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valbert4 committed Mar 15, 2024
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A surface code with weight-four stabilizer generators defined on a triangular lattice patch with a single twist defect at the center of the patch.
The codes use about \(25\%\) fewer physical per logical qubit for a given distance compared to the surface code.
The also yield a way to implement gate \(S\) without state distillation.
The codes are defined an a plane tiled with equilateral triangles and having a twist defect at its center.
Each triangle can encode a qubit where one side is a string of \(Z\)s as logical \(\bar{Z}\), one side is a string of \(X\)s as logical \(\bar{X}\), and the last side is a mixed-type string as logical \(\bar{Y}\).
The size of the triangular patches and which patch encodes data versus act as ancillas for gates depends on the initialization and measurement procedures.
See Ref. \cite{arXiv:1612.04795} for tables and figures.
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# The codes have simple syndrome extraction circuits and have a high threshold close to that of surface codes.
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# Triangle codes also
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The codes are defined an a plane tiled with equilateral triangles and having a twist defect at its center.
Each triangle can encode a qubit where one side is a string of \(Z\)s as logical \(\bar{Z}\), one side is a string of \(X\)s as logical \(\bar{X}\), and the last side is a mixed-type string as logical \(\bar{Y}\).
The size of the triangular patches and which patch encodes data versus act as ancillas for gates depends on the initialization and measurement procedures.
See Ref. \cite{arXiv:1612.04795} for tables and figures.


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