Show simple item record

dc.contributor.authorRoss, Neil Julien
dc.date.accessioned2015-08-25T14:27:03Z
dc.date.available2015-08-25T14:27:03Z
dc.date.issued2015
dc.identifier.urihttp://hdl.handle.net/10222/60819
dc.description.abstractThis 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.isoenen_US
dc.subjectQuantum Computationen_US
dc.subjectQuantum circuit synthesisen_US
dc.subjectClifford+Ten_US
dc.subjectClifford+Ven_US
dc.subjectQuipperen_US
dc.titleAlgebraic and Logical Methods in Quantum Computationen_US
dc.typeThesisen_US
dc.date.defence2015-08-18
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.degreeDoctor of Philosophyen_US
dc.contributor.external-examinerPrakash Panangadenen_US
dc.contributor.graduate-coordinatorDavid Ironen_US
dc.contributor.thesis-readerDorette Pronken_US
dc.contributor.thesis-readerRichard Wooden_US
dc.contributor.thesis-supervisorPeter Selingeren_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.manuscriptsYesen_US
dc.contributor.copyright-releaseNot Applicableen_US
 Find Full text

Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record