Quantum search for unknown number of target items by hybridizing fixed-point method with trail-and-error method<xref rid="cpb_28_12_120301fn1" ref-type="fn">*</xref><fn id="cpb_28_12_120301fn1"><label>*</label><p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11504430 and 61502526) and the National Basic Research Program of China (Grant No. 2013CB338002).</p></fn>

Quantum search for unknown number of target items by hybridizing fixed-point method with trail-and-error method**

Project supported by the National Natural Science Foundation of China (Grant Nos. 11504430 and 61502526) and the National Basic Research Program of China (Grant No. 2013CB338002).

Li Tan^{1, 2}, Zhang Shuo^{1, 2}, Fu Xiang-Qun^{1, 2}, Wang Xiang^{1, 2}, Wang Yang^{1, 2}, Lin Jie^{1, 2}, Bao Wan-Su^{1, 2, †}

Circuit for the quantum Oracle Sfφ with arbitrary phases, defined by Eq. (5), where Sfπ denotes the quantum Oracle with phase-π (defined by Eq. (33)), Q_f is the quantization of the classical Oracle, Qf† corresponds to the un-computation step to restore the ancillary qubits, and U1φ is the quantum gate adding a phase of e^iφ to |1⟩ state.