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)

I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.

The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simple extension creates a new perspective from which to see the quantum algorithm. First, it highlights the relevance of time-symmetric quantum mechanics to quantum computation: the problem-setting and (...) problem solution, in their quantum version, constitute pre- and post-selection, hence the process as a whole is bound to be affected by both boundary conditions. Second, it forces us to enter into relational quantum mechanics. There must be a representation of the quantum algorithm with respect to Bob, and another one with respect to Alice, from whom the outcome of the initial measurement, specifying the setting and thus the solution of the problem, must be concealed. Time-symmetrizing the quantum algorithm to take into account both boundary conditions leaves the representation to Bob unaltered. It shows that the representation to Alice is a sum over histories in each of which she remains shielded from the information coming to her from the initial measurement, not from that coming to her backwards in time from the final measurement. In retrospect, all is as if she knew in advance, before performing her problem-solving action, half of the information that specifies the solution of the problem she will read in the future and could use this information to reach the solution with fewer computation steps. This elucidates the quantum computational speedup in all the quantum algorithms examined. (shrink)