Algebraic Quantum Codes: Linking Quantum Mechanics and Discrete Mathematics

Abstract

We present a general framework of quantum error-correcting codes (QECCs) as a subspace of a complex Hilbert space and the corresponding error models. Then we illustrate how QECCs can be constructed using techniques from algebraic coding theory. Additionally, we discuss secondary constructions for QECCs, leading to propagation rules for the parameters of QECCs.

arXiv comment19 pages; written for both mathematicians and physicists

References in corpus (7)

• Good Quantum Error-Correcting Codes Exist
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Cited by in corpus (7)

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• Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes
• An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance
• Quasi-cyclic codes of index 2
• Puncturing Quantum Stabilizer Codes
• Fast Algorithms and Implementations for Computing the Minimum Distance of Quantum Codes
• The Subfield Metric and its Application to Quantum Error Correction