A Family of Quantum Codes with Exotic Transversal Gates

• URL: http://arxiv.org/abs/2305.07023v4
• Date: Thu, 26 Oct 2023 19:08:24 GMT
• Title: A Family of Quantum Codes with Exotic Transversal Gates
• Authors: Eric Kubischta and Ian Teixeira
• Abstract summary: An algorithm shows the binary icosahedral group $2I$ together with a $T$-like gate forms the most efficient single-qubit gate set. To carry out the algorithm fault tolerantly requires a code that implements $ico$ly. We fill this void by constructing a family of distanced = 3$ codes that all implement $2I$ly.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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