Floquet Majorana XYZ Codes with Tunable Logical Dynamics

Abstract

We construct Floquet codes from the Majorana XYZ subsystem code with local realizations both in qubits and directly in microscopic Majorana modes with lattice size $L\times L$. For a three-step cycle, odd $L$ supports one static logical qubit, whereas even $L$ supports two. For even $L$ with $L=4n+2$, both logical qubits admit time-independent Pauli representatives. For $L=4n$, by contrast, one Pauli of the second logical qubit remains fixed throughout the cycle, while every representative of its conjugate must evolve through the measurement cycle. This distinction follows from a parity-dependent algebraic obstruction and disappears when the cycle is reduced to two steps, which restores a fully static logical pair. Thus, the same encoded logical degree of freedom can be switched between static and partially dynamical forms by the measurement schedule. With one open direction, suitable protocols can be implemented using only local Majorana parity measurements. To our knowledge, this is the first Floquet-code family with both a local qubit representation and a direct microscopic Majorana realization.