Blind quantum computation with fewer quantum and delegated cost of client

Blind quantum computation (for measuring the client Alice) protocol changes the role of the client from state preparation to measurement. In order to further save the quantum cost and delegated cost of Alice, two protocols are proposed to complete a certain single-qubit gate with fewer measurements and qubits while remaining loss tolerant in this paper. Finally, the protocols are feasibility from three aspects: blindness, correctness and universality.