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

• URL: http://arxiv.org/abs/2411.15035v1
• Date: Fri, 22 Nov 2024 16:08:33 GMT
• Title: Color code with a logical control-$S$ gate using transversal $T$ rotations
• Abstract summary: 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 $CCZ$. Here we present a color code with a logical control-$S$ gate that is accomplished with $Tdagger$ rotations on its physical qubits.
• Score: 2.1756081703276
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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