Systems and methods for analog processing of problem graphs having arbitrary size and/or connectivity
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.
1. 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 plurality of problems, each problem representable as a problem graph having a number of decision variables;
selecting, from the plurality of problems, a first problem based on one of more properties of the first problem;
selecting, from the plurality of problems, a second problem based on at least one of the one or more properties of the first problem and one or more properties of the second problem;
determining, for each of the first and the second problems, a placement of the problem graph representing the problem in a placement graph;
determining an executable representation of the placement graph together with the placements of the first and the second problems, the representation executable by the quantum processor in one or more executions;
providing the executable representation to the quantum processor for execution;
receiving, from the quantum processor, an output based on at least one execution of the executable representation by the quantum processor; and
generating a first solution to the first problem and a second solution to the second problem by disaggregating representations of the first and the second solutions from the output.
2. The method of claim 1 further comprising determining, for each of the plurality of problems, the problem graph for the problem, the problem graph comprising a sub-graph representing the problem in the placement graph and wherein, for each of the first and the second problems, determining a placement of the problem graph comprises determining a placement of the sub-graph in the placement graph.
3. The method of claim 1 wherein selecting the second problem comprises generating a plurality of clusters of problems based on the one or more properties for each of the plurality of problems, selecting a cluster based on the one or more properties of the cluster's constituent problems, and selecting one or more of the cluster's constituent problems based on the one or more properties of at least one of the cluster's constituent problems.
4. The method of claim 1 wherein, for at least one of the first and the second problems, the one or more properties of the problem are selected from the group consisting of: a size of the problem, a temperature at which the problem is to be executed, a number of samples to be obtained from the problem, an annealing schedule of the problem, a position of the problem in a queue, and a priority of the problem.
5. The method of claim 1 wherein selecting the second problem comprises selecting a smallest problem from at least a subset of the plurality of problems.
6. The method of claim 1 further comprising iteratively selecting one or more further problems from at least a subset of the plurality of problems and determining a placement for each of the one or more further problems in the placement graph until at least one of: no more of the one or more further problems are placeable in the placement graph without removing an already-placed problem from the placement graph or placements have been determined for each problem in the at least a subset of problems.
7. The method of claim 6 wherein determining the placement of at least one of the one or more further problems comprises moving the placement of a previously-placed problem from a first region to a second region in the placement graph, wherein the placement of the at least one of the one or more further problems comprises at least part of the first region.
8. The method of claim 1 wherein generating the first and the second solutions comprises:
dividing the output into a plurality of subgraphs, each subgraph corresponding to at least one of the plurality of problems and based on the placement of the corresponding problem's problem graph in the placement graph; and
associating, for each problem graph, one or more output values of one or more of the plurality of qubits in a corresponding subgraph of the respective the problem graph with one or more vertices in the problem graph.
9. The method of claim 1 wherein the second problem is a variation of the first problem.
10. The method of claim 9 wherein the variation comprises a spin reversal transformation.
11. The method of claim 7 further comprising receiving a plurality of data values and a machine learning model, wherein the first problem comprises a first instantiation of the machine learning model with a first one of the plurality of data values and the second problem comprises a second instantiation of the machine learning model with a second one of the plurality of data values.
12. 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 plurality of problems, each problem representable as a problem graph having a number of decision variables;
selects, from the plurality of problems, a first problem based on one of more properties of the first problem;
selects, from the plurality of problems, a second problem based on at least one of the one or more properties of the first problem and one or more properties of the second problem;
determines, for each of the first and the second problems, a placement of the problem graph representing the problem in a placement graph;
determines an executable representation of the placement graph together with the placements of the first and the second problems, the representation executable by the quantum processor in one or more executions;
provides the executable representation to the quantum processor for execution;
receives, from the quantum processor, an output based on at least one execution of the executable representation by the quantum processor; and
generates a first solution to the first problem and a second solution to the second problem by disaggregating representations of the first and the second solutions from the output.