Kerstin Beer

Graph structures are ubiquitous throughout the natural sciences. Here we develop an approach that exploits the quantum source's graph structure to improve learning via an arbitrary quantum neural network (QNN) ansatz. In particular, we devise and optimize a self-supervised objective to capture the information-theoretic closeness of the quantum states in the training of a QNN. Numerical simulations show that our approach improves the learning efficiency and the generalization behavior of the base QNN. On a practical note, scalable quantum implementations of the learning procedure described in this paper are likely feasible on the next generation of quantum computing devices.

The ultimate limits for the quantum machine learning of quantum data are investigated by obtaining a generalisation of the celebrated No Free Lunch (NFL) theorem. We find a lower bound on the quantum risk (the probability that a trained hypothesis is incorrect when presented with a random input) of a quantum learning algorithm trained via pairs of input and output states when averaged over training pairs and unitaries. The bound is illustrated using a recently introduced QNN architecture.

Neural networks enjoy widespread success in both research and industry and, with the advent of quantum technology, it is a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose a truly quantum analogue of classical neurons, which form quantum feedforward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function, providing both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing deep-network optimisation. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing the optimisation of deep networks. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing modular tensor categories and fusion rings. Rather than providing an in-depth mathematical development we concentrate instead on presenting the "highlights for a physicist".

Contextuality describes the local consistency but global inconsistency of data. In this paper, we review and generalize the bundle diagram representation introduced in [S. Abramsky, R. S. Barbosa, K. Kishida, R. Lal, and S. Mansfield, Contextuality, Cohomology and Paradox, 24th EACSL Annual Conference on Computer Science Logic, Vol. 41 (CSL, 2015), p. 211-228 ] to graphically demonstrate the contextuality of diverse empirical models (a collection of probability distributions for jointly measurable observables).