Classification of quantum wire in tensor network states with a local Pauli symmetry
department or school: Science, Faculty of
department or school: Physics and Astronomy, Department of
data provider: DSpace
degree campus: UBCV
creator: Herringer, Paul
issued: 2021-10-21T19:40:49Z
issued: 2021
related degree: Master of Science - MSc
degree grantor: University of British Columbia
description: Certain symmetry-protected topological (SPT) phases also possess the property that every state in the phase is a universal resource for measurement-based quantum computation (MBQC). These phases are called computational phases of quantum matter. Computational phases have been classified in 1D, and several examples are known in 2D. 2D computational phases are of interest because we can simulate any quantum computation using a 2D phase. Therefore, the classification of 2D phases may lead to a better understanding of the relationship between symmetry and quantum computation. Many known 2D phases have a projected entangled pair state (PEPS) representation where the local tensor symmetries define a quantum cellular automaton (QCA) acting on correlation space. However, not every tensor symmetry defines a QCA, which motivates the definition and study of a larger class of PEPS tensors called stabilizer tensors. Stabilizer tensors have symmetries that act as a tensor product of Pauli operators on correlation space but do not necessarily define a QCA. In this thesis, I present a classification of stabilizer tensors by their channel capacity for quantum wire. In particular, I consider the quantum wire capacity of translationally invariant, cylindrical PEPS constructed from stabilizer tensors and find that it falls into one of 13 classes. Furthermore, I prove that no other types of channel capacity exist for stabilizer tensors, regardless of the size of the cylinder. I also discuss the significance of this result for the classification of 2D computational phases along with possible next steps.
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/80016
note: Classification of Quantum Wire inTensor Network States with a LocalPauli SymmetrybyPaul HerringerB.Sc. Honours in Physics, University of Calgary, 2019A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2021© Paul Herringer 2021The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:Classification of Quantum Wire in Tensor Network States with aLocal Pauli Symmetrysubmitted by Paul Herringer in partial fulfillment of the requirements forthe degree of Master of Science in PhysicsExamining committee:Robert Raussendorf, Physics and Astronomy, UBCSupervisorMark van Raamsdonk, Physics and Astronomy, UBCSupervisory Committee MemberiiAbstractCertain symmetry-protected topological (SPT) phases also possess the prop-erty that every state in the phase is a universal resource for measurement-based quantum computation (MBQC) [21]. These phases are called com-putational phases of quantum matter. Computational phases have beenclassified in 1D, and several examples are known in 2D [21, 22, 26]. 2Dcomputational phases are of interest because we can simulate any quantumcomputation using a 2D phase. Therefore, the classification of 2D phasesmay lead to a better understanding of the relationship between symmetryand quantum computation.Many known 2D phases have a projected entangled pair state (PEPS)representation where the local tensor symmetries define a quantum cellularautomaton (QCA) acting on correlation space [26]. However, not every ten-sor symmetry defines a QCA, which motivates the definition and study of alarger class of PEPS tensors called stabilizer tensors. Stabilizer tensors havesymmetries that act as a tensor product of Pauli operators on correlationspace but do not necessarily define a QCA.In this thesis, I present a class…
has type: Thesis/Dissertation
date issued: 2021-11
is shown at: 10.14288/1.0402579
language: eng
degree discipline: Physics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Raussendorf, Robert
type: Text
identifier URI: http://hdl.handle.net/2429/80016