English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Floquet codes are a novel class of quantum error-correcting codes withdynamically generated logical qubits, which arise from a periodic schedule ofnon-commuting measurements. We engineer new examples of Floquet codes withmeasurement schedules that $\textit{rewind}$ during each period. The rewindingschedules are advantageous in our constructions for both obtaining a desiredset of instantaneous stabilizer groups and for constructing boundaries. Ourfirst example is a Floquet code that has instantaneous stabilizer groups thatare equivalent -- via finite-depth circuits -- to the 2D color code andexhibits a $\mathbb{Z}_3$ automorphism of the logical operators. Our secondexample is a Floquet code with instantaneous stabilizer codes that have thesame topological order as the 3D toric code. This Floquet code exhibits asplitting of the topological order of the 3D toric code under the associatedsequence of measurements i.e., an instantaneous stabilizer group of a singlecopy of 3D toric code in one round transforms into an instantaneous stabilizergroup of two copies of 3D toric codes up to nonlocal stabilizers, in thefollowing round. We further construct boundaries for this 3D code and arguethat stacking it with two copies of 3D subsystem toric code allows for atransversal implementation of the logical non-Clifford $CCZ$ gate. We also showthat the coupled-layer construction of the X-cube Floquet code can be modifiedby a rewinding schedule such that each of the instantaneous stabilizer codes isfinite-depth-equivalent to the X-cube model up to toric codes; the X-cubeFloquet code exhibits a splitting of the X-cube model into a copy of the X-cubemodel and toric codes under the measurement sequence. Our final example is ageneralization of the honeycomb code to 3D, which has instantaneous stabilizercodes with the same topological order as the 3D fermionic toric code.

Engineering Floquet codes by rewinding