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(QSplines)最近提议将量子激活功能的高度要求作为量子算法中引入非线性。然而,QSplines将HHL用作亚常规,要求正确执行一个容错量计算机。这项工作提议采用通用QSplines(GQSplines),这是使用混合量子级计算来接近非线性量子激活功能的一种新颖方法。GQSplines克服了原QSplines在量子硬件方面的高要求,可以使用近期量子计算机执行。此外,拟议方法依靠非线性近似的灵活问题代表,适合嵌入现有的量子神经网络结构。此外,我们提供使用Penny的GQSplines实际应用GQSplines,并显示我们的模型在安装质量方面超越了原QSplines。</s>