Ising Model Spin Reduction for Hamiltonian Path Problems
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Solution Overview
Problem
The existing methods for converting Hamiltonian path and cycle problems into Ising models require a large number of spins, leading to increased computational resources and time, which is unsustainable for large-scale problems due to hardware constraints and resource limitations.
Innovation Solution
The system converts a Hamiltonian cycle problem into an Ising model by associating each edge of the graph with a spin, reducing the number of required spins to the number of edges, allowing for efficient solution calculation using an Ising machine.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the Hamiltonian path problem is converted into the Ising model using existing methods, then the problem can be solved using quantum annealing computers, but the number of spins required excessively increases to the square of the number of nodes
Solution Approach 1:
The patent segments the Hamiltonian path problem into sub-problems by introducing auxiliary variables and constraints. Instead of directly mapping all node pairs to spins, it divides the problem into edge selection sub-problems and path connectivity sub-problems, allowing the Ising model to be constructed with fewer spins while maintaining solution accuracy through systematic constraint satisfaction.
Solution Approach 2:
The patent introduces a new dimensional approach by adding temporal or hierarchical dimensions to the Ising model formulation. It uses multi-layer constructions where spins represent not only node connections but also path sequence and constraint satisfaction across different layers, effectively reducing the spin count by encoding multiple problem aspects in a structured dimensional framework.
2Productivity
If the number of spins is reduced to the number of edges, then calculation resources are significantly reduced, but the conversion process becomes more complex
Solution Approach 1:
The patent applies preliminary action by pre-processing the graph structure before Ising model construction. It performs preliminary steps including identifying essential edges, pre-calculating constraint relationships, and preparing auxiliary variable mappings in advance. This pre-processing reduces the complexity of the actual conversion process by organizing the problem data into a format that directly maps to the reduced-spin Ising model.
Solution Approach 2:
The patent introduces intermediary elements such as auxiliary variables and constraint functions that mediate between the original Hamiltonian path problem and the reduced-spin Ising model. These intermediaries handle the complexity of path connectivity and constraint satisfaction, allowing the core spin system to remain simple while still encoding the full problem through well-structured intermediary relationships.
Data Source
AI summary
An information processing system as an embodiment of the present invention includes: a first computer that generates an edge group that is a group of edges connected to corresponding nodes for each of the nodes in a graph of a Hamiltonian path problem, a binary variable indicating whether the edges included in the edge group are selected as a path for each of edge groups, and an Ising model with the binary variable as a spin; and a second computer that calculates a solution of the Ising model. The first computer acquires a solution of the Hamiltonian path problem based on the solution of the Ising model calculated by the second computer.