Computational systems implement problem solving using hybrid digital/quantum computing approaches. A problem may be represented as a problem graph which is larger and/or has higher connectivity than a working and/or hardware graph of a quantum processor. A quantum processor may be used determine approximate solutions, which solutions are provided as initial states to one or more digital processors which may implement classical post-processing to generate improved solutions. Techniques for solving problems on extended, more-connected, and/or “virtual full yield” variations of the processor's actual working and/or hardware graphs are provided. A method of operation in a computational system comprising a quantum processor includes partitioning a problem graph into sub-problem graphs, and embedding a sub-problem graph onto the working graph of the quantum processor. The quantum processor and a non-quantum processor-based device generate partial samples. A controller causes a processing operation on the partial samples to generate complete samples.