Abstract The objective of time-optimal control that helps to minimize relaxation losses, is the evolution of a quantum state from a given initial mixed state to a final target mixed state in minimum time. In this paper, we study a time-optimal control problem of the dynamic of a pure two-level system with unbounded control using Pontryagin's minimum principle and obtain the minimal time for some initial and final states. The results will apply to basically all qubit systems that one can consider such as NMR spectroscopy, trapped ions, superconducting qubits, etc. We also show that these results hold for pure states, and only the direction n ˆ is important in the evolution of a quantum state. In this work, the problem of computing minimum time to produce any unitary transformation U f ∈ S U ( 2 ) is reduced to finding the minimum time to steer the system from an initial to a final state.

中文翻译：

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两能级量子系统的时间最优控制

摘要 有助于最小化弛豫损失的时间最优控制的目标是在最短的时间内从给定的初始混合态到最终目标混合态的量子态演化。在本文中，我们使用庞特里亚金极小原理研究了具有无界控制的纯两级系统动力学的时间最优控制问题，并获得了一些初始和最终状态的最小时间。结果将适用于人们可以考虑的基本上所有量子位系统，例如 NMR 光谱、俘获离子、超导量子位等。我们还表明，这些结果适用于纯态，并且只有方向 n ˆ 在 a 的演化中很重要量子态。在这项工作中，