Systems and methods for analog processing of problem graphs having arbitrary size and/or connectivity

A method of operation in a computational system, the computational system comprising a quantum processor comprising a plurality of qubits and one or more coupling devices arranged to form a working graph for embedding a problem graph, the computational system further comprising at least one non-quantum processor-based device, the method comprising:

• receiving a problem represented as a problem graph having a number of decision variables, the problem graph is at least one of larger than the working graph or has a connectivity that is higher than a connectivity of the working graph;
• generating one or more solutions by:
• embedding a portion of the problem graph onto the working graph;
• causing a performing of at least one processing operation by the quantum processor to generate one or more samples as potential solutions based on the working graph;
• and
• causing, by at least one controller, a performing of at least one post-processing operation on the one or more samples by the at least one non-quantum processor-based device to generate a set of post-processing results based on the problem graph.

A computational system, comprising:

• at least one quantum processor comprising a plurality of qubits and one or more coupling devices arranged to form a working graph for embedding a problem graph;
• at least one non-quantum post-processing processor-based device;
• at least one processor-based controller communicatively coupled to the at least one quantum processor and the at least one non-quantum post-processing processor-based device, in operation the at least one processor-based controller:
• receives a problem represented as a problem graph having a number of decision variables, the problem graph is at least one of larger than the working graph or has a connectivity that is higher than a connectivity of the working graph;
• for a number of iterations i to a number n where n is a positive integer:
• partitions the problem graph into a plurality of sub-problem graphs, each sub-problem graph embeddable onto the working graph of the quantum processor;
• for each of the sub-problem graphs:
• embeds the sub-problem graph onto the working graph;
• and
• causes a performing of at least one processing operation by the quantum processor to generate a plurality of samples as potential solutions;
• and
• causes a performing of at least one post-processing operation on the plurality of samples by the at least one non-quantum processor-based device to generate a set of post-processing results;
• wherein, for each of the sub-problem graphs, the at least one processor-based controller sets weights at the boundary of the working graph based at least in part on known information regarding sub-problem graphs which are adjacent the sub-problem graph which is being embedded.

A computational system, comprising:

• at least one quantum processor comprising a plurality of qubits and one or more coupling devices arranged to form a working graph for embedding a problem graph;
• at least one non-quantum post-processing processor-based device;
• at least one processor-based controller communicatively coupled to the at least one quantum processor and the at least one non-quantum post-processing processor-based device, in operation the at least one processor-based controller:
• receiving a problem represented as a problem graph having a number of decision variables, the problem graph is at least one of larger than the working graph or has a connectivity that is higher than a connectivity of the working graph;
• generating one or more solutions by:
• embedding a portion of the problem graph onto the working graph;
• causing a performing of at least one processing operation by the quantum processor to generate one or more samples as potential solutions based on the working graph;
• and
• causing, by at least one controller, a performing of at least one post-processing operation on the one or more samples by the at least one non-quantum processor-based device to generate a set of post-processing results based on the problem graph.