The Smallest Code with Transversal T
Quantum Physics
2022-10-26 v1
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.
Cite
@article{arxiv.2210.14066,
title = {The Smallest Code with Transversal T},
author = {Stergios Koutsioumpas and Darren Banfield and Alastair Kay},
journal= {arXiv preprint arXiv:2210.14066},
year = {2022}
}
Comments
8 pages, no figures