Training-efficient density quantum machine learning

Quantum machine learning requires powerful, flexible and efficiently trainable models to be successful in solving challenging problems. In this work, we present density quantum neural networks, a learning model incorporating randomisation over a set of trainable unitaries. These models generalise quantum neural networks using parameterised quantum circuits, and allow a trade-off between expressibility and efficient trainability, particularly on quantum hardware. We demonstrate the flexibility of the formalism by applying it to two recently proposed model families. The first are commuting-block quantum neural networks (QNNs) which are efficiently trainable but may be limited in expressibility. The second are orthogonal (Hamming-weight preserving) quantum neural networks which provide well-defined and interpretable transformations on data but are challenging to train at scale on quantum devices. Density commuting QNNs improve capacity with minimal gradient complexity overhead, and density orthogonal neural networks admit a quadratic-to-constant gradient query advantage with minimal to no performance loss. We conduct numerical experiments on synthetic translationally invariant data and MNIST image data with hyperparameter optimisation to support our findings. Finally, we discuss the connection to post-variational quantum neural networks, measurement-based quantum machine learning and the dropout mechanism.

Quantum Vision Transformers

We design and analyse quantum transformers, 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 of parametrised quantum circuits for data loading and orthogonal neural layers, we introduce three quantum attention mechanisms, including a quantum transformer based on compound matrices. These quantum architectures can be built using shallow quantum circuits and can provide qualitatively different classification models. We performed extensive simulations of the quantum transformers on standard medical image datasets that showed competitive, and at times better, performance compared with the best classical transformers and other classical benchmarks. The computational complexity of our quantum attention layer proves to be advantageous compared with the classical algorithm with respect to the size of the classified images. Our quantum architectures have thousands of parameters compared with the best classical methods with millions of parameters. Finally, we have implemented our quantum transformers on superconducting quantum computers and obtained encouraging results for up to six qubit experiments.