Logical gates on Floquet codes via folds and twists

TL;DR

This paper demonstrates how to implement logical gates such as Hadamard, S, and CNOT on Floquet codes using techniques like folds and twists, with numerical evidence of their robustness and error thresholds.

Contribution

It introduces methods to perform logical gates on Floquet codes using fold-transversal operations and Dehn twists, expanding their computational capabilities.

Findings

Logical gates achieve a threshold of 0.25-0.35%

Sub-threshold exponential error suppression verified

Performance close to quantum memory benchmark

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.