Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code

Brown, Benjamin J. and Laubscher, Katharina and Kesselring, Markus S. and Wootton, James R.. (2017) Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code. Physical Review X, 7. 021029.

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Official URL: https://edoc.unibas.ch/64118/

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The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes, and even by braiding engineered Majorana modes using twist defects. Here, we present a unified framework to describe these methods, which can be used to better compare different schemes and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyze ways in which different schemes can be combined and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code, without loss of distance, using code deformations, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.
Faculties and Departments:05 Faculty of Science > Departement Physik > Physik > Theoretische Physik Mesoscopics (Loss)
UniBasel Contributors:Wootton, James R. and Laubscher, Katharina
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Physical Society
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:23 May 2018 07:40
Deposited On:23 May 2018 07:40

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