Computational approach to quantum encoder design for purity optimization
Date
2007
Authors
Yamamoto, Naoki
Fazel, Maryam
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Abstract
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 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.
Description
Keywords
Keywords: Algorithms; Computational methods; Constraint theory; Error analysis; Optimization; Problem solving; Decohering channel; Minimum output purity; Purity optimization; Quantum encoder design; Quantum theory
Citation
Collections
Source
Physical Review A: Atomic, Molecular and Optical Physics
Type
Journal article
Book Title
Entity type
Access Statement
License Rights
Restricted until
2037-12-31
Downloads
File
Description