Enabling Non-linear Quantum Operations Through Variational Quantum Splines

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.