Logical gates on Floquet codes via folds and twists

• URL: http://arxiv.org/abs/2512.17999v1
• Date: Fri, 19 Dec 2025 19:00:06 GMT
• Title: Logical gates on Floquet codes via folds and twists
• Authors: Alexandra E. Moylett, Bhargavi Jonnadula,
• Abstract summary: We show how two techniques from static quantum error-correcting codes can be implemented on Floquet codes.<n>First, we present a way of implementing fold-transversal operations on Floquet codes in order to yield logical Hadamard and S gates.<n>Second, we present a way of implementing logical CNOT gates on Floquet codes via Dehn twists.
• Score: 45.88028371034407
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 logical Hadamard and S gates. 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 show that they are applicable to a wide family of Floquet codes defined on colour code lattices. Through numerical benchmarking of the logical operations on the CCS Floquet code, we establish a logical-gate threshold of 0.25-0.35% and verify sub-threshold 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, we explain in detail how to implement logical gates on Floquet codes by operating on the embedded codes.

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