QKAN Implementation

An implementation of Quantum Kolmogorov-Arnold Networks (QKAN) focusing on efficient model optimization through quantum computing frameworks. This project explores the intersection of quantum computing and neural networks, implementing a step-based architecture for quantum-compatible neural network training.

Overview

QKAN introduces a novel approach to neural network optimization by adapting Kolmogorov-Arnold Networks for quantum systems. The implementation breaks down complex quantum-classical interactions into clear, modular steps:

• ChebyshevStep: Implements quantum-compatible Chebyshev polynomial transformations
• MulStep: Handles weighted polynomial operations in quantum context
• LCUStep: Manages Linear Combination of Unitaries for polynomial combination
• SUMStep: Performs efficient quantum summation operations
• QKANLayer: Orchestrates the complete quantum-neural network layer

Key Features

• Modular, step-based quantum neural network implementation
• Clean integration with Qiskit quantum computing framework
• Comprehensive test suite for each component
• Efficient quantum state preparation and manipulation
• Clear separation of classical and quantum operations

Technical Details

Core Components

class QKANLayer:
    """
    Quantum Kolmogorov-Arnold Network layer implementation.
    Orchestrates quantum neural network operations through distinct steps:
    1. Chebyshev polynomial transformations
    2. Quantum multiplication operations
    3. Linear combination of unitaries
    4. Quantum summation
    """

Implementation Structure

• Each step is implemented as a separate class with clear responsibilities
• Extensive unit testing ensures reliable quantum operations
• Efficient quantum circuit construction and optimization
• Careful management of quantum resources and gate complexity

Testing and Verification

Each component includes comprehensive unit tests demonstrating:

• Correct quantum state manipulation
• Accurate polynomial transformations
• Proper handling of quantum circuits
• Verification of unitary operations

Getting Started

# Example usage
layer = QKANLayer(N=4, K=4, max_degree=3)
x = np.random.uniform(-1, 1, 4)
weights = [np.random.uniform(-1, 1, 16) for _ in range(4)]
output = layer.forward(x, weights)

Future Directions

Currently exploring:

• Enhanced model optimization techniques
• Improved quantum circuit efficiency
• Extended polynomial basis functions
• Integration with various quantum backends
• Active model training and performance evaluation in progress
• Investigating speedup potential in quantum vs classical implementations

Dependencies

• Qiskit
• NumPy
• PyTest (for testing)
• FABLE (for quantum block encoding)