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We investigate the minimal Kitaev spin liquid on a single hexagon with threeIsing-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 freeMajorana fermions, and hence, 5 qubits are constructed. These qubits areprotected by particle-hole symmetry even for $K_{z}\neq 0$. Braiding of theseMajorana fermions is possible by temporally controlling a spin-correlationHamiltonian. In addition, the fusion is possible by measuring the spincorrelation. By switching on the Heisenberg interaction together with magneticfield, only one zero-energy state persists, which can be used as aninitialization of qubits. Furthermore, it is shown that $3L+2$ qubits areconstructed on the Kitaev spin liquid model on connected $L$ hexagons. All theprocesses of initialization, operation and readout of qubits are executable interms of spin operators.

Braiding and fusion of Majorana fermions in minimal Kitaev spin liquid on a single hexagon with $5$ qubits