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arXiv 2008.06076quant-ph
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实现多体量子动力学的快速高保真最优控制

Achieving fast high-fidelity optimal control of many-body quantum dynamics

Jesper Hasseriis Mohr Jensen, Frederik Skovbo Møller, Jens Jakob Sørensen, Jacob Friis Sherson

摘要:

我们证明了最近的精确梯度最优控制方法的效率,通过将其应用到一个具有挑战性的多体问题,跨越超流的莫特绝缘体相变的玻色-哈伯德模型。系统的大小需要一个矩阵的产品状态表示,这与算法的要求无缝集成。我们观察到在0.99-0.9999的范围内的结晶度与相关的最小过程持续时间估计显示指数结晶度持续时间权衡跨越几个数量级。相应的最佳解决方案的特点是在一个主要的线性扫过的临界点,然后由bang-bang-like结构。这是完全不同的平滑和单调的解决方案,确定早期的无梯度优化,阻碍了定位在政权的高复杂性协议在低过程持续时间。总体而言,比较表明显着的方法改进,也为多体系统在理想的开环设置。认识到理想化的开环控制可能会恶化在实际实验中,我们讨论了使用这种方法与闭环控制相结合的优点-特别是,高保真度的物理见解与前者提取可用于制定实用的,低维的搜索空间,后者。

英文摘要:

We demonstrate the efficiency of a recent exact-gradient optimal control methodology by applying it to a challenging many-body problem, crossing the superfluid to Mott-insulator phase transition in the Bose-Hubbard model. The system size necessitates a matrix product state representation and this seamlessly integrates with the requirements of the algorithm. We observe fidelities in the range 0.99-0.9999 with associated minimal process duration estimates displaying an exponential fidelity-duration trade-off across several orders of magnitude. The corresponding optimal solutions are characterized in terms of a predominantly linear sweep across the critical point followed by bang-bang-like structure. This is quite different from the smooth and monotonic solutions identified by earlier gradient-free optimizations which are hampered in locating the higher complexity protocols in the regime of high-fidelities at low process durations. Overall, the comparison suggests significant methodological improvements also for many-body systems in the ideal open-loop setting. Acknowledging that idealized open-loop control may deteriorate in actual experiments, we discuss the merits of using such an approach in combination with closed-loop control -- in particular, high-fidelity physical insights extracted with the former can be used to formulate practical, low-dimensional search spaces for the latter.

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