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arXiv · 2601.21863

A Bravyi-K\"onig theorem for Floquet codes generated by locally conjugate instantaneous stabiliser groups

Jelena Mackeprang·Jonas Helsen
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Abstract

The Bravyi-K\"onig (BK) theorem is an important no-go theorem for the dynamics of topological stabiliser quantum error correcting codes. It states that any logical operation on a $D$-dimensional topological stabiliser code that can be implemented by a short-depth circuit acts on the codespace as an element of the $D$-th level of the Clifford hierarchy. In recent years, a new type of quantum error correcting codes based on Pauli stabilisers, dubbed Floquet codes, has been introduced. In Floquet codes, syndrome measurements are arranged such that they dynamically generate a codespace at each time step. Here, we show that the BK theorem holds for a definition of Floquet codes based on locally conjugate stabiliser groups. Moreover, we introduce and define a class of generalised unitaries in Floquet codes that need not preserve the codespace at each time step, but that combined with the measurements constitute a valid logical operation. We derive a canonical form of these generalised unitaries and show that the BK theorem holds for them too.

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Jelena Mackeprang, Jonas Helsen. 2026-01-29. A Bravyi-K\"onig theorem for Floquet codes generated by locally conjugate instantaneous stabiliser groups. https://arxiv.org/abs/2601.21863

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