The X-Cube Floquet Code

Inspired by the coupled-layer construction of the X-Cube model, we introduce the X-Cube Floquet code. The X-Cube Floquet code is defined on a three-dimensional lattice, built from intersecting 4.8.8 lattice layers in the $xy$, $yz$, and $xz$ directions. It consists of a period sequence of two-qubit measurements including both intra-layer and inter-layer measurements. Within a single Floquet cycle, the codespace switches between that of the X-Cube model and layers of entangled, two-dimensional toric codes, as a consequence of the coupled-layers construction. The encoded logical qubits' dynamics are analyzed, and we argue that the new code has a non-zero error threshold. We provide a new Hamiltonian realization of the X-Cube model and, more generally, explore the phase diagram related to the sequence of measurements that define the X-Cube Floquet code.