Paper ID: 2303.04788

Enabling Non-Linear Quantum Operations through Variational Quantum Splines

Matteo Antonio Inajetovic, Filippo Orazi, Antonio Macaluso, Stefano Lodi, Claudio Sartori

The postulates of quantum mechanics impose only unitary transformations on quantum states, which is a severe limitation for quantum machine learning algorithms. Quantum Splines (QSplines) have recently been proposed to approximate quantum activation functions to introduce non-linearity in quantum algorithms. However, QSplines make use of the HHL as a subroutine and require a fault-tolerant quantum computer to be correctly implemented. This work proposes the Generalised Hybrid Quantum Splines (GHQSplines), a novel method for approximating non-linear quantum activation functions using hybrid quantum-classical computation. The GHQSplines overcome the highly demanding requirements of the original QSplines in terms of quantum hardware and can be implemented using near-term quantum computers. Furthermore, the proposed method relies on a flexible problem representation for non-linear approximation and it is suitable to be embedded in existing quantum neural network architectures. In addition, we provide a practical implementation of the GHQSplines using Pennylane and show that our model outperforms the original QSplines in terms of quality of fitting.

Submitted: Mar 8, 2023