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arXiv · 2210.14066

The Smallest Code with Transversal T

Stergios Koutsioumpas·Darren Banfield·Alastair Kay
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Abstract

We prove that the smallest distance 3 Quantum Error Correcting Code with a transversal gate outside the Clifford group is the well-known 15-qubit Reed-Muller code, also known as a tri-orthogonal code. Our result relies on fewer assumptions than previous works. We further extend this result by finding the minimal code that also possesses any other non Clifford transversal single-qubit gate.

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Stergios Koutsioumpas, Darren Banfield, Alastair Kay. 2022-10-25. The Smallest Code with Transversal T. https://arxiv.org/abs/2210.14066

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