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Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective

Chandra, D, Babar, Z, Nguyen, Hung, Alanis, D, Botsinis, P, Ng, S and Hanzo, L (2017) Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective IEEE Access, 6 (1). pp. 13729-13757.

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We conceive and investigate the family of classical topological error correction codes (TECCs), which have the bits of a codeword arranged in a lattice structure. We then present the classical-toquantum isomorphism to pave the way for constructing their quantum dual pairs, namely, the quantum TECCs (QTECCs). Finally, we characterize the performance of QTECCs in the face of the quantum depolarizing channel in terms of both the quantum-bit error rate (QBER) and fidelity. Specifically, from our simulation results, the threshold probability of the QBER curves for the color codes, rotated-surface codes, surface codes, and toric codes are given by 1.8 × 10−2 , 1.3 × 10−2 , 6.3 × 10−2 , and 6.8 × 10−2 , respectively. Furthermore, we also demonstrate that we can achieve the benefit of fidelity improvement at the minimum fidelity of 0.94, 0.97, and 0.99 by employing the 1/7-rate color code, the 1/9-rate rotated-surface code, and 1/13-rate surface code, respectively.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
Chandra, D
Babar, Z
Alanis, D
Botsinis, P
Ng, S
Hanzo, L
Date : 18 December 2017
Funders : EPSRC
DOI : 10.1109/ACCESS.2017.2784417
Copyright Disclaimer : Copyright 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Uncontrolled Keywords : Quantum error correction codes, quantum stabilizer codes, quantum topological codes, lattice code, LDPC
Depositing User : Melanie Hughes
Date Deposited : 05 Apr 2018 11:28
Last Modified : 11 Dec 2018 11:24

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