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Quantum error correction protects quantum search algorithms against decoherence

Quantum error correction protects quantum search algorithms against decoherence
Quantum error correction protects quantum search algorithms against decoherence
When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10?3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered.
1-13
Botsinis, Panagiotis
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Babar, Zunaira
23ede793-1796-449d-b5aa-93a297e5677a
Alanis, Dimitrios
39e04fad-7530-44f2-b7d3-1b20722a0bd2
Chandra, Daryus
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Nguyen, Hung
086ec465-fbca-42d1-88d2-5f8a25c9fc31
Ng, Soon Xin
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1
Botsinis, Panagiotis
d7927fb0-95ca-4969-9f8c-1c0455524a1f
Babar, Zunaira
23ede793-1796-449d-b5aa-93a297e5677a
Alanis, Dimitrios
39e04fad-7530-44f2-b7d3-1b20722a0bd2
Chandra, Daryus
a2f091a8-9772-4633-8e3b-d3220b10a2ec
Nguyen, Hung
086ec465-fbca-42d1-88d2-5f8a25c9fc31
Ng, Soon Xin
e19a63b0-0f12-4591-ab5f-554820d5f78c
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1

Botsinis, Panagiotis, Babar, Zunaira, Alanis, Dimitrios, Chandra, Daryus, Nguyen, Hung, Ng, Soon Xin and Hanzo, Lajos (2016) Quantum error correction protects quantum search algorithms against decoherence Scientific Reports, 6, (38095), pp. 1-13. (doi:10.1038/srep38095).

Record type: Article

Abstract

When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10?3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered.

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More information

Accepted/In Press date: 4 November 2016
e-pub ahead of print date: 7 December 2016
Published date: 7 December 2016
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 403900
URI: https://eprints.soton.ac.uk/id/eprint/403900
PURE UUID: 7bb565e8-380f-407b-92a7-e615eff66bb8
ORCID for Zunaira Babar: ORCID iD orcid.org/0000-0002-7498-4474
ORCID for Daryus Chandra: ORCID iD orcid.org/0000-0003-2406-7229
ORCID for Soon Xin 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: 16 Dec 2016 09:35
Last modified: 09 Jan 2018 17:40

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Contributors

Author: Panagiotis Botsinis
Author: Zunaira Babar ORCID iD
Author: Dimitrios Alanis
Author: Daryus Chandra ORCID iD
Author: Hung Nguyen
Author: Soon Xin Ng ORCID iD
Author: Lajos Hanzo ORCID iD

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