Exact solution for the max-min quantum error recovery problem

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

This paper considers the max-min quantum error recovery problem; the recovery channel to be designed maximizes the fidelity between input and output states of a given noisy channel, while the minimum is taken over all possible pure input states. In general, this kind of max-min problem is cast as a non-convex optimization problem and is thus very hard to solve even with the aid of high-quality computational tools. Nevertheless, it is shown that, when the input takes a qubit, the problem is exactly convex for any size of error process. The Sum of Squares (SOS) characterization of a specific class of polynomial functions plays a crucial role in deriving this result.

Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Pages1433-1438
Number of pages6
DOIs
Publication statusPublished - 2009
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: 2009 Dec 152009 Dec 18

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period09/12/1509/12/18

Fingerprint

Error Recovery
Min-max
Exact Solution
Polynomials
Min-max Problem
Recovery
Nonconvex Optimization
Nonconvex Problems
Sum of squares
Polynomial function
Qubit
Fidelity
Maximise
Optimization Problem
Output
Class

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

Cite this

Yamamoto, N. (2009). Exact solution for the max-min quantum error recovery problem. In Proceedings of the IEEE Conference on Decision and Control (pp. 1433-1438). [5400142] https://doi.org/10.1109/CDC.2009.5400142

Exact solution for the max-min quantum error recovery problem. / Yamamoto, Naoki.

Proceedings of the IEEE Conference on Decision and Control. 2009. p. 1433-1438 5400142.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yamamoto, N 2009, Exact solution for the max-min quantum error recovery problem. in Proceedings of the IEEE Conference on Decision and Control., 5400142, pp. 1433-1438, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 09/12/15. https://doi.org/10.1109/CDC.2009.5400142
Yamamoto N. Exact solution for the max-min quantum error recovery problem. In Proceedings of the IEEE Conference on Decision and Control. 2009. p. 1433-1438. 5400142 https://doi.org/10.1109/CDC.2009.5400142
Yamamoto, Naoki. / Exact solution for the max-min quantum error recovery problem. Proceedings of the IEEE Conference on Decision and Control. 2009. pp. 1433-1438
@inproceedings{0e2706dcf4f6476297fcaa28b66ad40a,
title = "Exact solution for the max-min quantum error recovery problem",
abstract = "This paper considers the max-min quantum error recovery problem; the recovery channel to be designed maximizes the fidelity between input and output states of a given noisy channel, while the minimum is taken over all possible pure input states. In general, this kind of max-min problem is cast as a non-convex optimization problem and is thus very hard to solve even with the aid of high-quality computational tools. Nevertheless, it is shown that, when the input takes a qubit, the problem is exactly convex for any size of error process. The Sum of Squares (SOS) characterization of a specific class of polynomial functions plays a crucial role in deriving this result.",
author = "Naoki Yamamoto",
year = "2009",
doi = "10.1109/CDC.2009.5400142",
language = "English",
isbn = "9781424438716",
pages = "1433--1438",
booktitle = "Proceedings of the IEEE Conference on Decision and Control",

}

TY - GEN

T1 - Exact solution for the max-min quantum error recovery problem

AU - Yamamoto, Naoki

PY - 2009

Y1 - 2009

N2 - This paper considers the max-min quantum error recovery problem; the recovery channel to be designed maximizes the fidelity between input and output states of a given noisy channel, while the minimum is taken over all possible pure input states. In general, this kind of max-min problem is cast as a non-convex optimization problem and is thus very hard to solve even with the aid of high-quality computational tools. Nevertheless, it is shown that, when the input takes a qubit, the problem is exactly convex for any size of error process. The Sum of Squares (SOS) characterization of a specific class of polynomial functions plays a crucial role in deriving this result.

AB - This paper considers the max-min quantum error recovery problem; the recovery channel to be designed maximizes the fidelity between input and output states of a given noisy channel, while the minimum is taken over all possible pure input states. In general, this kind of max-min problem is cast as a non-convex optimization problem and is thus very hard to solve even with the aid of high-quality computational tools. Nevertheless, it is shown that, when the input takes a qubit, the problem is exactly convex for any size of error process. The Sum of Squares (SOS) characterization of a specific class of polynomial functions plays a crucial role in deriving this result.

UR - http://www.scopus.com/inward/record.url?scp=77950836068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950836068&partnerID=8YFLogxK

U2 - 10.1109/CDC.2009.5400142

DO - 10.1109/CDC.2009.5400142

M3 - Conference contribution

AN - SCOPUS:77950836068

SN - 9781424438716

SP - 1433

EP - 1438

BT - Proceedings of the IEEE Conference on Decision and Control

ER -