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

TL;DR

This paper introduces a new color code implementation that achieves a logical control-$S$ gate through transversal $T$ and $T^\

Contribution

It presents a novel color code scheme enabling a logical control-$S$ gate using only transversal $T$ and $T^\

Findings

Achieves logical control-$S$ gate with transversal $T$ rotations.

Demonstrates how color code structure facilitates non-Clifford gates.

Enhances fault-tolerant quantum computation methods.

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.