Asymmetric Quantum Codes: New Codes from Old
Giuliano G. La Guardia
TL;DR
This paper develops new methods for constructing asymmetric quantum error-correcting codes, expanding the toolkit for quantum code design and deriving new code families from well-known classical codes.
Contribution
It introduces and applies several construction techniques to generate asymmetric quantum codes from classical codes like Reed-Muller, QR, BCH, and affine-invariant codes.
Findings
Multiple new families of asymmetric quantum codes are constructed.
Construction methods include puncturing, extending, expanding, and direct sum.
Codes derived from classical codes improve quantum error correction capabilities.
Abstract
In this paper we extend to asymmetric quantum error-correcting codes (AQECC) the construction methods, namely: puncturing, extending, expanding, direct sum and the (u|u + v) construction. By applying these methods, several families of asymmetric quantum codes can be constructed. Consequently, as an example of application of quantum code expansion developed here, new families of asymmetric quantum codes derived from generalized Reed-Muller (GRM) codes, quadratic residue (QR), Bose-Chaudhuri-Hocquenghem (BCH), character codes and affine-invariant codes are constructed.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Coding theory and cryptography · Quantum-Dot Cellular Automata