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- W4385292904 abstract "Floquet codes are a novel class of quantum error-correcting codes with dynamically generated logical qubits, which arise from a periodic schedule of non-commuting measurements. We engineer new examples of Floquet codes with measurement schedules that $textit{rewind}$ during each period. The rewinding schedules are advantageous in our constructions for both obtaining a desired set of instantaneous stabilizer groups and for constructing boundaries. Our first example is a Floquet code that has instantaneous stabilizer groups that are equivalent -- via finite-depth circuits -- to the 2D color code and exhibits a $mathbb{Z}_3$ automorphism of the logical operators. Our second example is a Floquet code with instantaneous stabilizer codes that have the same topological order as the 3D toric code. This Floquet code exhibits a splitting of the topological order of the 3D toric code under the associated sequence of measurements i.e., an instantaneous stabilizer group of a single copy of 3D toric code in one round transforms into an instantaneous stabilizer group of two copies of 3D toric codes up to nonlocal stabilizers, in the following round. We further construct boundaries for this 3D code and argue that stacking it with two copies of 3D subsystem toric code allows for a transversal implementation of the logical non-Clifford $CCZ$ gate. We also show that the coupled-layer construction of the X-cube Floquet code can be modified by a rewinding schedule such that each of the instantaneous stabilizer codes is finite-depth-equivalent to the X-cube model up to toric codes; the X-cube Floquet code exhibits a splitting of the X-cube model into a copy of the X-cube model and toric codes under the measurement sequence. Our final example is a generalization of the honeycomb code to 3D, which has instantaneous stabilizer codes with the same topological order as the 3D fermionic toric code." @default.
- W4385292904 created "2023-07-27" @default.
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- W4385292904 date "2023-07-25" @default.
- W4385292904 modified "2023-10-16" @default.
- W4385292904 title "Engineering Floquet codes by rewinding" @default.
- W4385292904 doi "https://doi.org/10.48550/arxiv.2307.13668" @default.
- W4385292904 hasPublicationYear "2023" @default.
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