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Quantum Machine Learning For Classical Data

Wossnig, Leonard P.; (2021) Quantum Machine Learning For Classical Data. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of re- search falls under the umbrella of quantum machine learning, a research area of computer science which has recently received wide attention. In particular, we in- vestigate to what extent quantum computers can be used to accelerate supervised machine learning algorithms. The aim of this is to develop a clear understanding of the promises and limitations of the current state-of-the-art of quantum algorithms for supervised machine learning, but also to define directions for future research in this exciting field. We start by looking at supervised quantum machine learning (QML) algorithms through the lens of statistical learning theory. In this frame- work, we derive novel bounds on the computational complexities of a large set of supervised QML algorithms under the requirement of optimal learning rates. Next, we give a new bound for Hamiltonian simulation of dense Hamiltonians, a major subroutine of most known supervised QML algorithms, and then derive a classical algorithm with nearly the same complexity. We then draw the parallels to recent ‘quantum-inspired’ results, and will explain the implications of these results for quantum machine learning applications. Looking for areas which might bear larger advantages for QML algorithms, we finally propose a novel algorithm for Quantum Boltzmann machines, and argue that quantum algorithms for quantum data are one of the most promising applications for QML with potentially exponential advantage over classical approaches.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Quantum Machine Learning For Classical Data
Event: UCL
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Copyright © The Author 2021. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10126651
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