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Computational approach to quantum encoder design for purity optimization

Yamamoto, Naoki and Fazel, Maryam (2007) Computational approach to quantum encoder design for purity optimization. Physical Review A, 76 (1). Art. No. 012327. ISSN 1050-2947. doi:10.1103/PhysRevA.76.012327.

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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.

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Additional Information:©2007 The American Physical Society. (Received 28 August 2006; revised 7 May 2007; published 26 July 2007) We wish to thank P. Parrilo for pointing out the SOS characterization. N.Y. would like to acknowledge stimulating discussions with S. Hara and H. Siahaan. M.F. thanks M. Yanagisawa for helpful discussions. This work was supported in part by the JSPS Grant-in-Aid No. 06693.
Subject Keywords:quantum computing; information theory; encoding; optimisation; error analysis
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Record Number:CaltechAUTHORS:YAMpra07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8779
Deposited By: Archive Administrator
Deposited On:15 Sep 2007
Last Modified:08 Nov 2021 20:53

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