Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911071458033664 |
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| author | Sabatino, Foster Brooks, Matthew Tahan, Charles Hoffman, Silas |
| author_facet | Sabatino, Foster Brooks, Matthew Tahan, Charles Hoffman, Silas |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice Sabatino, Foster Brooks, Matthew Tahan, Charles Hoffman, Silas Quantum Physics 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 |
| title | Simulated Non-Abelian Statistics of Majorana Zero Modes from a Kitaev Lattice |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.15405 |