Surface code quantum computing by lattice surgery

In recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them...

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Main Authors: Dominic Horsman, Austin G Fowler, Simon Devitt, Rodney Van Meter
Format: Article
Language:English
Published: IOP Publishing 2012-01-01
Series:New Journal of Physics
Online Access:https://doi.org/10.1088/1367-2630/14/12/123011
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author Dominic Horsman
Austin G Fowler
Simon Devitt
Rodney Van Meter
author_facet Dominic Horsman
Austin G Fowler
Simon Devitt
Rodney Van Meter
author_sort Dominic Horsman
collection DOAJ
description In recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect-based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance-3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.
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spelling doaj.art-55c33ac990f744119ac8ad58092f4d032023-08-08T11:09:17ZengIOP PublishingNew Journal of Physics1367-26302012-01-01141212301110.1088/1367-2630/14/12/123011Surface code quantum computing by lattice surgeryDominic Horsman0Austin G Fowler1Simon Devitt2Rodney Van Meter3Keio University Shonan Fujisawa Campus , Fujisawa, Kanagawa 252-0882, JapanCQC2T, School of Physics, University of Melbourne , VIC 3010, AustraliaNational Institute for Informatics , 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, JapanFaculty of Environment and Information Studies, Keio University , Fujisawa, Kanagawa 252-0882, JapanIn recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect-based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance-3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.https://doi.org/10.1088/1367-2630/14/12/123011
spellingShingle Dominic Horsman
Austin G Fowler
Simon Devitt
Rodney Van Meter
Surface code quantum computing by lattice surgery
New Journal of Physics
title Surface code quantum computing by lattice surgery
title_full Surface code quantum computing by lattice surgery
title_fullStr Surface code quantum computing by lattice surgery
title_full_unstemmed Surface code quantum computing by lattice surgery
title_short Surface code quantum computing by lattice surgery
title_sort surface code quantum computing by lattice surgery
url https://doi.org/10.1088/1367-2630/14/12/123011
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AT simondevitt surfacecodequantumcomputingbylatticesurgery
AT rodneyvanmeter surfacecodequantumcomputingbylatticesurgery