining a corresponding objective function value for the respective state via the digital computer; shaping the probability distribution of the quantum processor based on the processing of the samples via the digital computer, wherein shaping the probability distribution of the quantum processor includes changing the configuration of the number of programmable parameters for the quantum processor based on the determined corresponding objective function value for each sample to produce a shaped probability distribution, wherein the shaped probability distribution assigns high probability to samples from a neighborhood of a minimum of the objective function; generating at least one additional sample from the shaped probability distribution via the quantum processor, wherein each additional sample corresponds to a respective state of the quantum processor; processing the at least one additional sample via the digital computer, wherein processing each additional sample via the digital computer includes inputting the respective state into the objective function and determining a corresponding objective function value for the respective state via the digital computer; evolving the model via the digital computer based at least partially on the processing of the at least one additional sample via the digital computer; and determining an at least approximate solution to the problem via the digital computer based on the processing of the at least one additional sample via the digital computer, wherein determining an at least approximate solution to the problem via the digital computer includes determining an at least approximate minimization of the objective function via the digital computer. constructing a model of the problem via the digital computer, wherein the problem includes an at least approximate minimization of an objective function and the model captures at least one statistical commonality with the objective function; generating samples from the probability distribution via the quantum processor, wherein each sample corresponds to a respective state of the quantum processor, wherein a shape of the probability distribution depends on a configuration of a number of programmable parameters for the quantum processor, and wherein a number of low-energy states of the quantum processor respectively correspond to a number of high probability samples of the probability distribution; processing the samples via the digital computer, wherein processing each sample via the digital computer includes inputting the respective state into the objective function and determining a corresponding objective function value for the respective state via the digital computer; shaping the probability distribution of the quantum processor based on the processing of the samples via the digital computer, wherein shaping the probability distribution of the quantum processor includes changing the configuration of the number of programmable parameters for the quantum processor based on the determined corresponding objective function value for each sample to produce a shaped probability distribution, wherein the shaped probability distribution assigns high probability to samples from a neighborhood of a minimum of the objective function; generating at least one additional sample from the shaped probability distribution via the quantum processor, wherein each additional sample corresponds to a respective state of the quantum processor; processing the at least one additional sample via the digital computer, wherein processing each additional sample via the digital computer includes inputting the respective state into the objective function and determining a corresponding objective function value for the respective state via the digital computer; evolving the model via the digital computer based at least partially on the processing of the at least one additional sample via the digital computer; and determining an at least approximate solution to the problem via the digital computer based on the processing of the at least one additional sample via the digital computer, wherein determining an at least approximate solution to the problem via the digital computer includes determining an at least approximate minimization of the objective function via the digital computer.