Enhancing Encoding Rate through Alternate Floquetification

Quantum error correction codes protect quantum systems against environmental noise, enabling fault-tolerant quantum computing. Among various codes, color codes have received considerable attention for their geometric locality, high error thresholds, and transversal logical operators. A canonical example is the $[[4,2,2]]$ code implemented on a square lattice, which identifies single-qubit errors through four-qubit check measurements. By applying Floquetification to the $[[4,2,2]]$ color code, a $[[12,2,2]]$ Floquet code based on a double hexagon lattice has recently been developed, leading to a decrease in measurement weight from four to two. However, the aforementioned improvement is offset by a decrease in the encoding rate from $1 / 2$ to $1 / 6$, thus requiring an increased number of physical qubits. In this work, we provide a Floquetification process tailored for the $[[4,2,2]]$ code. This leads to a new $[[10,4,2]]$ Floquet code on a double pentagon lattice that not only retains weight two measurements but also enhances the encoding rate compared to the $[[12,2,2]]$ Floquet code.