Quantum Optimization Feedback Gain Convergence
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Solution Overview
Problem
The Feedback-based Algorithm for Quantum Optimization (FALQON) faces challenges in converging feedback amounts for determining quantum circuit parameters, leading to difficulties in obtaining executable solutions for certain combination optimization problems, particularly as the problem size increases.
Innovation Solution
A combination optimization calculation method and system that utilize a quantum computer with a quantum circuit having a phase rotation parameter and a classical computer to calculate and add feedback amounts, with the classical computer multiplying the feedback by a gain that approaches zero as the quantum circuit is added, leveraging the convergence conditions of the quantum annealing method.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If FALQON is used to determine quantum circuit parameters sequentially, then parameter search processing is eliminated, but the feedback amount may not converge and an executable solution may not be obtained
Solution Approach 1:
The patent introduces a gain parameter γ(t) that changes over time according to a specific function. This gain parameter is multiplied with the feedback amount to modify its magnitude dynamically. By changing the parameter γ(t) from 1 to a value approaching zero, the system controls the feedback strength to ensure convergence of the feedback amount while maintaining the elimination of parameter search processing.
2Ease of manufacture
If the feedback amount is multiplied by a constant gain, then the calculation is simple, but the feedback amount may not converge for certain problems
Solution Approach 1:
The patent transitions from using a constant gain to a dynamic gain γ(t) that changes over time. The gain function γ(t) is designed to start at 1 and approach zero as the quantum circuit is added. This dynamic adjustment allows the system to adapt the feedback strength based on the problem size and iteration stage, ensuring convergence for problems that would otherwise fail to converge with constant gain.
3Reliability
If the gain approaches zero as the quantum circuit is added, then the feedback amount converges, but the calculation complexity increases
Solution Approach 1:
The patent employs a gain function γ(t) that changes according to a specific mathematical formula based on time t and problem parameters. The gain function is designed to approach zero as the quantum circuit is added, which ensures convergence of the feedback amount. While this introduces some calculation complexity, the function follows a predictable pattern that can be efficiently computed.
Data Source
AI summary
A method for calculating combination optimization using a quantum computer configured to execute quantum calculation by a quantum circuit having a parameter representing a phase rotation amount, and a classical computer that calculates a feedback amount based on an output of the quantum computer and newly adds, to the quantum computer, the quantum circuit having the calculated feedback amount as the parameter includes: multiplying, in the classical computer, the feedback amount by a gain having a positive value such that a magnitude of the gain approaches zero as the quantum circuit is added.