Classifying reversible logic gates with ancillary bits

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dc.contributor.advisorCockett, J. Robin B.
dc.contributor.authorComfort, Cole Robert
dc.contributor.committeememberCoecke, Bob
dc.contributor.committeememberGour, Gilad
dc.contributor.committeememberScheidler, Renate
dc.date2019-11
dc.date.accessioned2019-07-25T14:46:25Z
dc.date.available2019-07-25T14:46:25Z
dc.date.issued2019-07-23
dc.description.abstractIn this thesis, two models of reversible computing are classified, and the relation of reversible computing to quantum computing is explored. First, a finite, complete set of identities is given for the symmetric monoidal category generated by the computational ancillary bits along with the controlled-not gate. In doing so, it is proven that this category is equivalent to the category of partial isomorphisms between non-empty finitely-generated commutative torsors of characteristic 2. Next, a finite, complete set of identities is given for the symmetric monoidal category generated by the computational ancillary bits along with the Toffoli gate. In doing so, it is proven that this category is equivalent to the category of partial isomorphisms between finite powers of the two element set. The relation between reversible and quantum computing is also explored. In particular, the category with the controlled-not gate as a generator is extended to be complete for the real stabilizer fragment of quantum mechanics. This is performed by translating the identities to and from the angle-free fragment of the ZX-calculus, and showing that these translations are inverse to each other.en_US
dc.identifier.citationComfort, C. R. (2019). Classifying reversible logic gates with ancillary bits (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/36765
dc.identifier.urihttp://hdl.handle.net/1880/110665
dc.language.isoengen_US
dc.publisher.facultyScienceen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectReversibleen_US
dc.subjectreversible computingen_US
dc.subjectquantumen_US
dc.subjectquantum computingen_US
dc.subjectquantum informationen_US
dc.subjectcategory theoryen_US
dc.subjectmonoidal categoriesen_US
dc.subjectrestriction categoriesen_US
dc.subjectcategorical quantum mechanicsen_US
dc.subjecttheoretical computer scienceen_US
dc.subject.classificationEducation--Mathematicsen_US
dc.subject.classificationPhysicsen_US
dc.subject.classificationComputer Scienceen_US
dc.titleClassifying reversible logic gates with ancillary bitsen_US
dc.typemaster thesisen_US
thesis.degree.disciplineComputer Scienceen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameMaster of Science (MSc)en_US
ucalgary.item.requestcopytrueen_US
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