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The realization of quantum gates in topological quantum computation stillconfronts significant challenges in both fundamental and practical aspects.Here, we propose a deterministic and fully topologically protectedmeasurement-based scheme to realize the issue of implementing Clifford quantumgates on the Majorana qubits. Our scheme is based on rigorous proof that thesingle-qubit gate can be performed by leveraging the neighboring Majorana qubitbut not disturbing its carried quantum information, eliminating the need forancillary Majorana zero modes (MZMs) in topological quantum computing.Benefiting from the ancilla-free construction, we show the minimum measurementsequences with four steps to achieve two-qubit Clifford gates by constructingtheir geometric visualization. To avoid the uncertainty of the measurement-onlystrategy, we propose manipulating the MZMs in their parameter space to correctthe undesired measurement outcomes while maintaining complete topologicalprotection, as demonstrated in a concrete Majorana platform. Our schemeidentifies the minimal operations of measurement-based topological anddeterministic Clifford gates and offers an ancilla-free design of topologicalquantum computation.

Deterministic topological quantum gates for Majorana qubits without ancillary modes