QuKAN: A Quantum Circuit Born Machine Approach to Quantum Kolmogorov Arnold Networks

Area of Science:

• Quantum Computing
• Machine Learning
• Artificial Intelligence

Background:

• Kolmogorov Arnold Networks (KANs) offer efficient function approximation by learning on edges, unlike traditional Multi-Layer Perceptrons (MLPs).
• The potential of KANs within quantum machine learning remains largely unexplored.

Purpose of the Study:

• To introduce and evaluate Quantum KAN (QuKAN) architectures for quantum machine learning applications.
• To explore both hybrid and fully quantum implementations of KANs using Quantum Circuit Born Machines (QCBMs).

Main Methods:

• Implementation of KAN architectures in hybrid and fully quantum forms using QCBMs.
• Adaptation of KAN transfer learning by utilizing pre-trained residual functions.
• Translation of KAN residual function architectures into quantum models for the fully quantum version.

Main Results:

• Demonstration of the feasibility of the proposed Quantum KAN (QuKAN) architecture.
• Evidence of the interpretability and performance of QuKAN models.
• Successful integration of classical KAN components with quantum subroutines in the hybrid model.

Conclusions:

• Quantum KANs (QuKANs) present a viable and effective approach for quantum machine learning.
• The developed QuKAN architecture demonstrates promising capabilities in terms of feasibility, interpretability, and performance.
• This work opens new avenues for exploring advanced neural network architectures in quantum computing.