Daniel Olliver

1. [1]

   [1]Olliver, D. · 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

   Whether exact (twisted) equivariance survives at circuit level depends on the code. It is obstructed for surface-code extraction circuits and exact for the honeycomb Floquet code, whose C3 rotation mixes the logical qubits. Tying that symmetry into the decoder flips the honeycomb task from unlearnable to learned.

   • 999 spacetime maps
   • 1,728 schedules
   • ≥256× sample-efficiency separation
   • 116-check audit

   DOI10.5281/zenodo.20715320Read the preprint

   • Abstract, PDF and citation
   • Code on GitHub
   • pip install demsym
   • Play against the trained net
   • Discussed on LinkedIn

   Cite

   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

2. [2]

   [2]Olliver, D. · Preprint · Zenodo · 27 July 2026

   The lattice’s teeth: primitive reciprocal axes govern which Fourier components neural cellular automata can grow

   Neural cellular automata are trained on square grids by default; this paper treats the lattice as an experimental variable. An apparent advantage of hexagonal over square grids turned out to be a normalisation artefact in cross-lattice comparisons, and the paper documents and retracts it. The second result is a primitive-axis rule: a trained NCA grows only the Fourier components whose wavevectors lie on a primitive reciprocal-lattice axis of its grid. A pre-registered out-of-sample test partially refuted that rule as stated. What survives is the gate itself: growth stays direction-selective and no geometry-forbidden component grows, so the constraint is real and soft, not sharp.

   • primitive-axis recovery 0.55–0.88 (restart means)
   • all others ≤ 0.11 (restart means)
   • 96 out-of-sample trainings
   • decider R² −0.39 (needed ≥ 0.8)

   DOI10.5281/zenodo.21614035Read the preprint

   • Abstract, PDF and citation
   • Different study · Lenia-class patterns, not NCAThe lattice’s teeth: when the substrate owns the pattern

   Cite

   Olliver, D. (2026). The lattice’s teeth: primitive reciprocal axes govern which Fourier components neural cellular automata can grow [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.21614035

More on LinkedIn: another research post

Note 01Quantum hardware · 3 devices

Anyon braiding on three quantum computers

Topological order on the Kitaev honeycomb, measured on superconducting hardware with a matched-depth control beside every claim. Fluxes stayed conserved (+0.64) while a control destroyed them (+0.12). A single anyon flipped its plaquette to −0.905 ± 0.010 while the neighbour sat at +0.924 ± 0.015.

ResultThe −1 braiding statistics (Fig. 1), reproduced on ibm_marrakesh, ibm_kingston and ibm_fez with error bars. Not new physics: measured by one person, on three independent machines.

• Read the note
• Braid anyons yourself

Note 02Quantum error correction · related: paper [1]

Symmetry-tied neural decoders for quantum error correction

A decoder reads a quantum machine’s error alarms and has to name the fault. Labelled data from real devices is scarce, so the right inductive bias matters more than raw scale.

ResultOn the surface code under phenomenological noise, at identical parameter count, the symmetry-tied decoder wins at every training size, is ~4× more sample-efficient, and comes within 0.0005 of the matching-decoder baseline (0.9943 vs 0.9948). On the honeycomb Floquet code, the identical plain twin stays at the majority-class baseline through 64,000 training samples while the symmetry-tied one reaches 0.744 at that size, and the tied net trained on 1,000 samples beats the plain one trained on 256,000.

• Read the note
• Paper [1]
• Play the trained decoder

• 
  Panel (a) of three: the field term gaps the phase into Chern number ±1. Full figure in the note.

  Note 03Exact computation

  The non-Abelian phase, computed end to end

  Computed exactly: Chern number ±1, one chiral Majorana edge mode and Majorana zero modes bound to vortices. Braided numerically, exchanges that share a vortex refuse to commute (Ivanov-pattern match 0.975); disjoint exchanges commute to 0.005.

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• 

  Note 04Quantum machine learning

  Equivariant readouts for quantum machine learning

  A readout with exact C3 commutation ([P,H] error = 0) gives large sample-efficiency gains when data is scarce.

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• 

  Note 05Materials ML

  Topological-materials ML: match the symmetry, exactly

  The matched C3 prior wins at every scarce size; the larger C6 group, broken by the sublattice mass term, underperforms it everywhere.

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• 

  Note 06Forecasting · real city data

  The equivariance law, held on real city data

  The hex-equivariant model beats the directional one in 10 of 10 city-seasons; the gain holds while few stations have history and shrinks once most do.

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• 
  Left panel only; full figure in the note.

  Note 07Pattern formation · Lenia-class

  The lattice’s teeth: when the substrate owns the pattern

  At normal scales the patterns don’t care which lattice they grow on. Below ~3 lattice constants the substrate owns them: 11,946 measured patterns, replicated on independent hardware.

  Read the note

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