Demonstrates a logical control-S gate using color code in physical qubits, indicating efficient fault-tolerance through transversal rotations.
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† rotations on its physical qubits.
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Benjamin J. Brown (2025) studied this question.
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