Efficient quantum circuits for machine learning activation functions including constant T-depth ReLU

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>T</a:mi></a:math>-depth. Specifically, we present novel implementations of ReLU and leaky ReLU activation functions, achieving constant <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>T</b:mi></b:math>-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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>T</c:mi></c:math>-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. Published by the American Physical Society 2024