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

• URL: http://arxiv.org/abs/2503.15405v1
• Date: Wed, 19 Mar 2025 16:45:19 GMT
• Title: Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice
• Authors: Foster Sabatino, Matthew Brooks, Charles Tahan, Silas Hoffman,
• Abstract summary: We simulate the non-Abelian exchange of Majorana zero modes (MZMs) on a quantum computer.<n>We detail the protocol for braiding two and four MZMs in terms of a spin Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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

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