We develop a hybrid quantum-classical algorithm to solve an optimal population transfer problem for a molecule subject to a laser pulse. The evolution of the molecular wave function under the laser pulse is simulated on a quantum computer, while the optimal pulse is iteratively shaped via a machine learning (evolutionary) algorithm. A method to encode on the quantum computer the $n$-electrons wave function is discussed, the circuits accomplishing its quantum simulation are derived and the scalability in terms of number of operations is discussed. Performance on noisy intermediate-scale quantum devices (IBM Q X2) is provided to assess the current technological gap. Furthermore the hybrid algorithm is tested on a quantum emulator to compare performance of the evolutionary algorithm with standard ones. Our results show that such algorithms are able to outperform the optimization with a downhill simplex method and provide performance comparable to more advanced (but quantum-computer unfriendly) algorithms such as Rabitz's or gradient-based optimization.

中文翻译：

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量子计算机的量子最优控制：一种具有机器学习优化功能的混合算法

我们开发了一种混合量子经典算法，以解决受激光脉冲影响的分子的最佳种群转移问题。在量子计算机上模拟了激光脉冲下分子波函数的演化，而最佳脉冲则通过机器学习（进化）算法进行迭代整形。一种在量子计算机上编码的方法$ñ$讨论了电子波函数，推导了完成其量子模拟的电路，并讨论了运算数量的可扩展性。提供嘈杂的中级量子设备（IBM Q X2）的性能以评估当前的技术差距。此外，在量子仿真器上测试了混合算法，以比较进化算法与标准算法的性能。我们的结果表明，此类算法能够以下坡单纯形法胜过优化，并提供与Rabitz或基于梯度的优化等更高级（但量子计算机不友好）算法相媲美的性能。