  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.
