For quantum state preparation, a non-unitary operator is typically designed to decay undesirable states contained in an initial state using ancilla qubits and a probabilistic action. Probabilistic algorithms do not accelerate the computational process compared to classical ones. In this study, quantum amplitude amplification (QAA) and multi-step probabilistic algorithms are combined to achieve quadratic acceleration. This method outperforms quantum phase estimation in terms of infidelity. The quadratic acceleration was confirmed by the probabilistic imaginary-time evolution (PITE) method.
@article{arxiv.2308.03605,
title = {Quadratic acceleration of multi-step probabilistic algorithms for state preparation},
author = {Hirofumi Nishi and Taichi Kosugi and Yusuke Nishiya and Yu-ichiro Matsushita},
journal= {arXiv preprint arXiv:2308.03605},
year = {2023}
}