Optimized Protocols for Realizing Majorana Zero Modes in Optical Lattices

Kitaev’s topological superconductor is one of the paradigmatic models of topological phases, yet its experimental realization remains challenging. Building on recent advances demonstrating the universal simulability of analog systems [1], we present a realization of the Kitaev chain in one-dimensional optical lattices with ultracold atoms and demonstrate the braiding statistics of its quasiparticles, known as Majorana Zero Modes (MZMs). To achieve this, we develop a constrained direct quantum optimal control algorithm, which optimizes control pulses on the physical platform using feedback data from Matrix Product State (MPS) dynamical simulations. Within this framework, we realize robust braiding of MZMs by adiabatically evolving the Hamiltonian. Our results establish a theoretical framework for the realization of topologically protected phases of matter in fermionic neutral-atom quantum simulators.

[1] Hu, Hong-Ye, et al. "Universal Dynamics with Globally Controlled Analog Quantum Simulators." arXiv preprint arXiv:2508.19075 (2025).