Enabling Non-Linear Quantum Operations through Variational Quantum Splines

• URL: http://arxiv.org/abs/2303.04788v3
• Date: Mon, 4 Dec 2023 15:40:19 GMT
• Title: Enabling Non-Linear Quantum Operations through Variational Quantum Splines
• Authors: Matteo Antonio Inajetovic, Filippo Orazi, Antonio Macaluso, Stefano Lodi, Claudio Sartori
• Abstract summary: We propose a novel method for approximating non-linear quantum activation functions using hybrid quantum-classical computation. 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.
• Score: 1.3874486202578669
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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