  The self-attention mechanism (SAM) has demonstrated remarkable success in
various applications. However, training SAM on classical computers becomes
computationally challenging as the number of trainable parameters grows.
Quantum neural networks (QNNs) have been developed as a novel learning model
that promises to provide speedup for pattern recognition using near-term Noisy
Intermediate-Scale Quantum (NISQ) computers. In this work, we propose a
completely natural way of implementing SAM in QNNs, resulting in the quantum
self-attention mechanism (QSAM). The fundamental operations of SAM, such as
calculating attention scores and producing attention features, are realized by
only designing the data encoding and ansatz architecture appropriately. As
these are the fundamental components of QNNs, our QSAM can be executed
efficiently on near-term NISQ devices. Our QSAM models achieve better
performance in terms of both accuracy and circuit complexity on the text
categorization task. Moreover, the robustness of QSAM against various typical
types of quantum noise is demonstrated, indicating the model's suitability for
NISQ devices. The present QSAM will serve as the fundamental building blocks
for developing large models of quantum attention neural networks for quantum
advantageous applications.
