Time optimal control of two-level quantum systems |
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Institution: | 1. Department of Theoretical Physics and Astrophysics, University of Tabriz, Tabriz 51664, Iran;2. Physics Department, Faculty of Science, Imam Khomeini International University, Qazvin, Iran |
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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 is important in the evolution of a quantum state. In this work, the problem of computing minimum time to produce any unitary transformation is reduced to finding the minimum time to steer the system from an initial to a final state. |
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Keywords: | Time-optimal Mixed state Pontryagin's minimum principle Unitary transformation |
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