The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit, for the reader's consideration, a tentative resolution to it. In particular, I argue, in this dissertation, that the physical explanation for quantum speedup is precisely the fact that the phenomenon of quantum entanglement enables a quantum computer to fully exploit the representational capacity of Hilbert space. This is impossible for classical systems, joint states of which must always be representable as product (...) states. I begin the dissertation by considering, in Chapter 2, the most popular of the candidate physical explanations for quantum speedup: the many worlds explanation of quantum computation. I argue that, although it is inspired by the neo-Everettian interpretation of quantum mechanics, unlike the latter it does not have the conceptual resources required to overcome objections such as the so-called `preferred basis objection'. I further argue that the many worlds explanation, at best, can serve as a good description of the physical process which takes place in so-called network-based computation, but that it is incompatible with other models of computation such as cluster state quantum computing. I next consider, in Chapter 3, a common component of most other candidate explanations of quantum speedup: quantum entanglement. I investigate whether entanglement can be said to be a necessary component of any explanation for quantum speedup, and I consider two major purported counter-examples to this claim. I argue that neither of these, in fact, show that entanglement is unnecessary for speedup, and that, on the contrary, we should conclude that it is. In Chapters 4 and 5 I then ask whether entanglement can be said to be sufficient as well. In Chapter 4 I argue that despite a result that seems to indicate the contrary, entanglement, considered as a resource, can be seen as sufficient to enable quantum speedup. Finally, in Chapter 5 I argue that entanglement is sufficient to explain quantum speedup as well. (shrink)

Of the many and varied applications of quantum information theory, perhaps the most fascinating is the sub-field of quantum computation. In this sub-field, computational algorithms are designed which utilise the resources available in quantum systems in order to compute solutions to computational problems with, in some cases, exponentially fewer resources than any known classical algorithm. While the fact of quantum computational speedup is almost beyond doubt, the source of quantum speedup is still a matter of debate. In this paper I (...) argue that entanglement is a necessary component for any explanation of quantum speedup and I address some purported counter-examples that some claim show that the contrary is true. In particular, I address Cleve et al.'s solution to Deutsch's problem, Biham et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill & Laflamme's deterministic quantum computation with one qubit model of quantum computation. I argue that these examples do not demonstrate that entanglement is unnecessary for the explanation of quantum speedup, but that they rather illuminate and clarify the role that entanglement does play. (shrink)