Quantum-Classical Graph Isomorphism Matching
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Solution Overview
Problem
Determining graph isomorphism and data matching using quantum computers is computationally expensive due to the need for expressing complex real-world problems in a resolvable manner, requiring more processing cycles than traditional methods.
Innovation Solution
A computer-implemented method using a quantum computer in conjunction with a classical computer, where the classical computer augments graphs, determines adjacency matrices and unitary operator representations, and implements a quantum circuit to iteratively find a permutation that minimizes a loss function, determining graph isomorphism or data matching by repeating an iteration block until a threshold is met.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quantum computing is used to determine graph isomorphism and data matching, then processing efficiency is improved, but computational expense increases
Solution Approach 1:
The patent divides the data matching problem into graph representation and quantum processing segments. Classical computers handle graph augmentation and adjacency matrix generation, while quantum computers perform the isomorphism determination through quantum circuits. This segmentation allows each system to operate in its optimal domain, improving overall efficiency while managing computational expense.
Solution Approach 2:
The patent transforms the data matching problem into a graph isomorphism problem by changing the representation parameters. Data is converted into graphs with specific structural parameters, and the matching problem is reframed as finding isomorphic graphs. This parameter transformation enables the use of quantum algorithms that operate on graph structures, improving processing efficiency.
2Measurement precision
If quantum circuits are implemented to find graph isomorphism, then matching accuracy is improved, but device complexity increases
Solution Approach 1:
The patent performs preliminary actions by augmenting graphs with additional vertices and edges before quantum processing. Classical computers prepare the graphs by adding ancillary vertices and generating adjacency matrices in advance. This preliminary preparation simplifies the quantum circuit requirements and improves matching accuracy by ensuring the graphs are in the optimal form for quantum isomorphism testing.
Solution Approach 2:
The patent introduces adjacency matrices as an intermediary representation between the graph structure and quantum circuit operations. The classical computer generates adjacency matrices from graphs, and these matrices serve as intermediaries that are then processed by quantum circuits. This intermediary step bridges the classical and quantum domains, improving accuracy while managing complexity.
3Reliability
If iteration blocks are repeated to minimize loss function, then solution reliability is improved, but loss of time increases
Solution Approach 1:
The patent implements a feedback mechanism where the quantum circuit executes and measures a quantum state, determines a loss function value, and uses this feedback to update the permutation. The classical computer adjusts the permutation based on the loss feedback, and the process repeats until convergence. This feedback loop improves solution reliability by iteratively optimizing the matching while providing a clear termination criterion to manage iteration time.
Data Source
AI summary
The computer implemented image matching method involves the use of a quantum computer communicating with a classical computer. The method includes the following steps: (a) The classical computer receives input data. (b) The classical computer generates an input graph representing the input data, (c) The classical computer augments the input graph, (d) An iteration block is performed. (e) The iteration block is repeated using the new permutation parameter, the permuted first adjacency matrix, and a new existing graph until a threshold is met. In the first iteration of the iteration block, the accumulated permutation is the identity, making the permuted first adjacency matrix equal to the first adjacency matrix. The first graph is isomorphic with the second graph when the loss is minimized, indicating a match between the first data and the existing data.