Performance of Planar Floquet Codes with Majorana-Based Qubits

Abstract

Quantum error correction is crucial for any quantum computing platform to achieve truly scalable quantum computation. The surface code and its variants have been considered the most promising quantum error correction scheme due to their high threshold, low overhead, and relatively simple structure that can naturally be implemented in many existing qubit architectures, such as superconducting qubits. The recent development of Floquet codes by Hastings and Haah offers another promising approach. By going beyond the usual paradigm of stabilizer codes, Floquet codes achieve similar performance while being constructed entirely from two-qubit measurements. This makes them particularly suitable for platforms where two-qubit measurements can be implemented directly, such as the measurement-only topological qubits based on Majorana zero modes (MZMs) proposed by Karzig et al. Here, we explain how two variants of Floquet codes can be implemented on MZM-based architectures without any auxiliary qubits for syndrome measurement and with shallow syndrome-extraction sequences. We then numerically demonstrate their favorable performance. In particular, we show that they improve the threshold for scalable quantum computation in MZM-based systems by an order of magnitude and significantly reduce space and time overheads below threshold.