Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice

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 the spin Hamiltonian. Projecting this onto a subspace of states that only mix with each other, 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 apply it to both simulated quantum computers and cloud quantum computers.