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Quantum topological error correction codes are capable of improving the performance of Clifford Gates

Quantum topological error correction codes are capable of improving the performance of Clifford Gates
Quantum topological error correction codes are capable of improving the performance of Clifford Gates
The employment of quantum error correction codes (QECCs) within quantum computers potentially offers a reliability improvement for both quantum computation and communications tasks. However, incorporating quantum gates for performing error correction potentially introduces more sources of quantum decoherence into the quantum computers. In this scenario, the primary challenge is to find the sufficient condition required by each of the quantum gates for beneficially employing QECCs in order to yield reliability improvements given that the quantum gates utilized by the QECCs also introduce quantum decoherence. In this treatise, we approach this problem by firstly presenting the general framework of protecting quantum gates by the amalgamation of the transversal configuration of quantum gates and quantum stabilizer codes (QSCs), which can be viewed as syndrome-based QECCs. Secondly, we provide examples of the advocated framework by invoking quantum topological error correction codes (QTECCs) for protecting both transversal Hadamard gates and CNOT gates. The simulation and analytical results explicitly show that by utilizing QTECCs, the fidelity of the quantum gates can be beneficially improved, provided that quantum gates satisfying a certain minimum depolarization fidelity threshold (Fth) are available. For instance, for protecting transversal Hadamard gates, the minimum fidelity values required for each of the gates in order to attain fidelity improvements are 99.74%, 99.73%, 99.87%, and 99.86%, when they are protected by colour, rotated-surface, surface, and toric codes, respectively. These specific Fth values are obtained for a very large number of physical qubits (n → ∞), when the quantum coding rate of the QTECCs approaches zero (rQ → 0). Ultimately, the framework advocated can be beneficially exploited for employing QSCs to protect large-scale quantum computers.
quantum error correction codes, quantum stabilizer codes, fault-tolerant, quantum topological codes, quantum gates
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 (2019) Quantum topological error correction codes are capable of improving the performance of Clifford Gates. IEEE Access. (doi:10.1109/ACCESS.2019.2936795).

Record type: Article

Abstract

The employment of quantum error correction codes (QECCs) within quantum computers potentially offers a reliability improvement for both quantum computation and communications tasks. However, incorporating quantum gates for performing error correction potentially introduces more sources of quantum decoherence into the quantum computers. In this scenario, the primary challenge is to find the sufficient condition required by each of the quantum gates for beneficially employing QECCs in order to yield reliability improvements given that the quantum gates utilized by the QECCs also introduce quantum decoherence. In this treatise, we approach this problem by firstly presenting the general framework of protecting quantum gates by the amalgamation of the transversal configuration of quantum gates and quantum stabilizer codes (QSCs), which can be viewed as syndrome-based QECCs. Secondly, we provide examples of the advocated framework by invoking quantum topological error correction codes (QTECCs) for protecting both transversal Hadamard gates and CNOT gates. The simulation and analytical results explicitly show that by utilizing QTECCs, the fidelity of the quantum gates can be beneficially improved, provided that quantum gates satisfying a certain minimum depolarization fidelity threshold (Fth) are available. For instance, for protecting transversal Hadamard gates, the minimum fidelity values required for each of the gates in order to attain fidelity improvements are 99.74%, 99.73%, 99.87%, and 99.86%, when they are protected by colour, rotated-surface, surface, and toric codes, respectively. These specific Fth values are obtained for a very large number of physical qubits (n → ∞), when the quantum coding rate of the QTECCs approaches zero (rQ → 0). Ultimately, the framework advocated can be beneficially exploited for employing QSCs to protect large-scale quantum computers.

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IEEE_QTECC2_final - Accepted Manuscript
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More information

Accepted/In Press date: 17 August 2019
e-pub ahead of print date: 21 August 2019
Keywords: quantum error correction codes, quantum stabilizer codes, fault-tolerant, quantum topological codes, quantum gates

Identifiers

Local EPrints ID: 433641
URI: http://eprints.soton.ac.uk/id/eprint/433641
ISSN: 2169-3536
PURE UUID: fcd7c9d9-4a28-484a-adc8-5af813f3ed55
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: 28 Aug 2019 16:30
Last modified: 14 May 2020 00:53

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