Entanglement-assisted Reed�Solomon codes over qudits: theory and architecture

Nadkarni, PJ and Garani, SS (2021) Entanglement-assisted Reed�Solomon codes over qudits: theory and architecture. In: Quantum Information Processing, 20 (4).

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Abstract

We develop a systematic theory for the construction of quantum codes from classical Reed�Solomon over Fpk, where p is prime and k� Z+. Based on two classical n, n- dm+ 1 , dm Reed�Solomon codes over Fpk, we provide the construction of an n, n+ ne- 2 (dm- 1) , dm]] entanglement-assisted Reed�Solomon code over qudits of dimension d= pk that saturates the quantum Singleton bound and needs ne entangled qudits, which involves obtaining the explicit form of the stabilizers for the code. Our contributions towards the entanglement-assisted Reed�Solomon code are multi-fold as follows: (a) Based on the parity check matrices of the classical Reed�Solomon codes, the explicit form of the stabilizers of the entanglement-assisted Reed�Solomon code are provided and the rate-optimal code is obtained. (b) Based on the entanglement-assisted Reed�Solomon code, a burst error correcting code for qudits of dimension p that corrects a burst of k(tm- 1) qudits or less, where tm= � (dm- 1) / 2 � is provided. (c) Finally, we provide amenable circuits for encoding and error correction with quantum circuit complexity of O(n2) , useful for practical implementations. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

Item Type:	Journal Article
Publication:	Quantum Information Processing
Publisher:	Springer
Additional Information:	The copyright for this article belongs to Author,under exclusive licence to Springer Science Business Media, LLC part of Springer Nature
Keywords:	Error correction; Matrix algebra; Optimal systems; Quantum computers; Quantum entanglement, Burst error correcting codes; Explicit form; Optimal codes; Parity check matrices; Quantum circuit; Quantum codes; Singleton bound; Systematic theories, Codes (symbols)
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology)
Date Deposited:	13 Jul 2021 10:52
Last Modified:	13 Jul 2021 10:52
URI:	http://eprints.iisc.ac.in/id/eprint/68804

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