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Code deformation and lattice surgery are gauge fixing. / Vuillot, Christophe; Lao, Lingling; Criger, Ben; García Almudever, Carmina; Bertels, Koen; Terhal, Barbara M.

In: New Journal of Physics, Vol. 21, No. 3, 033028, 2019.

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@article{1d8889345fe14a1a9ced01d062e70729,
title = "Code deformation and lattice surgery are gauge fixing",
abstract = "The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realized in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate setsin subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations.Wedemonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel.",
keywords = "quantum error correction, quantum stabilizer codes, quantum subsystem codes, surface code, quantum code deformation, fault-tolerant quantum computation",
author = "Christophe Vuillot and Lingling Lao and Ben Criger and {Garc{\'i}a Almudever}, Carmina and Koen Bertels and Terhal, {Barbara M.}",
year = "2019",
doi = "10.1088/1367-2630/ab0199",
language = "English",
volume = "21",
journal = "New Journal of Physics",
issn = "1367-2630",
publisher = "IOP Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - Code deformation and lattice surgery are gauge fixing

AU - Vuillot, Christophe

AU - Lao, Lingling

AU - Criger, Ben

AU - García Almudever, Carmina

AU - Bertels, Koen

AU - Terhal, Barbara M.

PY - 2019

Y1 - 2019

N2 - The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realized in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate setsin subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations.Wedemonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel.

AB - The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realized in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate setsin subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations.Wedemonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel.

KW - quantum error correction

KW - quantum stabilizer codes

KW - quantum subsystem codes

KW - surface code

KW - quantum code deformation

KW - fault-tolerant quantum computation

UR - http://www.scopus.com/inward/record.url?scp=85064988372&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/ab0199

DO - 10.1088/1367-2630/ab0199

M3 - Article

VL - 21

JO - New Journal of Physics

T2 - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 3

M1 - 033028

ER -

ID: 53039528