A Family of Quantum Codes with Exotic Transversal Gates

Understand

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.