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Anyon braiding on three quantum computers

Topological order on the Kitaev honeycomb — flux conservation, a localized anyon, and the −1 braiding statistics — measured on real superconducting hardware and reproduced across three independent machines.

What was measured

The Kitaev honeycomb model is the canonical topologically ordered system, and its construction is impossible on a square lattice — a coordination theorem, not a benchmark. Three signatures were prepared and measured on IBM processors: conservation of the plaquette Z₂ flux under Kitaev dynamics (against a symmetry-breaking field control), creation of a single localized anyon with an untouched neighbour, and braiding — dragging one excitation around another flips a logical observable, the −1 mutual exchange statistics that topological quantum computing is built on.

Headline numbers

Braiding: ⟨Z̄⟩ vacuum +0.845 ± 0.030 → braid −0.843 ± 0.035; contractible-loop control +0.845 ± 0.033 (separation ≈ 1.69 vs ~0.03 device scatter)
Flux conservation: ⟨W_p⟩ +0.642 ± 0.016 under Kitaev dynamics vs +0.115 ± 0.030 under the field control (t₀ = +0.918 ± 0.030)
Localized anyon: target plaquette flips to −0.905 ± 0.010 while its neighbour sits untouched at +0.924 ± 0.015
All three results on ibm_marrakesh, ibm_kingston and ibm_fez

Method & discipline

Every circuit was simulator-gated before submission; hardware runs used dynamical decoupling, bootstrap shot-noise errors, and cross-device standard deviations as the honest dominant error bar. The braiding observable is the logical-operator anticommutation of an 8-qubit toric code (the Kitaev model's anisotropic limit), with a contractible loop as the null control.

Honest limits: this is textbook physics demonstrated rigorously, not novel research; the braiding is abelian (toric-code class), not the non-Abelian regime universal topological computation requires; the code distance is small.

Part of a ~30-experiment program run under one hard rule: no result is recorded before its run completes. Methods and logs: github.com/dwatces.