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Quantum Information Processing

Good and asymptotically good quantum codes derived from algebraic geometry

Giuliano G. La Guardia, Francisco Revson F. Pereira

Published May 13, 2017• 20 citations
Publisher
DOI
10.1007/s11128-017-1618-7

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It is known that quantum error correction can be achieved using classical binary codes or additive codes over F/sub 4/. Asymptotically good quantum codes have been constructed from algebraic-geometry codes and a bound on (/spl delta/, R) was computed from the Tsfasman-Vladut-Zink bound of the theory of classical algebraic-geometry codes. In this correspondence, by the use of a concatenation technique we construct a family of asymptotically good quantum codes exceeding the bound in a small interval.
Quantum error correction is an essential aspect of quantum information theory, providing protection for quantum states against noise and decoherence. This thesis investigates the construction of quantum error correction codes derived from classical algebraic geometry (AG) codes. We present two distinct construction techniques, highlighting the flexibility and self-orthogonality of AG codes, and demonstrate their ability to produce asymptotically good quantum codes. Additionally, we explore strategies to fine-tune the parameters of classical AG codes, ensuring they possess the desired properties for quantum code construction. This work serves as a comprehensive guide to the fundamental concepts and common methodologies underlying quantum algebraic geometry codes.