Daniel Olliver

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Preprint · Zenodo · 16 June 2026

Circuit-level equivariance is code-dependent: obstruction in the surface code, exactness in the honeycomb Floquet code, and consequences for neural decoders

Daniel Olliver · Independent researcher, Auckland, New Zealand

Abstract

Whether exact (twisted) equivariance survives at circuit level is a property of the code: obstructed for surface-code extraction circuits (999 spacetime maps, 1,728 schedules, with a mirror-axis impossibility lemma), exact for the honeycomb Floquet code, whose C3 rotation mixes the logical qubits (GL(2,F2)). The exactly-tied decoder flips the honeycomb task from unlearnable to learned (≥256× sample-efficiency separation; noise-rate sweep included). Solver released as the demsym package (pip install demsym); every number traces to a logged run via a 116-check audit. Code: github.com/dwatces/equivariant-quantum-ml

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DOI10.5281/zenodo.20715320Read the preprint

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APA

Olliver, D. (2026). Circuit-level equivariance is code-dependent: obstruction in the surface code, exactness in the honeycomb Floquet code, and consequences for neural decoders [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.20715320

BibTeX

@misc{olliver_2026_20715320,
  author    = {Olliver, Daniel},
  title     = {Circuit-level equivariance is code-dependent: obstruction in the surface code, exactness in the honeycomb Floquet code, and consequences for neural decoders},
  month     = jun,
  year      = 2026,
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.20715320},
  url       = {https://doi.org/10.5281/zenodo.20715320},
}

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