  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.
