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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

R2 v1 2026-06-28T04:28:19.916Z