Ancilla-free scheme of deterministic topological quantum gates for Majorana qubits

The realization of quantum gates in topological quantum computation still confronts significant challenges in both fundamental and practical aspects. Here, we propose an ancilla-free, deterministic, and topologically protected measurement-based scheme to realize the implementation of Clifford quantum gates on the Majorana qubits. Our scheme is based on a rigorous proof that the single-qubit gate can be performed by leveraging the neighboring Majorana qubit but not disturbing its carried quantum information, enabling an ancilla-free scheme for the topological quantum computing with Majorana qubits. Benefiting from the ancilla-free construction, we show the minimum measurement sequences with four steps to achieve two-qubit Clifford gates by constructing their geometric visualization. The uncertainty of the current strategy can be avoided by manipulating the Majorana modes in their parameter space, as shown in a concrete Majorana platform, correcting the undesired measurement outcomes while maintaining topological protection. Our scheme identifies the minimal operations of measurement-based topological and deterministic Clifford gates and offers an ancilla-free design of topological quantum computation.