Variational Quantum Circuit Updates With Adaptive Step Size
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Solution Overview
Problem
Conventional gradient-based methods for variational quantum eigenvalue calculations often require excessive iterations and prolonged calculation times due to the use of a fixed parameter (step size or learning rate) that may not be optimally suited for each stage of the optimization process.
Innovation Solution
Adopting a variable step size (ηk) determined by the ratio of consecutive cost function values (f(θi,k) and f(θi,k-1) to dynamically adjust the amount of change in parameter updates during the variational quantum eigenvalue calculation, using equations (2) and (3) to accelerate convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a fixed parameter (step size) is used in gradient-based optimization, then the update process is simple to implement, but the number of iterations increases and calculation time becomes long
Solution Approach 1:
The patent applies the dynamics principle by transforming the fixed step size parameter into a dynamic one that automatically adjusts during the optimization process. The step size is modified based on the ratio of consecutive cost function values, allowing the system to adapt its behavior according to the optimization progress. This resolves the contradiction by maintaining implementation simplicity while significantly reducing calculation time through adaptive parameter adjustment.
Solution Approach 2:
The patent implements parameter changes by modifying the step size parameter based on the optimization trajectory. Specifically, the step size is scaled by a factor derived from the ratio of consecutive cost function values (f(θ_k)/f(θ_{k-1})). This parameter change enables the optimization process to take larger steps when progress is rapid and smaller steps when approaching convergence, thereby reducing total iteration count while maintaining ease of implementation through a straightforward parameter update rule.
2Ease of operation
If a fixed parameter (step size) is used in gradient-based optimization, then the implementation is straightforward, but the energy convergence slows down
Solution Approach 1:
The patent applies dynamics by making the step size parameter adaptive rather than fixed. The step size dynamically adjusts based on the ratio of consecutive cost function values, enabling faster energy convergence while keeping the implementation straightforward. This resolves the contradiction by allowing the system to accelerate convergence without complicating the update process.
Solution Approach 2:
The patent implements feedback by using the ratio of consecutive cost function values to adjust the step size in subsequent iterations. This feedback mechanism allows the optimization process to learn from past performance and adapt accordingly, achieving faster energy convergence while maintaining straightforward implementation through a simple feedback-based parameter adjustment rule.
3Loss of time
If the step size is increased to accelerate convergence, then calculation time reduces, but the optimization may overshoot and fail to converge
Solution Approach 1:
The patent applies dynamics by making the step size adaptive rather than fixed or uniformly large. The step size automatically adjusts based on the ratio of consecutive cost function values, allowing large steps when progress is rapid while automatically reducing steps when approaching convergence or encountering oscillations. This resolves the contradiction by maintaining fast convergence while ensuring reliability through dynamic adaptation.
Solution Approach 2:
The patent implements parameter changes by scaling the step size based on the ratio of consecutive cost function values. When the cost function decreases rapidly, the step size can be larger; when the decrease slows or oscillations occur, the step size automatically reduces. This parameter change strategy enables reduced calculation time while maintaining convergence reliability through automatic parameter adaptation.
4Reliability
If the step size is decreased to ensure stable convergence, then reliability improves, but the number of iterations increases and calculation time extends
Solution Approach 1:
The patent applies dynamics by transforming the static, conservatively small step size into a dynamic parameter that adjusts based on optimization progress. The step size starts larger to enable rapid initial convergence and automatically reduces when approaching the minimum or encountering oscillations. This resolves the contradiction by achieving both high reliability and reduced calculation time through adaptive parameter adjustment.
Solution Approach 2:
The patent implements parameter changes by scaling the step size based on the ratio of consecutive cost function values. This allows the system to use larger step sizes during phases where stability is less critical (early optimization) and automatically reduce step sizes when stability becomes crucial (near convergence). This parameter adaptation achieves both reduced calculation time and maintained reliability.
Data Source
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AI summary
An information processing apparatus performs, a plurality of iterations, an update process of updating a value of a first parameter, which is a variable in a cost function, the value of the first parameter being applied to a variational quantum circuit for a variational quantum eigenvalue calculation. The information processing apparatus determines a value of a second parameter representing a weight for an amount of change to be applied to the value of the first parameter in each iteration of the update process, using the ratio between first and second values of the cost function, which are calculated by the variational quantum eigenvalue calculation using the values of the first parameter obtained in the k-th and (k-1)-th iterations of the update process, respectively. The information processing apparatus performs the (k+1)-th iteration of the update process using the amount of change weighted by the determined value of the second parameter.