Sub-Graph Isomorphism via Quantum QUBO Solving
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Solution Overview
Problem
The sub-graph isomorphism problem, which determines whether a first graph contains a sub-graph isomorphic to a second graph, is NP-complete, making it computationally expensive and difficult to solve efficiently using traditional methods.
Innovation Solution
A method involving a classical computer to determine the adjacency matrices of both graphs, formulate an objective optimization problem to find a partial permutation matrix, convert this problem into a QUBO matrix, and solve it using a quantum computer to identify the isomorphic sub-graph.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional iterative methods are used to solve sub-graph isomorphism, then the problem can be solved, but the computational complexity is extremely high and processing time is excessive
Solution Approach 1:
The patent replaces classical iterative computational methods with quantum mechanical principles. The quantum computer uses quantum superposition and entanglement to represent and manipulate graph states, transforming the mechanical iterative search process into a quantum parallel computation that can evaluate multiple potential isomorphisms simultaneously, thereby dramatically reducing computation time.
Solution Approach 2:
The patent changes the fundamental parameters of computation by transitioning from classical bits to quantum bits (qubits). This parameter change enables the system to represent graph vertices and edges in a quantum state space, allowing for exponential parallelism in evaluating sub-graph isomorphism conditions that would be intractable for classical computers.
2Productivity
If the sub-graph isomorphism problem is expressed for quantum computer processing, then quantum computing efficiency can be exploited, but the problem expression and variable formulation requires additional computational cycles
Solution Approach 1:
The patent applies preliminary action by pre-defining the quantum circuit architecture and operator sequences needed for sub-graph isomorphism detection. The quantum algorithm is designed in advance with predetermined gate sequences that encode the isomorphism checking logic, so that once the problem is input, the quantum computer can execute the pre-planned computation without requiring complex real-time formulation adjustments.
Data Source
AI summary
A sub-graph isomorphism determination method comprising the steps of: determining, by the classical computer, a first adjacency matrix of a first graph and a second adjacency matrix of a second graph; wherein the first graph comprises a greater number of vertices than the second graph; determining, by the classical computer, an objective optimization problem subject to one or more constraints; wherein an objective of the objective optimization problem is to determine a partial permutation matrix; determining, by the classical computer, a QUBO matrix suitable for implementing the objective optimization problem; solving, by a quantum computer, a QUBO formulation including the QUBO matrix, thereby providing the partial permutation matrix; applying, by the classical computer, the partial permutation matrix to the first adjacency matrix, thereby producing a partially permuted first adjacency matrix; wherein the partially permuted first adjacency matrix corresponds to a sub-graph of the first graph that is isomorphic with the second graph.