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Paper 1

A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation

Campbell McLauchlan, Benjamin Béri

Year

2022

Journal

arXiv preprint

DOI

arXiv:2211.11777

arXiv

2211.11777

Majorana zero modes (MZMs) are promising candidates for topologically-protected quantum computing hardware, however their large-scale use will likely require quantum error correction. Majorana surface codes (MSCs) have been proposed to achieve this. However, many MSC properties remain unexplored. We present a unified framework for MSC "twist defects" $\unicode{x2013}$ anyon-like objects encoding quantum information. We show that twist defects in MSCs can encode twice the amount of topologically protected information as in qubit-based codes or other MSC encoding schemes. This is due to twists encoding both logical qubits and "logical MZMs," with the latter enhancing the protection microscopic MZMs can offer. We explain how to perform universal computation with logical qubits and logical MZMs while potentially using far fewer resources than in other MSC schemes. All Clifford gates can be implemented on logical qubits by braiding twist defects. We introduce lattice-surgery-based techniques for computing with logical MZMs and logical qubits, achieving the effect of Clifford gates with zero time overhead. We also show that logical MZMs may result in improved spatial overheads for sufficiently low rates of quasi-particle poisoning. Finally, we introduce a novel MSC analogue of transversal gates that achieves encoded Clifford gates in small codes by braiding microscopic MZMs. MSC twist defects thus open new paths towards fault-tolerant quantum computation.

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Paper 2

Decoder Switching: Breaking the Speed-Accuracy Tradeoff in Real-Time Quantum Error Correction

Riki Toshio, Kaito Kishi, Jun Fujisaki, Hirotaka Oshima, Shintaro Sato, Keisuke Fujii

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.25222

arXiv

2510.25222

The realization of fault-tolerant quantum computers hinges on the construction of high-speed, high-accuracy, real-time decoding systems. The persistent challenge lies in the fundamental trade-off between speed and accuracy: efforts to improve the decoder's accuracy often lead to unacceptable increases in decoding time and hardware complexity, while attempts to accelerate decoding result in a significant degradation in logical error rate. To overcome this challenge, we propose a novel framework, decoder switching, which balances these competing demands by combining a faster, soft-output decoder ("weak decoder") with a slower, high-accuracy decoder ("strong decoder"). In usual rounds, the weak decoder processes error syndromes and simultaneously evaluates its reliability via soft information. Only when encountering a decoding window with low reliability do we switch to the strong decoder to achieve more accurate decoding. Numerical simulations suggest that this framework can achieve accuracy comparable to, or even surpassing, that of the strong decoder, while maintaining an average decoding time on par with the weak decoder. We also develop an online decoding scheme tailored to our framework, named double window decoding, and elucidate the criteria for preventing an exponential slowdown of quantum computation. These findings break the long-standing speed-accuracy trade-off, paving the way for scalable real-time decoding devices.

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