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Computational approach to quantum encoder design for purity optimization

Yamamoto, Naoki; Fazel, Maryam

Description

In this paper, we address the problem of designing a quantum encoder that maximizes the minimum output purity of a given decohering channel, where the minimum is taken over all possible pure inputs. This problem is cast as a max-min optimization problem with a rank constraint on an appropriately defined matrix variable. The problem is computationally very hard because it is nonconvex with respect to both the objective function (output purity) and the rank constraint. Despite this difficulty, we...[Show more]

dc.contributor.authorYamamoto, Naoki
dc.contributor.authorFazel, Maryam
dc.date.accessioned2015-12-10T21:54:36Z
dc.identifier.issn1050-2947
dc.identifier.urihttp://hdl.handle.net/1885/39013
dc.description.abstractIn this paper, we address the problem of designing a quantum encoder that maximizes the minimum output purity of a given decohering channel, where the minimum is taken over all possible pure inputs. This problem is cast as a max-min optimization problem with a rank constraint on an appropriately defined matrix variable. The problem is computationally very hard because it is nonconvex with respect to both the objective function (output purity) and the rank constraint. Despite this difficulty, we provide a tractable computational algorithm that produces the exact optimal solution for codespace of dimension 2. Moreover, this algorithm is easily extended to cover the general class of codespaces, in which case the solution is suboptimal in the sense that the suboptimized output purity serves as a lower bound of the exact optimal purity. The algorithm consists of a sequence of semidefinite programmings and can be performed easily. Two typical quantum error channels are investigated to illustrate the effectiveness of our method.
dc.publisherAmerican Physical Society
dc.sourcePhysical Review A: Atomic, Molecular and Optical Physics
dc.subjectKeywords: Algorithms; Computational methods; Constraint theory; Error analysis; Optimization; Problem solving; Decohering channel; Minimum output purity; Purity optimization; Quantum encoder design; Quantum theory
dc.titleComputational approach to quantum encoder design for purity optimization
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume76
dc.date.issued2007
local.identifier.absfor100503 - Computer Communications Networks
local.identifier.ariespublicationu3379551xPUB170
local.type.statusPublished Version
local.contributor.affiliationYamamoto, Naoki, College of Engineering and Computer Science, ANU
local.contributor.affiliationFazel, Maryam, California Institute of Technology
local.description.embargo2037-12-31
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage012327-1-/012327-13
local.identifier.doi10.1103/PhysRevA.76.012327
local.identifier.absseo890399 - Information Services not elsewhere classified
dc.date.updated2015-12-09T07:27:27Z
local.identifier.scopusID2-s2.0-34547409473
CollectionsANU Research Publications

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