Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice
Abstract
We simulate the non-Abelian exchange of Majorana zero modes (MZMs) on a quantum computer. Rather than utilizing MZMs at the boundaries of quantum Ising chains, which are typically represented as nonlocal operators on a quantum computer, using a Kitaev lattice allows us to exploit a local representation of MZMs. We detail the protocol for braiding two and four MZMs in terms of a spin Hamiltonian, i.e. physical qubit Hamiltonian. Projecting this onto a subspace of states, we extract an effective Hamiltonian which drives a non-Abelian Berry's phase. Using several approximations, we construct a set of gates which mimics this accumulation of non-Abelian phase and process this construction on a quantum computer. For two and four MZMs, we realize braiding fidelities of approximately 85% and 47%, respectively
Keywords
Cite
@article{arxiv.2503.15405,
title = {Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice},
author = {Foster Sabatino and Matthew Brooks and Charles Tahan and Silas Hoffman},
journal= {arXiv preprint arXiv:2503.15405},
year = {2025}
}