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Quantum Error Correction Fault Tolerance

The Smallest Code with Transversal T

arXiv
Authors: Stergios Koutsioumpas, Darren Banfield, Alastair Kay

Year

2022

Paper ID

58046

Status

Preprint

Abstract Read

~2 min

Abstract Words

59

Citations

N/A

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.

Why This Paper Matters

  • This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
  • It adds a 2022 reference point for readers tracking recent quantum research.
  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2210.14066 [2] arXiv https://arxiv.org/abs/2210.14066 [3] Publisher https://arxiv.org/abs/2210.14066

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