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.

我们的研究主要关注于为容错量子计算架构开发激活函数的量子电路，重点在于最小化 $T$-depth。我们提出了 ReLU 和 leaky ReLU 激活函数的新实现，分别实现了恒定的 4 和 8 的 $T$-depth。借助量子查找表，我们还延伸研究到其他激活函数，如 sigmoid。通过调整量子比特的数量，我们能够定制精度和 $T$-depth，使得我们的研究结果在各种应用场景中更具适应性。这项研究对于提升量子机器学习的实用性和应用具有重要意义。