Parallel Ising Solver via Symplectic Euler Integration
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Solution Overview
Problem
Current Ising machines face limitations in solving large-scale Ising problems due to constraints on the number of quantum bits and are inefficient for parallel computing, as existing methods like simulated annealing are sequential and unsuitable for handling large-scale problems quickly.
Innovation Solution
A calculation device with a processor configuration that performs parallel updates using new equations of motion, separating the time derivatives of first and second variables, and employing the symplectic Euler method for stable discrete solutions, allowing for faster computation of large-scale Ising problems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If simulated annealing is used to solve Ising problems, then large-scale Ising problems can be handled, but the sequential update algorithm makes it unsuitable for parallel computing and slow in solving large-scale problems
Solution Approach 1:
The patent divides the update process into two separate stages: first updating all odd-indexed spins, then updating all even-indexed spins. This segmentation allows independent parallel execution of updates across different spin groups, resolving the contradiction between handling large-scale problems and maintaining computational speed through parallel processing.
Solution Approach 2:
The patent introduces a dynamic update mechanism where the update pattern alternates between odd-indexed and even-indexed spins across different time steps. This dynamic approach enables parallel computing while maintaining the effectiveness of solving large-scale Ising problems, overcoming the limitation of sequential algorithms.
2Productivity
If quantum computers are used to solve Ising problems, then fast computation is achieved, but the number of quantum bits is limited and cannot handle large-scale problems
Solution Approach 1:
The patent replaces quantum mechanical systems with a classical computational system that uses ordinary differential equations and numerical integration. This substitution enables the use of classical computers with arbitrary precision and scale, overcoming the hardware limitations of quantum computers while maintaining fast computation speeds through efficient parallel algorithms.
Solution Approach 2:
The patent changes the fundamental parameters of the computation by using continuous real numbers as variables instead of discrete quantum states. This parameter transformation allows the system to handle large-scale problems with any number of variables, eliminating the quantum bit limitation while preserving computational efficiency through the symplectic Euler method.
3Ease of operation
If sequential update algorithms are used, then simplicity of implementation is maintained, but parallel computing capability is lost and large-scale problems become difficult to solve fast
Solution Approach 1:
The patent segments the update operations into distinct odd-indexed and even-indexed groups, allowing parallel execution while maintaining algorithmic clarity. This segmentation approach preserves ease of implementation through systematic update patterns while dramatically improving computational efficiency through parallel processing capability.
Solution Approach 2:
The patent employs periodic alternation between updating odd-indexed and even-indexed spins in successive time steps. This periodic action pattern provides a simple, regular update rule that is easy to implement while enabling efficient parallel computation, resolving the contradiction between algorithm simplicity and computational efficiency.
Data Source
AI summary
According to an embodiment, a calculation device includes a memory and one or more processors coupled to the memory. The one or more processors are configured to: repeat a processing procedure including a first variable update and a second variable update; and display an image on a display device. The one or more processors are further configured to: while repeating the processing procedure, output values of the updated first variables xi and second variables yi, and when repetition of the processing procedure is finished, output a sign of the last updated first variable xi; and display on the display device a monitoring image representing a temporal change in at least some of the first variables xi and the second variables yi, based on the output values of the first variables xi and the second variables yi.