Efficient Quantum Circuits for Machine Learning Activation Functions including Constant T-depth ReLU

TL;DR

This paper introduces efficient quantum circuits for activation functions in quantum machine learning, achieving constant T-depth implementations of ReLU and leaky ReLU, and adaptable designs for other functions like sigmoid.

Contribution

Develops novel quantum circuit implementations of activation functions with minimal T-depth, including constant-depth ReLU and leaky ReLU, and adaptable designs for various functions using quantum lookup tables.

Findings

ReLU with T-depth of 4

Leaky ReLU with T-depth of 8

Flexible activation functions via quantum lookup tables

Abstract

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.