Braiding and fusion of Majorana fermions in minimal Kitaev spin liquid on a single hexagon with $5$ qubits
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914627015671808 |
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| author | Ezawa, Motohiko |
| author_facet | Ezawa, Motohiko |
| contents | We investigate the minimal Kitaev spin liquid on a single hexagon with three Ising-type exchange interactions proportional to $K_{x}$, $K_{y}$ and $K_{z}$. In the limit $K_{z}=0$, we find 32-fold zero-energy states, leading to 10 free Majorana fermions, and hence, 5 qubits are constructed. These qubits are protected by particle-hole symmetry even for $K_{z}\neq 0$. Braiding of these Majorana fermions is possible by temporally controlling a spin-correlation Hamiltonian. In addition, the fusion is possible by measuring the spin correlation. By switching on the Heisenberg interaction together with magnetic field, only one zero-energy state persists, which can be used as an initialization of qubits. Furthermore, it is shown that $3L+2$ qubits are constructed on the Kitaev spin liquid model on connected $L$ hexagons. All the processes of initialization, operation and readout of qubits are executable in terms of spin operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01051 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Braiding and fusion of Majorana fermions in minimal Kitaev spin liquid on a single hexagon with $5$ qubits Ezawa, Motohiko Strongly Correlated Electrons Mesoscale and Nanoscale Physics Superconductivity Quantum Physics We investigate the minimal Kitaev spin liquid on a single hexagon with three Ising-type exchange interactions proportional to $K_{x}$, $K_{y}$ and $K_{z}$. In the limit $K_{z}=0$, we find 32-fold zero-energy states, leading to 10 free Majorana fermions, and hence, 5 qubits are constructed. These qubits are protected by particle-hole symmetry even for $K_{z}\neq 0$. Braiding of these Majorana fermions is possible by temporally controlling a spin-correlation Hamiltonian. In addition, the fusion is possible by measuring the spin correlation. By switching on the Heisenberg interaction together with magnetic field, only one zero-energy state persists, which can be used as an initialization of qubits. Furthermore, it is shown that $3L+2$ qubits are constructed on the Kitaev spin liquid model on connected $L$ hexagons. All the processes of initialization, operation and readout of qubits are executable in terms of spin operators. |
| title | Braiding and fusion of Majorana fermions in minimal Kitaev spin liquid on a single hexagon with $5$ qubits |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Superconductivity Quantum Physics |
| url | https://arxiv.org/abs/2401.01051 |