Quantum codes over Eisenstein-Jacobi integers

In this study, we construct quantum error correcting codes over Eisenstein-Jacobi integers by using the CSS code construction. Since there is an isomorphism between Eisenstein- Jacobi integers and finite fields, direct constructions of quantum codes over Eisenstein-Jacobi integers can be obtained. T...

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Bibliographic Details
Published in2017 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO) pp. 1 - 5
Main Authors Yildiz, Eda, Demirkale, Fatih
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.04.2017
Subjects
Computers
CSS code construction
Eisenstein-Jacobi integers
Encoding
error correcting codes
Error correction codes
Hilbert space
Jacobian matrices
Quantum code
Quantum computing
Quantum mechanics
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Summary:In this study, we construct quantum error correcting codes over Eisenstein-Jacobi integers by using the CSS code construction. Since there is an isomorphism between Eisenstein- Jacobi integers and finite fields, direct constructions of quantum codes over Eisenstein-Jacobi integers can be obtained. Therefore, we define error bases, error matrices and a new distance with giving illustrative examples. Also, we prove the commutative property of error operators with respect to this new distance. Obtaining these codes can lead an answer for the existence question for some new parameters.
DOI:10.1109/ICMSAO.2017.7948934