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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2601.21863 |
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| _version_ | 1866915761239359488 |
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| author | Mackeprang, Jelena Helsen, Jonas |
| author_facet | Mackeprang, Jelena Helsen, Jonas |
| contents | The Bravyi-König (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21863 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Bravyi-König theorem for Floquet codes generated by locally conjugate instantaneous stabiliser groups Mackeprang, Jelena Helsen, Jonas Quantum Physics The Bravyi-König (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. |
| title | A Bravyi-König theorem for Floquet codes generated by locally conjugate instantaneous stabiliser groups |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.21863 |