  In this work, quantum transformers are designed and analysed in detail by
extending the state-of-the-art classical transformer neural network
architectures known to be very performant in natural language processing and
image analysis. Building upon the previous work, which uses parametrised
quantum circuits for data loading and orthogonal neural layers, we introduce
three types of quantum transformers for training and inference, including a
quantum transformer based on compound matrices, which guarantees a theoretical
advantage of the quantum attention mechanism compared to their classical
counterpart both in terms of asymptotic run time and the number of model
parameters. These quantum architectures can be built using shallow quantum
circuits and produce qualitatively different classification models. The three
proposed quantum attention layers vary on the spectrum between closely
following the classical transformers and exhibiting more quantum
characteristics. As building blocks of the quantum transformer, we propose a
novel method for loading a matrix as quantum states as well as two new
trainable quantum orthogonal layers adaptable to different levels of
connectivity and quality of quantum computers. We performed extensive
simulations of the quantum transformers on standard medical image datasets that
showed competitively, and at times better performance compared to the classical
benchmarks, including the best-in-class classical vision transformers. The
quantum transformers we trained on these small-scale datasets require fewer
parameters compared to standard classical benchmarks. Finally, we implemented
our quantum transformers on superconducting quantum computers and obtained
encouraging results for up to six qubit experiments.
