Performance of planar Floquet codes with Majorana-based qubits

TL;DR

This paper explores the implementation of Floquet codes on Majorana-based qubits, demonstrating improved error thresholds and reduced overheads, making them promising for scalable quantum computing in topological qubit platforms.

Contribution

It introduces two variants of Floquet codes suitable for Majorana zero mode architectures, enabling efficient error correction without auxiliary qubits and with shallow measurement sequences.

Findings

Floquet codes can be implemented on Majorana-based qubits without auxiliary qubits.

The proposed codes significantly increase the error threshold for scalable quantum computing.

They reduce space and time overheads in quantum error correction below threshold.

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 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 measurement-only topological qubits based on Majorana zero modes (MZMs). 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.