Hybrid genetic optimisation for quantum feature map design.
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Date
2024
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Abstract
Good feature maps are crucial for machine learning kernel methods for effective mapping
of non-linearly separable input data into a higher dimension feature space, thus
allowing the data to be linearly separable in feature space. Recent works have proposed
automating the task of quantum feature map circuit design with methods such
as variational ansatz parameter optimization and genetic algorithms. A problem commonly
faced by genetic algorithm methods is the high cost of computing the genetic
cost function. To mitigate this, this work investigates the suitability of two metrics
as alternatives to test set classification accuracy. Accuracy has been applied successfully
as a genetic algorithm cost function for quantum feature map design in previous
work. The first metric is kernel-target alignment, which has previously been used
as a training metric in quantum feature map design by variational ansatz training.
Kernel-target alignment is a faster metric to evaluate than test set accuracy and does
not require any data points to be reserved from the training set for its evaluation. The
second metric is an estimation of kernel-target alignment which further accelerates
the genetic fitness evaluation by an adjustable constant factor. The second aim of
this work is to address the issue of the limited gate parameter choice available to the
genetic algorithm. This is done by training the parameters of the quantum feature
map circuits output in the final generation of the genetic algorithm using COBYLA
to improve either kernel-target alignment or root mean squared error. This hybrid
approach is intended to complement the genetic algorithm structure optimization
approach by improving the feature maps without increasing their size. Eight new
approaches are compared to the accuracy optimization approach across nine varied
binary classification problems from the UCI machine learning repository, demonstrating
that kernel-target alignment and its approximation produce feature map circuits
enabling comparable accuracy to the original approach, with larger margins on training
data that improve further with variational training.
Description
Masters Degree. University of KwaZulu-Natal, Durban.