article

Subsystem surface codes with three-qubit check operators

Authors:

Guillaume Duclos-Cianci,

Martin SucharaAuthors Info & Claims

Quantum Information & Computation, Volume 13, Issue 11-12

Pages 963 - 985

Published: 01 November 2013 Publication History

Abstract

We propose a simplified version of the Kitaev's surface code in which error correction requires only three-qubit parity measurements for Pauli operators XXX and ZZZ. The new code belongs to the class of subsystem stabilizer codes. It inherits many favorable properties of the standard surface code such as encoding of multiple logical qubits on a planar lattice with punctured holes, efficient decoding by either minimum-weight matching or renormalization group methods, and high error threshold. The new subsystem surface code (SSC) gives rise to an exactly solvable Hamiltonian with 3-qubit interactions, topologically ordered ground state, and a constant energy gap. We construct a local unitary transformation mapping the SSC Hamiltonian to the one of the ordinary surface code thus showing that the two Hamiltonians belong to the same topological class. We describe error correction protocols for the SSC and determine its error thresholds under several natural error models. In particular, we show that the SSC has error threshold approximately 0:6% for the standard circuit-based error model studied in the literature. We also consider a model in which three-qubit parity operators can be measured directly. We show that the SSC has error threshold approximately 0:97% in this setting.

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Cited By

Gayatri VSarvepalli P(2018)Decoding Topological Subsystem Color Codes and Generalized Subsystem Surface Codes2018 IEEE Information Theory Workshop (ITW)10.1109/ITW.2018.8613474(1-5)Online publication date: 25-Nov-2018
https://dl.acm.org/doi/10.1109/ITW.2018.8613474
Bacon DFlammia SHarrow AShi J(2017)Sparse Quantum Codes From Quantum CircuitsIEEE Transactions on Information Theory10.1109/TIT.2017.266319963:4(2464-2479)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1109/TIT.2017.2663199
Fu XRiesebos LLao LAlmudever CSebastiano FVersluis RCharbon EBertels KPalermo GFeo JTumeo AFranke H(2016)A heterogeneous quantum computer architectureProceedings of the ACM International Conference on Computing Frontiers10.1145/2903150.2906827(323-330)Online publication date: 16-May-2016
https://dl.acm.org/doi/10.1145/2903150.2906827
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cover image Quantum Information & Computation

Quantum Information & Computation Volume 13, Issue 11-12

November 2013

180 pages

ISSN:1533-7146

Issue’s Table of Contents

Publisher

Rinton Press, Incorporated

Paramus, NJ

Publication History

Published: 01 November 2013

Revised: 02 April 2013

Received: 09 November 2012

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Cited By

Gayatri VSarvepalli P(2018)Decoding Topological Subsystem Color Codes and Generalized Subsystem Surface Codes2018 IEEE Information Theory Workshop (ITW)10.1109/ITW.2018.8613474(1-5)Online publication date: 25-Nov-2018
https://dl.acm.org/doi/10.1109/ITW.2018.8613474
Bacon DFlammia SHarrow AShi J(2017)Sparse Quantum Codes From Quantum CircuitsIEEE Transactions on Information Theory10.1109/TIT.2017.266319963:4(2464-2479)Online publication date: 1-Apr-2017
https://dl.acm.org/doi/10.1109/TIT.2017.2663199
Fu XRiesebos LLao LAlmudever CSebastiano FVersluis RCharbon EBertels KPalermo GFeo JTumeo AFranke H(2016)A heterogeneous quantum computer architectureProceedings of the ACM International Conference on Computing Frontiers10.1145/2903150.2906827(323-330)Online publication date: 16-May-2016
https://dl.acm.org/doi/10.1145/2903150.2906827
Bacon DFlammia SHarrow AShi JServedio RRubinfeld R(2015)Sparse Quantum Codes from Quantum CircuitsProceedings of the forty-seventh annual ACM symposium on Theory of Computing10.1145/2746539.2746608(327-334)Online publication date: 14-Jun-2015
https://dl.acm.org/doi/10.1145/2746539.2746608

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