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Preparation of quantum state lies at the heart of quantum information processing. The greedy algorithm provides a potential method to effectively prepare quantum states. However, the standard greedy algorithm, in general, cannot take the global maxima and instead becomes stuck on a local maxima. Based on the standard greedy algorithm, in this paper we propose a revised version to design dynamic pulses to realize universal quantum state preparation, i.e., preparing any arbitrary state from another arbitrary one. As applications, we implement this scheme to the universal preparation of single- and two-qubit state in the context of semiconductor quantum dots and superconducting circuits. Evaluation results show that our scheme outperforms the alternative numerical optimizations with higher preparation quality while possesses the comparable high efficiency. Compared with the emerging machine learning, it shows a better accessibility and does not require any training. Moreover, the numerical results show that the pulse sequences generated by our scheme are robust against various errors and noises. Our scheme opens a new avenue of optimization in few-level system and limited action space quantum control problems.

We investigate the influence of environment noise on the control cost and the quantum speed limit time (QSLT) in the process of almost exact state transmission (AEST) through a spin chain under pulse control. The chain is immersed in its surrounding non-Markovian, finite temperature heat baths. We find that AEST can be realized in weak system-bath coupling, low temperature, and strong non-Markovian baths under effective external control. Correspondingly, the control cost and QSLT increases with increasing bath temperature and coupling strength. It is noticeable that non-Markovianity from the baths can be helpful to reduce the control cost and shorten the QSLT. Furthermore, we find that there exists a trade-off between the control cost and transmission fidelity and higher fidelity requires higher cost. In addition, the minimum control cost has been found to obtain certain transmission fidelity., Comment: 9 pages, 4 figures