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PreprintCC BY 4.0arXiv

Noise Limits on Fault-Tolerant Fermionic Quantum Computing

  • Owen Allison
  • Luke Coffman
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Abstract

Determining the highest amount of noise that quantum circuits can handle is an interesting and crucial task in the development of fault-tolerant quantum computation. Previous work has constrained this upper limit for local depolarizing noise to ≈ 45 % for circuits constructed using the universal Clifford with T gate set by finding the noise threshold where the gate set loses universality. In this work, we use a similar method with the matchgate with non-Gaussian resource universal gate set to find a limit of p=(8 − 2 √6)/5 or ≈ 62 % for fermionic quantum computing that is independent of circuit depth. To do this, we use Uhlmann-Wootters concurrences for a 4-mode fermionic Choi state representing a resourceful gate combined with local depolarizing noise to determine when the combined channel is convex Gaussian. These bounds are not directly comparable due to differences in noise model making the bound of ≈ 62 % the best known for fermions.

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Cite

BibTeXRIS
BibTeX
@misc{allison2026noise,
  title = {{Noise Limits on Fault-Tolerant Fermionic Quantum Computing}},
  author = {Owen Allison and Luke Coffman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09467},
  eprint = {2609.09467},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09467},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Noise Limits on Fault-Tolerant Fermionic Quantum Computing
AU  - Owen Allison
AU  - Luke Coffman
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09467
UR  - https://arxiv.org/abs/2609.09467
AB  - Determining the highest amount of noise that quantum circuits can handle is an interesting and crucial task in the development of fault-tolerant quantum computation. Previous work has constrained this upper limit for local depolarizing noise to ≈ 45 % for circuits constructed using the universal Clifford with T gate set by finding the noise threshold where the gate set loses universality. In this work, we use a similar method with the matchgate with non-Gaussian resource universal gate set to find a limit of p=(8 − 2 √6)/5 or ≈ 62 % for fermionic quantum computing that is independent of circuit depth. To do this, we use Uhlmann-Wootters concurrences for a 4-mode fermionic Choi state representing a resourceful gate combined with local depolarizing noise to determine when the combined channel is convex Gaussian. These bounds are not directly comparable due to differences in noise model making the bound of ≈ 62 % the best known for fermions.
ER  -