The Conceptual VAE

In this report we present a new model of concepts, based on the framework of variational autoencoders, which is designed to have attractive properties such as factored conceptual domains, and at the same time be learnable from data. The model is inspired by, and closely related to, the Beta-VAE model of concepts, but is designed to be more closely connected with language, so that the names of concepts form part of the graphical model.

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Relaxations of Graph Isomorphism

We introduce a nonlocal game that captures and extends the notion of graph isomorphism. This game can be won in the classical case if and only if the two input graphs are isomorphic. Thus, by considering quantum strategies we are able to define the notion of quantum isomorphism. We also consider the case of more general non-signalling strategies, and show that such a strategy exists only if the graphs are fractionally isomorphic.

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On the Computational Complexity of Detecting Possibilistic Locality

We consider the computational task of determining whether or not a given table of possibilities constitutes a departure from possibilistic local realism. By considering the case in which one party has access to measurements with two outcomes and the other three, it is possible to see at exactly which point this task becomes computationally difficult.

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Quantum Speed-Ups for Semidefinite Programming

We give a quantum algorithm for solving semidefinite programs (SDPs). The quantum algorithm is constructed by a combination of quantum Gibbs sampling and the multiplicative weight method. In particular, it is based on a classical algorithm of Arora and Kale for approximately solving SDPs. We present a modification of their algorithm to eliminate the need for solving an inner linear program which may be of independent interest.

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A Universal Completion of the ZX-calculus

In this paper, we give a universal completion of the ZX-calculus for the whole of pure qubit quantum mechanics. This proof is based on the completeness of another graphical language, the ZW-calculus, with direct translations between these two graphical systems.

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Training of Quantum Circuits on a Hybrid Quantum Computer

Generative modelling is a flavour of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. This study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes.

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Hardware-Efficient Variational Quantum Algorithms for Time Evolution

Parameterised quantum circuits are a promising technology for achieving a quantum advantage. An important application is the variational simulation of time evolution of quantum systems. To make the most of quantum hardware, variational algorithms need to be as hardware-efficient as possible. Here we present alternatives to the time-dependent variational principle that are hardware-efficient and do not require matrix inversion.

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