In recent years, Quantum Machine Learning (QML) has increasingly captured the interest of researchers. Among the components in this domain, activation functions hold a fundamental and indispensable role. Our research focuses on the development of activation functions quantum circuits for integration into fault-tolerant quantum computing architectures, with an emphasis on minimizing $T$-depth. Specifically, we present novel implementations of ReLU and leaky ReLU activation functions, achieving constant $T$-depths of 4 and 8, respectively. Leveraging quantum lookup tables, we extend our exploration to other activation functions such as the sigmoid. This approach enables us to customize precision and $T$-depth by adjusting the number of qubits, making our results more adaptable to various application scenarios. This study represents a significant advancement towards enhancing the practicality and application of quantum machine learning.

翻译：近年来，量子机器学习（Quantum Machine Learning, QML）日益引起研究者的关注。在该领域的组成部分中，激活函数扮演着基础且不可或缺的角色。我们的研究聚焦于开发可集成至容错量子计算架构的激活函数量子电路，着重于最小化$T$深度。具体而言，我们提出了ReLU和带泄漏ReLU激活函数的新型实现，分别实现了4和8的恒定$T$深度。利用量子查找表，我们将探索扩展至其他激活函数，如sigmoid函数。该方法使我们能够通过调整量子比特数来自定义精度和$T$深度，从而使我们的结果更适应各种应用场景。本研究为提升量子机器学习的实用性和应用性迈出了重要一步。