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.

翻译：量子力学的公设仅允许对量子态进行酉变换，这严重限制了量子机器学习算法的发展。近年来，量子样条（QSplines）被提出用于近似量子激活函数，从而在量子算法中引入非线性。然而，QSplines 将 HHL 算法作为子程序，其正确实现需要容错量子计算机。本文提出广义混合量子样条（GHQSplines），一种利用混合量子-经典计算近似非线性量子激活函数的新方法。GHQSplines 克服了原始 QSplines 对量子硬件的严苛要求，可在近期量子计算机上实现。此外，所提方法基于灵活的问题表示进行非线性近似，适合嵌入现有量子神经网络架构中。我们利用 Pennylane 实现了 GHQSplines 的实际应用，并展示出该模型在拟合质量上优于原始 QSplines。