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.
Category (publication): Algorithms
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.
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.
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.
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.
Adversarial Quantum Circuit Learning for Pure State Approximation
In this work, we derive an adversarial algorithm for the problem of approximating an unknown quantum pure state. Although this could be done on universal quantum computers, the adversarial formulation enables us to execute the algorithm on near-term quantum computers.
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.
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.
The Problem with Grover-Rudolph State Preparation for Quantum Monte-Carlo
We prove that there is no quantum speed-up when using quantum Monte-Carlo integration to estimate the mean (and other moments) of analytically-defined log-concave probability distributions prepared as quantum states using the Grover-Rudolph method.
Estimation of Correlations and Non-Separability in Quantum Channels via Unitarity Benchmarking
The ability to transfer coherent quantum information between systems is a fundamental component of quantum technologies and leads to coherent correlations within the global quantum process. Motivated by recent techniques in randomised benchmarking, we develop a range of results for efficient estimation of correlations within a bipartite quantum channel.