dc.contributor.author | Ross, Neil Julien | |
dc.date.accessioned | 2015-08-25T14:27:03Z | |
dc.date.available | 2015-08-25T14:27:03Z | |
dc.date.issued | 2015 | |
dc.identifier.uri | http://hdl.handle.net/10222/60819 | |
dc.description.abstract | This thesis contains contributions to the theory of quantum computation.
We first define a new method to efficiently approximate special unitary operators.
Specifically, given a special unitary U and a precision ε > 0, we show how to efficiently
find a sequence of Clifford+V or Clifford+T operators whose product approximates
U up to ε in the operator norm. In the general case, the length of the approximating
sequence is asymptotically optimal. If the unitary to approximate is diagonal then
our method is optimal: it yields the shortest sequence approximating U up to ε.
Next, we introduce a mathematical formalization of a fragment of the Quipper
quantum programming language. We define a typed lambda calculus called Proto-
Quipper which formalizes a restricted but expressive fragment of Quipper. The type
system of Proto-Quipper is based on intuitionistic linear logic and prohibits the duplication
of quantum data, in accordance with the no-cloning property of quantum
computation. We prove that Proto-Quipper is type-safe in the sense that it enjoys
the subject reduction and progress properties. | en_US |
dc.language.iso | en | en_US |
dc.subject | Quantum Computation | en_US |
dc.subject | Quantum circuit synthesis | en_US |
dc.subject | Clifford+T | en_US |
dc.subject | Clifford+V | en_US |
dc.subject | Quipper | en_US |
dc.title | Algebraic and Logical Methods in Quantum Computation | en_US |
dc.type | Thesis | en_US |
dc.date.defence | 2015-08-18 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Doctor of Philosophy | en_US |
dc.contributor.external-examiner | Prakash Panangaden | en_US |
dc.contributor.graduate-coordinator | David Iron | en_US |
dc.contributor.thesis-reader | Dorette Pronk | en_US |
dc.contributor.thesis-reader | Richard Wood | en_US |
dc.contributor.thesis-supervisor | Peter Selinger | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Yes | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |