Symmetry Protected Topological Order As A Requirement for Measurement-Based Quantum Gate Teleportation

Liu, Zhuohao

Symmetry Protected Topological Order As A Requirement for Measurement-Based Quantum Gate Teleportation

dc.contributor.advisor	Feder, David
dc.contributor.author	Liu, Zhuohao
dc.contributor.committeemember	Sanders, Barry
dc.contributor.committeemember	Barclay, Paul
dc.contributor.committeemember	Salahub, Dennis
dc.date	2025-06
dc.date.accessioned	2025-02-05T22:33:42Z
dc.date.available	2025-02-05T22:33:42Z
dc.date.issued	2025-01-20
dc.description.abstract	All known resource states for measurement-based quantum teleportation in correlation space possess symmetry protected topological order, but is this a sufficient or even necessary condition? This work considers two families of one-dimensional qubit states to answer this question in the negative. The first is a family of matrix-product states with bond dimension two that includes the cluster state as a special case, protected by a global non-onsite symmetry, which is unable to deterministically teleport gates and which is characterized by a finite correlation length and a degenerate entanglement spectrum in the thermodynamic limit. The second are states with bond dimension four that are a resource for deterministic universal teleportation of finite single-qubit gates, but which possess no symmetry.
dc.identifier.citation	Liu, Z. (2025). Symmetry protected topological order as a requirement for measurement-based quantum gate teleportation (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.identifier.uri	https://hdl.handle.net/1880/120553
dc.language.iso	en
dc.publisher.faculty	Graduate Studies
dc.publisher.institution	University of Calgary
dc.rights	University 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.
dc.subject	Quantum computing
dc.subject	Measurement-based quantum computing
dc.subject	Symmetry protected topological order
dc.subject.classification	Physics--Theory
dc.title	Symmetry Protected Topological Order As A Requirement for Measurement-Based Quantum Gate Teleportation
dc.type	master thesis
thesis.degree.discipline	Physics & Astronomy
thesis.degree.grantor	University of Calgary
thesis.degree.name	Master of Science (MSc)
ucalgary.thesis.accesssetbystudent	I do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.