PUBO Subproblem Isomorphism for Quantum Optimization
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Solution Overview
Problem
The processing capability of quantum computers is limited by the number of qubits, making it difficult to solve large problems efficiently, and the increasing demand for quantum computing resources leads to decreased availability per user.
Innovation Solution
A computer-implemented method that identifies polynomial unconstrained binary optimization subproblems within a larger problem, utilizing isomorphic portions of graphs representing the subproblems, and sends these isomorphic portions to a quantum computer for solving, allowing for the efficient use of quantum computers with limited processing capability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the problem size is increased to solve larger optimization problems, then the solution capability is improved, but the quantum computer's qubit limit is exceeded
Solution Approach 1:
The patent divides a large PUBO problem into multiple smaller subproblems, each of which can be solved by a quantum computer with limited qubits. The decomposition identifies subproblems with isomorphic or approximately isomorphic graphs, allowing the largest subproblem to fit within the quantum computer's qubit capacity while still making progress on the overall large-scale optimization problem.
2Adaptability or versatility
If quantum computing resources are allocated to more users, then user accessibility is improved, but the amount of resources available per user decreases
Solution Approach 1:
By segmenting large problems into smaller subproblems that fit within the quantum computer's qubit limit, the system enables multiple users to simultaneously access and solve their own problems without requiring excessive quantum resources per user. This segmentation allows quantum computing resources to be shared among more users while maintaining adequate resource allocation for each.
3Quantity of substance
If the problem is decomposed into smaller subproblems to fit quantum computer capacity, then the qubit requirement is reduced, but the processing time increases
Solution Approach 1:
The patent merges isomorphic or approximately isomorphic subproblems by identifying their structural similarities. Instead of solving each subproblem independently, the system solves one representative subproblem and reuses its solution for all isomorphic subproblems, thereby reducing redundant computation and minimizing the overall processing time despite the decomposition into multiple subproblems.
4Loss of time
If isomorphic subproblems are identified and solved together, then the processing time is reduced, but the algorithm complexity increases
Solution Approach 1:
The system performs preliminary analysis to identify isomorphic or approximately isomorphic subproblems before solving them. By pre-processing the problem decomposition and grouping subproblems based on their graph isomorphism, the system prepares the structure in advance, allowing for efficient batch solving of isomorphic subproblems and reducing the overall processing time despite the added algorithmic steps.
Data Source
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AI summary
The invention relates to a method of solving, by a quantum computer, or approximately solving, by a quantum computer, an isomorphic portion (301), according to a first isomorphism relation, of the first PUBO subproblem thereby obtaining solution values or approximate solution values of the variables (x1, x2, x3) of the isomorphic portion of the first PUBO subproblem; wherein the first subproblem is representable by a graph isomorphic, according to the first isomorphism relation, with respect to a graph representing a second PUBO subproblem or the graph representing the first subproblem is approximately isomorphic, according to the first isomorphism relation, with respect to the graph representing the second subproblem; wherein at least some coefficients of the first subproblem are proportional or approximately proportional with respect to coefficients of the second subproblem and the proportional or approximately proportion coefficients are associated with variables associated according to the first isomorphism relation; and wherein the first subproblem and the second subproblem are summands of a PUBO problem.