Logical gate set tomography — Draconitic Research

Abstract

Quantum error correction (QEC) can strongly suppress noise, but predicting whether a computation succeeds requires understanding not only how much effective noise persists after QEC, but what form that noise takes. To thoroughly characterize this noise, we introduce logical gate set tomography (``logical GST''). Logical GST produces detailed representations of noisy logical operations that can be used to derive higher-level metrics, such as gate fidelity and diamond distance, and to test for non-Markovian and coherent logical errors. We use logical GST to obtain the first full, self-consistent characterization of a universal single-qubit logical gate set, implemented in the seven-qubit Steane code using Quantinuum System Model H1, a 20-qubit trapped-ion quantum processor. In the experimental data from H1, logical GST identified predominantly logical Pauli-stochastic errors, found no evidence of logical non-Markovianity, and detected weak potential signatures of coherent logical error. By contrast, higher-shot datasets generated with Quantinuum's detailed system emulator, identify mechanisms for weak but statistically significant logical non-Markovianity and strong evidence of coherent logical error. Finally, we use logical GST to perform error attribution with the system emulator, revealing how specific physical error sources shape logical error mechanisms.

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Cite

BibTeX RIS

BibTeX

@misc{wysocki2026logical,
  title = {{Logical gate set tomography}},
  author = {Piper C. Wysocki and Juan Gonzalez De Mendoza and Karl Mayer and Natalie C. Brown and Ciaran Ryan-Anderson and Jalan A. Ziyad and Jordan H. Hines and Daniel G. Hothem and Corey I. Ostrove and Timothy J. Proctor and Kevin C. Young and Robin J. Blume-Kohout and Charles H. Baldwin and Kenneth M. Rudinger},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19034},
  eprint = {2610.19034},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19034},
}

RIS

TY  - UNPB
TI  - Logical gate set tomography
AU  - Piper C. Wysocki
AU  - Juan Gonzalez De Mendoza
AU  - Karl Mayer
AU  - Natalie C. Brown
AU  - Ciaran Ryan-Anderson
AU  - Jalan A. Ziyad
AU  - Jordan H. Hines
AU  - Daniel G. Hothem
AU  - Corey I. Ostrove
AU  - Timothy J. Proctor
AU  - Kevin C. Young
AU  - Robin J. Blume-Kohout
AU  - Charles H. Baldwin
AU  - Kenneth M. Rudinger
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19034
UR  - https://arxiv.org/abs/2610.19034
AB  - Quantum error correction (QEC) can strongly suppress noise, but predicting whether a computation succeeds requires understanding not only how much effective noise persists after QEC, but what form that noise takes. To thoroughly characterize this noise, we introduce logical gate set tomography (``logical GST''). Logical GST produces detailed representations of noisy logical operations that can be used to derive higher-level metrics, such as gate fidelity and diamond distance, and to test for non-Markovian and coherent logical errors. We use logical GST to obtain the first full, self-consistent characterization of a universal single-qubit logical gate set, implemented in the seven-qubit Steane code using Quantinuum System Model H1, a 20-qubit trapped-ion quantum processor. In the experimental data from H1, logical GST identified predominantly logical Pauli-stochastic errors, found no evidence of logical non-Markovianity, and detected weak potential signatures of coherent logical error. By contrast, higher-shot datasets generated with Quantinuum's detailed system emulator, identify mechanisms for weak but statistically significant logical non-Markovianity and strong evidence of coherent logical error. Finally, we use logical GST to perform error attribution with the system emulator, revealing how specific physical error sources shape logical error mechanisms.
ER  -

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