Techniques for improving the performance of a quantum processor are described. The techniques include reading out a fraction of the qubits in a quantum processor and utilizing one or more post-processing operations to reconstruct qubits of the quantum processor that are not read. The reconstructed qubits may be determined using a perfect sampler to provide results that are strictly better than reading all of the qubits directly from the quantum processor. The composite sample that includes read qubits and reconstructed qubits may be obtained faster than if all qubits of the quantum processor are read directly.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computational system comprising: at least one quantum processor comprising: a plurality of qubits including a first set of qubits and a second set of qubits; a plurality of coupling devices, wherein each coupling device provides controllable communicative coupling between two of the plurality of qubits; a first readout subsystem responsive to a state of each of the qubits in the first set of qubits to generate a first set of detected samples, each detected sample in the first set of detected samples represents a respective one of the qubits in the first set of qubits; at least one post-processing processor-based device communicatively coupled to the at least one quantum processor; and at least one non-transitory computer-readable storage medium communicatively coupled to the at least one post-processing processor-based device and that stores at least one of processor-executable instructions or data, where in use the at least one post-processing processor-based device: receives the first set of detected samples that represents the qubits in the first set of qubits; and post-processes the first set of detected samples to generate a first set of derived samples, wherein each sample in the first set of derived samples represents a respective one of the qubits in the second set of qubits. 2. The computational system of claim 1 wherein each coupling device is positioned proximate a respective point where a respective one of the qubits in the first set of qubits is proximate one of the qubits in the second set of qubits and provides controllable communicative coupling between the qubit in the first set of qubits and the respective qubit in the second set of qubits. 3. The computational system of claim 1 wherein at least one qubit in the second set of qubits is not communicatively coupled to any qubit in the first set of qubits. 4. The computational system of claim 1 wherein the at least one post-processing processor-based device comprises at least one of a microprocessor, a digital signal processor (DSP), a graphical processing unit (GPU), or a field programmable gate array (FPGA). 5. The computational system of claim 1 wherein the at least one post-processing processor-based device: generates the derived samples that represent the second set of qubits by execution of an exact sampling procedure; and continues execution of the exact sampling procedure until one or more termination criteria occur. 6. The computational system of claim 1 wherein the at least one post-processing processor-based device: generates the derived samples that represent the second set of qubits by execution of a procedure selected from the list of a local gradient descent procedure on the detected samples and a Gibbs sampling procedure. 7. The computational system of claim 1 wherein the at least one post-processing processor-based device: generates at least two of the derived samples that represent the second set of qubits concurrently. 8. The computational system of claim 1 wherein, in use, the at least one quantum processor performs quantum annealing or adiabatic quantum computing. 9. The computational system of claim 1 wherein the qubits in the first set of qubits and the qubits in the second set of qubits are randomly selected. 10. The computational system of claim 1 wherein each of the qubits in the first and the second sets of qubits have a respective major axis, the major axes of the qubits of the first set parallel with one another along at least a majority of a length thereof, and the major axes of the qubits of the second set parallel with one another along at least a majority of a length thereof, the major axes of the qubits of the second set of qubits nonparallel with the major axes of the qubits of the first set of qubits, and each qubit in the first set of qubits crosses at least one qubit in the second set of qubits, and wherein each coupling device is positioned proximate a respective point where a respective one of qubits in the first set of qubits crosses one of the qubits in the second set of qubits and provides controllable communicative coupling between the qubit in the first set of qubits and the respective qubit in the second set of qubits. 11. The computational system of claim 10 wherein the respective major axis of each qubit in the first set of qubits is perpendicular to the respective major axis of each qubit in the second set of qubits such that each qubit in the first set of qubits perpendicularly crosses at least one qubit in the second set of qubits. 12. The computational system of claim 10 wherein at least a portion of each qubit in the first set of qubits is carried in a first layer and at least a portion of each qubit in the second set of qubits is carried in a second layer, such that at each respective point where one of the qubits in the first set of qubits crosses one of the qubits in the second set of qubits, the respective qubit in the first set of qubits is in the first layer and the qubit in the second set of qubits is in the second layer, the second layer different than the first layer. 13. The computational system of claim 1 wherein the first set of qubits includes at least four qubits and the second set of qubits includes at least four qubits. 14. The computational system of claim 1 wherein the quantum processor comprises a multi-layered superconducting integrated circuit. 15. The computational system of claim 1, further comprising: a second readout subsystem responsive to a state of each of the qubits in the second set of qubits to generate a second set of detected samples, wherein each detected sample in the second set of detected samples represents a respective one of the qubits in the second set of qubits; where, in use, the at least one post-processing processor-based device: receives the second set of detected samples that represents the qubits in the second set of qubits; and processes the second set of detected samples to generate a second set of derived samples, wherein each derived sample in the second set of derived samples represents a respective one of the qubits in the first set of qubits. 16. The computational system of claim 1 wherein the at least one post-processing processor-based device: generates the derived samples that represent the second set of qubits by sampling the derived samples that represent the second set of qubits conditioned on the first set of detected samples that represents the qubits in the first set of qubits. 17. 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. 18. The method of claim 17 wherein the plurality of qubits includes a third set of qubits and a fourth set of qubits, the method further 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 third set of qubits of the quantum processor via a readout subsystem, wherein the states for the qubits in the third 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 fourth set of qubits based on samples read via the readout system via the at least one processor-based device. 19. The method of claim 17 wherein processing the samples read via the readout system via the at least one processor-based device comprises processing the samples read via the readout system via at least one of a microprocessor, a digital signal processor (DSP), a graphical processing unit (GPU), or a field programmable gate array (FPGA). 20. The method of claim 17 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 executing at least one of: an optimization operation, an enumeration, a sampling operation or evaluation of estimators. 21. The method of claim 17 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 executing at least one of: a local gradient descent procedure or a Gibbs sampling procedure. 22. The method of claim 17, further comprising: selectively modifying which ones of the qubits of the quantum processor are in the first set of qubits and which ones of the qubits of the quantum processor are in the second set of qubits. 23. The method of claim 17 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 includes performing a classical heuristic optimization algorithm to determine 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. 24. The method of claim 23 wherein performing a classical heuristic optimization algorithm to determine 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 includes performing at least one of: a majority voting on chains of qubits post-processing operation, a local search to find a local minima post-processing operation, or a Markov Chain Monte Carlo simulation at a fixed temperature post-processing operation. 25. The method of claim 17 wherein evolving the quantum processor via an evolution subsystem includes performing at least one of adiabatic quantum computation or quantum annealing. 26. The method of claim 17 wherein operating the quantum processor as a sample generator comprises: reading out states for the qubits in the second set of qubits of the quantum processor via the 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; 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 first set of qubits based on the samples read via the readout system via the at least one processor-based device. 27. The method of claim 17 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.