  How to implement quantum oracle with limited resources raises concerns these
days. We design two ancilla-adjustable and efficient algorithms to synthesize
SAT-oracle, the key component in solving SAT problems. The previous work takes
2m-1 ancillary qubits and O(m) elementary gates to synthesize an m clauses
oracle. The first algorithm reduces the number of ancillary qubits to
2\sqrt{m}, with at most an eightfold increase in circuit size. The number of
ancillary qubits can be further reduced to 3 with a quadratic increase in
circuit size. The second algorithm aims to reduce the circuit depth. By
leveraging of the second algorithm, the circuit depth can be reduced to O(log
m) with m ancillary qubits.
