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

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 remain 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 that 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 the development of fault-tolerant topological quantum computation.