Year: 2003
Type: dissertation
Abstract: This thesis focuses on two different aspects of quantum computation: quantum complexity and quantum semantics. In the first part, I study the quantum complexity mainly within the quantum query model. Together with my colleagues, I introduce a new framework for quantum query complexity, phrased in terms of the minimal oracle and analyse limits and strengths of this new model in comparison to their classical and quantum counterparts. Working within the query model I study quantum one-way functions. I show that in the quantum setting, the problem of the existence of a quantum one-way permutation can be reduced to the problem of constructing polynomial size networks for performing the specific task of the reflection about a sequence of states. Furthermore, I extend these results to the domain of the state and operator complexity. I show that if a quantum one-way function exists, then we can construct a sequence of so called “hard” states with the property that the reflection operators about those states are efficiently implementable. In the second part, I study the extension of domain theory to the quantum setting and develop the semantics of quantum computation. By defining a quantum domain I introduce a rigourous definition of quantum computability for quantum states and operators. Furthermore I show that the denotational semantics of quantum computation has the same semantical structure as the denotational semantics of classical probabilistic computation introduced by Kozen. This could be considered as a foundation for designing functional programming languages for quantum computation. Finally, I continue with an abstract mathematical approach to study a general formalism for describing entanglement manipulation and introduce a new approach to derive a unique measure of entanglement for bipartite quantum pure states.
Source: Spiral (Imperial College London)
Author: Elham Kashefi
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2338608297