Improved GKP magic states from error-corrected non-Gaussian quantum states
Abstract
Gate teleportation, together with magic state distillation, is a promising route towards fault-tolerant, universal computation. In the context of bosonic quantum computation, Baragiola et al. PRL 123(20).200502 (2019) showed that within the framework of Gottesman--Kitaev--Preskill codes, encoded magic states suitable for distillation can be produced by error correcting Gaussian states, such as the vacuum. Here, we show that applying the same framework to simple non-Gaussian input states can significantly improve the quality of the magic states obtained, reducing the overall resources for the complete distillation procedure. We focus on superpositions of coherent states or Fock states, showing that many can lead to improvements in the generation of high-quality encoded magic states, which in some cases reduces the resources required for magic state distillation by about a factor $3$. We also investigate the primary source of these improvements and find that, unlike what was previously conjectured, the suitability of input states is not fully explained by symmetry arguments. Instead, the best states seem to avoid projection near stabilizer states as a result of the error correction procedure.
Related
- Exponential lower bounds on the fermionic Gaussian rank of magic states and the bosonic coherent state rank of Fock states
- Improved classical optimization of fermionic Hamiltonians beyond Gaussian states
- Pauli Flat Quantum States Mimicking Maximal Magic
- A new class of pure non-Gaussian quantum states
- Quantum Spectral Estimation with Multiple Initial States: Improved Error and Cost Scaling
BibTeX
@misc{david2026improved,
title = {{Improved GKP magic states from error-corrected non-Gaussian quantum states}},
author = {Sharon David and Jack Davis and Ulysse Chabaud and Francesco Arzani},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.07833},
eprint = {2607.07833},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05732574v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improved GKP magic states from error-corrected non-Gaussian quantum states
AU - Sharon David
AU - Jack Davis
AU - Ulysse Chabaud
AU - Francesco Arzani
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2607.07833
UR - https://hal.science/hal-05732574v1
AB - Gate teleportation, together with magic state distillation, is a promising route towards fault-tolerant, universal computation. In the context of bosonic quantum computation, Baragiola et al. PRL 123(20).200502 (2019) showed that within the framework of Gottesman--Kitaev--Preskill codes, encoded magic states suitable for distillation can be produced by error correcting Gaussian states, such as the vacuum. Here, we show that applying the same framework to simple non-Gaussian input states can significantly improve the quality of the magic states obtained, reducing the overall resources for the complete distillation procedure. We focus on superpositions of coherent states or Fock states, showing that many can lead to improvements in the generation of high-quality encoded magic states, which in some cases reduces the resources required for magic state distillation by about a factor $3$. We also investigate the primary source of these improvements and find that, unlike what was previously conjectured, the suitability of input states is not fully explained by symmetry arguments. Instead, the best states seem to avoid projection near stabilizer states as a result of the error correction procedure.
ER -