1. A method of operation in a problem solving system that comprises both a quantum processor and at least one processor-based device communicatively coupled to one another to at least approximately minimize an objective function, the quantum processor comprising a plurality of qubits including a first set of qubits and a second set of qubits, and a plurality of coupling devices, wherein each coupling device provides controllable communicative coupling between two of the plurality of qubits, the method comprising: operating the quantum processor as a sample generator to provide samples from a probability distribution, wherein a shape of the probability distribution depends on a configuration of a number of programmable parameters for the quantum processor and a number of low-energy states of the quantum processor respectively correspond to a number of high probability samples of the probability distribution, and wherein operating the quantum processor as a sample generator comprises: defining a configuration of the number of programmable parameters for the quantum processor via the at least one processor-based device, wherein the configuration of the number of programmable parameters corresponds to a probability distribution over the plurality of qubits of the quantum processor; programming the quantum processor with the configuration of the number of programmable parameters via a programming subsystem; evolving the quantum processor via an evolution subsystem; and reading out states for the qubits in the first set of qubits of the quantum processor via a readout subsystem, wherein the states for the qubits in the first set of qubits of the quantum processor correspond to samples from the probability distribution; processing the samples read via the readout system via the at least one processor-based device, wherein processing the samples read via the readout system via the at least one processor-based device comprises: determining respective states for the qubits in the second set of qubits based on samples read via the readout system via the at least one processor-based device, wherein determining respective states for the qubits in the second set of qubits based on samples read via the readout system via the at least one processor-based device comprises: sampling the states for the qubits in the second set of qubits conditioned on the states for the qubits that represent the first set of qubits read via the readout system.