High-Fidelity Quantum Simulation of Braiding Statistics and Non-Abelian Holonomic Gates Using Stückelberg Interferometry with Demkov–Kunike Pulses

Geometric phases and holonomies offer a robust route to quantum control and simulation. We introduce a high-fidelity quantum simulation framework based on the analytically solvable Demkov-Kunike (DK) model, which extends the standard Landau-Zener paradigm by providing richer control over evolution paths. We demonstrate how tailored DK pulse sequences can simulate the braiding statistics of Abelian anyons through Stückelberg interferometry, with a protocol for exact dynamical phase cancellation. Generalizing to a three-level Λ-system, we engineer a non-Abelian Wilczek-Zee connection and construct a universal set of holonomic quantum gates. A detailed analysis of the evolution operator and leakage probability for the three-level DK model is provided, identifying optimal adiabaticity regimes for high fidelity. We propose an experimental implementation using trapped ions, including a rigorous derivation of the effective DK Hamiltonian in a decoherence-free subspace. Numerical simulations confirm the expected interference signatures, gate non-commutativity, and enhanced robustness of geometric gates under decoherence. This work establishes DK pulses as a versatile tool for simulating topological-like phenomena and engineering geometric quantum gates in controllable quantum systems.