Complete Bipartite Ising Graphs for Parallel Ground-State Search
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Solution Overview
Problem
Existing methods for searching the ground state of an Ising model, such as Markov chain Monte Carlo (MCMC) and simulated annealing (SA), face difficulties in speeding up the process due to the dense interaction structure between spins, making it challenging to perform probabilistic processes simultaneously.
Innovation Solution
The method converts the interaction relationship of the Ising model into a complete bipartite graph, allowing simultaneous updates of spin values by using an information processing apparatus with specific storage and arithmetic units to efficiently search for the ground state.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the interaction between spins is represented as a dense structure (complete graph), then the Ising model can accurately represent combinatorial optimization problems, but simultaneous probabilistic processes for all spins cannot be performed, reducing processing speed
Solution Approach 1:
The patent divides the complete graph of spins into two separate complete graphs: one for even-numbered spins and one for odd-numbered spins. This segmentation allows independent probabilistic processes to be performed on each subset simultaneously, resolving the contradiction between maintaining accurate dense interaction representation and achieving parallel processing speed.
Solution Approach 2:
The patent introduces a temporal dimension by alternating between updating even spins and odd spins in successive time steps. This dimensional transformation from spatial (complete graph) to temporal (sequential updates) enables efficient parallel processing while maintaining the complete interaction structure through the alternating update mechanism.
2Reliability
If probabilistic processes are performed sequentially for each spin, then the dense interaction structure can be processed, but the overall computation time increases significantly
Solution Approach 1:
The patent segments the sequential processing into two parallel streams: one for even spins and one for odd spins. Each stream can process its spins independently using the same probabilistic algorithm, reducing total computation time while maintaining complete interaction processing through the alternating execution of both streams.
Solution Approach 2:
The patent ensures continuous useful action by alternately executing updates for even and odd spins without idle time. The alternating update mechanism keeps both processing streams continuously active, maximizing computational efficiency while processing all spin interactions completely.
3Productivity
If a semiconductor device is used to speed up ground state searching, then parallel processing is enabled, but the dense interaction structure prevents effective simultaneous updates
Solution Approach 1:
The patent segments the spin system into two independent subsets (even and odd spins) that can be processed simultaneously on the semiconductor device. This segmentation enables effective parallel processing without requiring complex hardware structures, as each subset can be updated independently using standard probabilistic update circuits.
Data Source
AI summary
Searching for a ground state of an Ising model is performed so that a combinatorial optimization problem is efficiently solved. An information processing apparatus stores an energy function setting an interaction between an i-th spin of a first spin group and a j-th spin of a second spin group so that the i-th spin of the first spin group and the j-th spin of the second spin group have the same value in a ground state in an interaction relationship of an Ising model represented as a complete bipartite graph connecting N spins of the first spin group and of the second spin group, and searches for the ground state of the Ising model based on the energy function and information unique to the spins. The search for the ground state of the Ising model is performed by applying an algorithm of simulated annealing method to the above-mentioned energy function.