论文标题
在具有关键性前体的有限量子系统中搜索最佳驾驶
Search for optimal driving in finite quantum systems with precursors of criticality
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
Using the adiabatic perturbation theory of driven dynamics [Phys. Rev. A 78, 052508 (2008)] we design a hierarchy of quantum state preparation protocols that systematically increase the fidelity at very long driving times. We test these and other protocols, including those based on the geometric analysis of the parameter space, in a single-qubit system and in a fully connected multi-qubit system showing in its infinite-size limit several quantum phase transitions. The new protocols excel in the asymptotic driving regime, above a crossover time from the Landau-Zener regime which increases with a decreasing minimal energy gap along the driving path (with the size of the system). In the medium-time domain, the performance of all tested protocols is indecisive.
