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arXiv · 2305.07023

A Family of Quantum Codes with Exotic Transversal Gates

Eric Kubischta·Ian Teixeira
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Abstract

Recently an algorithm has been constructed that shows the binary icosahedral group $\2I$ together with a $T$-like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code that implements $\ico$ transversally. However, no such code has ever been demonstrated in the literature. We fill this void by constructing a family of distance $d = 3$ codes that all implement $2I$ transversally. A surprising feature of this family is that the codes can be deduced entirely from symmetry considerations that only $2I$ affords.

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Eric Kubischta, Ian Teixeira. 2023-05-11. A Family of Quantum Codes with Exotic Transversal Gates. https://doi.org/10.1103/physrevlett.131.240601

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