dc.creatorHaah, Jeongwan
dc.date.accessioned2019-07-03T02:09:03Z
dc.date.available2019-07-03T02:09:03Z
dc.date.created2019-07-03T02:09:03Z
dc.date.issued2016-07-01
dc.identifierISSN: 2357-4100
dc.identifierhttps://repositorio.unal.edu.co/handle/unal/66450
dc.identifierhttp://bdigital.unal.edu.co/67478/
dc.description.abstractThis is a note from a series of lectures at Encuentro Colombiano de Computación Cuántica, Universidad de los Andes, Bogotá, Colombia, 2015. The purpose is to introduce additive quantum error correcting codes, with emphasis on the use of binary representation of Pauli matrices and modules over a translation group algebra. The topics include symplectic vector spaces, Cliord group, cleaning lemma, an error correcting criterion, entanglement spectrum, implications of the locality of stabilizer group generators, and the classication of translation-invariant one-dimensional additive codes and two-dimensional CSS codes with large code distances. In particular, we describe an algorithm to find a Cliord quantum circuit (CNOTs) to transform any two-dimensional translation-invariant CSS code on qudits of a prime dimension with code distance being the linear system size, into a tensor product of finitely many copies of the qudit toric code and a product state. Thus, the number of embedded toric codes is the complete invariant of these CSS codes under local Cliord circuits.
dc.languagespa
dc.publisherUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas
dc.relationUniversidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas
dc.relationRevista Colombiana de Matemáticas
dc.relationHaah, Jeongwan (2016) Algebraic Methods for Quantum Codes on Lattices. Revista Colombiana de Matemáticas, 50 (2). pp. 299-349. ISSN 2357-4100
dc.relationhttps://revistas.unal.edu.co/index.php/recolma/article/view/62214
dc.rightsAtribución-NoComercial 4.0 Internacional
dc.rightshttp://creativecommons.org/licenses/by-nc/4.0/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightsDerechos reservados - Universidad Nacional de Colombia
dc.titleAlgebraic Methods for Quantum Codes on Lattices
dc.typeArtículo de revista


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