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 QSplines (GQSplines), a novel method for approximating non-linear quantum activation functions using hybrid quantum-classical computation. The GQSplines 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 GQSplines using Pennylane and show that our model outperforms the original QSplines in terms of quality of fitting.

翻译：量子力学公设仅允许对量子态进行酉变换，这严重制约了量子机器学习算法的发展。量子样条（QSplines）方法近期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特性。然而，QSplines需利用HHL量子子程序，且其正确实现依赖容错量子计算机。本文提出广义量子样条（GQSplines）——一种基于混合量子-经典计算的新型非线性量子激活函数近似方法。GQSplines克服了原始QSplines对量子硬件的高苛求条件，可在近期量子计算机上实现。此外，本方法采用灵活的问题表征框架进行非线性逼近，易于嵌入现有量子神经网络架构。我们基于Pennylane给出了GQSplines的实用化实现，实验表明该模型在拟合质量上优于原始QSplines。