Logic Functions and Quantum Error Correcting Codes

Simple item page
dc.creatorXu, Yajie
dc.creatorMa, Zhi
dc.creatorZhang, Chunyuan
dc.creatorLü, Xin
dc.date2007-12-21
dc.date2008-01-06
dc.date.accessioned2026-07-07T08:52:27Z
dc.date.available2026-07-07T08:52:27Z
dc.descriptionIn this paper, based on the relationship between logic functions and quantum error correcting codes(QECCs), we unify the construction of QECCs via graphs, projectors and logic functions. A construction of QECCs over a prime field GF(p) is given, and one of the results given by Ref[8] can be viewed as a corollary of one theorem in this paper. With the help of Boolean functions, we give a clear proof of the existence of a graphical QECC in mathematical view, and find that the existence of an [[n,k,d]] QECC over GF(p) requires similar conditions with that depicted in Ref[9]. The result that under the correspondence defined in Ref[17], every [[n,0,d]] QECC over GF(2) corresponding to a simple undirected graph has a Boolean basis state, which is closely related to the adjacency matrix of the graph, is given. After a modification of the definition of operators, we find that some QECCs constructed via projectors depicted in Ref[11] can have Boolean basis states. A necessary condition for a Boolean function being used in the construction via projectors is given. We also give some examples to illustrate our results.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/0712.3605
dc.identifierhttp://arxiv.org/abs/0712.3605
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145284
dc.subjectQuantum Physics
dc.titleLogic Functions and Quantum Error Correcting Codes
dc.typetext

Files

Collections

arXiv