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Enabling Non-linear Quantum Operations Through Variational Quantum Splines

Matteo Antonio Inajetovic; Filippo Orazi; Antonio Macaluso; Stefano Lodi; Claudio Sartori
In: CCS 2023 Conference Proceedings. International Conference on Computational Science (ICCS-2023), July 3-5, Prague, Czech Republic, Pages 177-192, Vol. 10477, ISBN 978-3-031-36030-5, Springer, 7/2023.


One of the major issues for building a complete quantum neural network is the implementation of non-linear activation functions in a quantum computer. In fact, the postulates of quantum mechanics impose only unitary transformations on quantum states, which is a severe limitation for quantum machine learning algorithms. Recently, the idea of QSplines has been proposed to approximate non-linear quantum activation functions by means of the HHL. However, QSplines rely on a problem formulation to be represented as a block diagonal matrix and need a fault-tolerant quantum computer to be correctly implemented. This work proposes two novel methods for approximating non-linear quantum activation functions using variational quantum algorithms. Firstly, we develop the variational QSplines (VQSplines) that allow overcoming the highly demanding requirements of the original QSplines and approximating non-linear functions using near-term quantum computers. Secondly, we propose a novel formulation for QSplines, the Generalized QSplines (GQSplines), which provide a more flexible representation of the problem and are suitable to be embedded in existing quantum neural network architectures. As a third meaningful contribution, we implement VQSplines and GQSplines using Pennylane to show the effectiveness of the proposed approaches in approximating typical non-linear activation functions in a quantum computer.


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