Bhargavi Jonnadula

Floquet codes have recently emerged as a new family of error-correcting codes, and have drawn significant interest across both theoretical and practical quantum computing. A central open question has been how to implement logical operations on these codes. In this work, we show how two techniques from static quantum error-correcting codes can also be implemented on Floquet codes. First, we present a way of implementing fold-transversal operations on Floquet codes in order to yield gates like the logical Hadamard. And second, we present a way of implementing logical CNOT gates on Floquet codes via Dehn twists. We discuss the requirements for these techniques and perform numerical benchmarking of logical operations on the CSS Floquet code. We establish a logical-gate threshold of 0.25-0.35% and verify subthreshold exponential error suppression. Our results show that these logical operations are robust, featuring a performance that is close to the baseline set by a quantum memory benchmark. Finally, if time permits, we shall discuss logical gates on other Floquet color code lattices and how to perform logical gates via embedded codes.