A Family of Quantum Codes with Exotic Transversal Gates
Eric Kubischta, Ian Teixeira

TL;DR
This paper constructs a family of quantum error-correcting codes that implement the binary icosahedral group transversally, enabling fault-tolerant quantum gates based on a recently identified universal gate set.
Contribution
It introduces a new family of distance 3 quantum codes that implement the binary icosahedral group transversally, derived solely from symmetry considerations.
Findings
Codes have distance d=3.
Codes implement the binary icosahedral group transversally.
Construction relies on symmetry properties of the group.
Abstract
Recently an algorithm has been constructed that shows the binary icosahedral group together with a -like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code that implements transversally. However, no such code has ever been demonstrated in the literature. We fill this void by constructing a family of distance codes that all implement transversally. A surprising feature of this family is that the codes can be deduced entirely from symmetry considerations that only affords.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum-Dot Cellular Automata
