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Quantum topological error correction codes: The classical-to-quantum isomorphism perspective

Quantum topological error correction codes: The classical-to-quantum isomorphism perspective
Quantum topological error correction codes: The classical-to-quantum isomorphism perspective
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-to-quantum isomorphism to pave the way for constructing their quantum dual pairs, namely the quantum topological error correction codes (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 colour codes, rotated-surface codes, surface codes and toric codes are given by $1.8 \times 10^{-2}$, $1.3 \times 10^{-2}$, $6.3 \times 10^{-2}$ and $6.8 \times 10^{-2}$, 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 colour code, the $1/9$-rate rotated-surface code and $1/13$-rate surface code, respectively.
2169-3536
Chandra, Daryus
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Babar, Zunaira
23ede793-1796-449d-b5aa-93a297e5677a
Nguyen, Hung Viet
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Alanis, Dimitrios
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Botsinis, Panagiotis
d7927fb0-95ca-4969-9f8c-1c0455524a1f
Ng, Soon
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1
Chandra, Daryus
a2f091a8-9772-4633-8e3b-d3220b10a2ec
Babar, Zunaira
23ede793-1796-449d-b5aa-93a297e5677a
Nguyen, Hung Viet
6f5a71ef-ea98-49e0-9be7-7f5bb9880f52
Alanis, Dimitrios
8ae8ead6-3974-4886-8e17-1b4bff1d94e0
Botsinis, Panagiotis
d7927fb0-95ca-4969-9f8c-1c0455524a1f
Ng, Soon
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1

Chandra, Daryus, Babar, Zunaira, Nguyen, Hung Viet, Alanis, Dimitrios, Botsinis, Panagiotis, Ng, Soon and Hanzo, Lajos (2017) Quantum topological error correction codes: The classical-to-quantum isomorphism perspective. IEEE Access. (doi:10.1109/ACCESS.2017.2784417).

Record type: Article

Abstract

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-to-quantum isomorphism to pave the way for constructing their quantum dual pairs, namely the quantum topological error correction codes (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 colour codes, rotated-surface codes, surface codes and toric codes are given by $1.8 \times 10^{-2}$, $1.3 \times 10^{-2}$, $6.3 \times 10^{-2}$ and $6.8 \times 10^{-2}$, 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 colour code, the $1/9$-rate rotated-surface code and $1/13$-rate surface code, respectively.

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QuantumTopologicalErrorCorrectionCodes - Accepted Manuscript
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Accepted/In Press date: 11 December 2017
e-pub ahead of print date: 18 December 2017

Identifiers

Local EPrints ID: 416356
URI: https://eprints.soton.ac.uk/id/eprint/416356
ISSN: 2169-3536
PURE UUID: 62662a3e-8e45-42a8-88c0-7e9dbdd8fd7c
ORCID for Daryus Chandra: ORCID iD orcid.org/0000-0003-2406-7229
ORCID for Zunaira Babar: ORCID iD orcid.org/0000-0002-7498-4474
ORCID for Hung Viet Nguyen: ORCID iD orcid.org/0000-0001-6349-1044
ORCID for Dimitrios Alanis: ORCID iD orcid.org/0000-0002-6654-1702
ORCID for Soon Ng: ORCID iD orcid.org/0000-0002-0930-7194
ORCID for Lajos Hanzo: ORCID iD orcid.org/0000-0002-2636-5214

Catalogue record

Date deposited: 14 Dec 2017 17:30
Last modified: 14 Mar 2019 01:55

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