Scheme for braiding Majorana zero modes in vortices using an STT-matrix

TL;DR

This paper introduces a programmable STT-matrix scheme for precise control and braiding of Majorana zero modes in vortices of topological superconductors, demonstrated through comprehensive numerical simulations.

Contribution

It proposes a novel, scalable method using an STT-matrix for deterministic vortex manipulation and MZM braiding in topological superconductors, supported by detailed simulation frameworks.

Findings

STT-matrix enables high-fidelity vortex control

Successful simulation of MZM braiding dynamics

Optimized parameters improve braiding fidelity

Abstract

Majorana zero modes (MZMs), promising for topological quantum computation, are naturally hosted in vortices of two-dimensional topological superconductors (TSCs). However, precise control and braiding of these vortex-bound MZMs remains a significant challenge. This work proposes and numerically demonstrates a novel braiding scheme utilizing a programmable matrix of spin transfer torque (STT) devices (STT-matrix) integrated with a TSC layer. By selectively activating individual STT elements, their localized stray fields enable deterministic manipulation, including driving, braiding, and fusion, of superconducting vortices and their associated MZMs. We establish a comprehensive simulation framework combining finite element analysis for STT-induced vortex formation, time-dependent Ginzburg-Landau equations for vortex dynamics and time-dependent Bogoliubov-de Gennes equations for MZM evolution. Simulations confirm the STT-matrix's capability for high-fidelity vortex manipulation and demonstrate MZM braiding dynamics. We quantify the impact of vortex acceleration and finite MZM coupling on braiding fidelity, showing it can be optimized by adjusting STT spacing and vortex separation. Furthermore, we demonstrate controlled MZM fusion and measure the resultant energy splitting. This STT-matrix-based approach offers a highly versatile, scalable, and potentially practical platform for operating MZMs within TSC vortices, advancing towards fault-tolerant topological quantum computation.