Fast black-box quantum state preparation based on linear combination of unitaries

Black-box quantum state preparation is a fundamental primitive in algorithms. Starting from Grover, series of techniques have been devised to reduce the complexity. In this work, we propose perform black-box using technique linear combination unitaries (LCU). We provide two algorithms based on different structure LCU. Our improve upon existed best results by reducing required additional qubits and Toffoli gates 2log(n) n, respectively, bit precision n. demonstrate IBM Quantum Experience cloud services. The further reduced complexity present brings closer reality.