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

TL;DR

This paper introduces a unified framework for Majorana surface code twist defects, enabling more efficient quantum information encoding and computation, with potential resource savings and enhanced fault tolerance.

Contribution

It presents a novel approach to MSC twist defects that encode both logical qubits and MZMs, facilitating universal quantum computation with fewer resources.

Findings

Twist defects encode twice the information of previous schemes.

Universal Clifford gates are implementable via braiding twist defects.

Logical MZMs can improve spatial overheads at low quasi-particle poisoning rates.

Abstract

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.