Abstract
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.
Keywords
Isomorphism (crystallography)
Mathematics
Commutative property
Code (set theory)
Quantum
Discrete mathematics
Algebra over a field
Pure mathematics
Computer science
Quantum mechanics
Physics
Subject Areas
Quantum Computing Algorithms and Architecture
·Artificial Intelligence ·Physical Sciences
Quantum Information and Cryptography
·Artificial Intelligence ·Physical Sciences
Quantum-Dot Cellular Automata
·Computational Theory and Mathematics ·Physical Sciences
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