Symmetry-protected gates of Majorana qubits in a high-$T_c$ superconductor platform

TL;DR

This paper proposes a novel platform combining high-$T_c$ superconductors and quantum spin-Hall insulators to realize and manipulate Majorana zero modes for topological quantum computing, demonstrating full braiding and phase gates.

Contribution

It introduces a new heterostructure platform enabling symmetry-protected braiding and quantum gates of Majorana modes, advancing toward universal topological quantum computation.

Findings

Achieves full braiding and phase gates of Majorana modes

Demonstrates robustness and symmetry protection of operations

Utilizes experimentally feasible materials and setups

Abstract

We propose a platform for braiding Majorana non-Abelian anyons based on a heterostructure between a $d$-wave high-$T_c$ superconductor and a quantum spin-Hall insulator. It has been recently shown that such a setup for a quantum spin-Hall insulator leads to a pair of Majorana zero modes at each corner of the sample, and thus can be regarded as a higher-order topological superconductor. We show that upon applying a Zeeman field in the region, these Majorana modes split in space and can be manipulated for braiding processes by tuning the field and pairing phase. We show that such a setup can achieve full braiding, exchanging, and arbitrary phase gates (including the $\pi/8$ magic gates) of the Majorana zero modes, all of which are robust and protected by symmetries. As many of the ingredients of our proposed platform have been realized in recent experiments, our results provide a new route toward universal topological quantum computation.