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arXiv · 2411.15035

Color code with a logical control-$S$ gate using transversal $T$ rotations

Benjamin J. Brown
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Abstract

The color code has been invaluable for the development of the theory of fault-tolerant logic gates using transversal rotations. Three-dimensional examples of the color code have shown us how its structure, specifically the intersection of the supports of logical operators, can give rise to non-Clifford $T$ and $CCZ$ gates. Here we present a color code with a logical control-$S$ gate that is accomplished with transversal $T$ and $T^\dagger$ rotations on its physical qubits.

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Benjamin J. Brown. 2024-11-22. Color code with a logical control-$S$ gate using transversal $T$ rotations. https://doi.org/10.1103/lwxd-fdlb

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