论文标题
用于量子电路和控制的量子几何机器学习
Quantum Geometric Machine Learning for Quantum Circuits and Control
论文作者
论文摘要
机器学习技术在量子控制中解决问题以及解决优化问题的已建立几何方法的应用自然导致了对如何使用机器学习方法来增强量子信息处理中问题的几何方法的探索。在这项工作中，我们审查并扩展了深度学习的应用到量子几何控制问题。具体而言，我们通过应用新颖的深度学习算法在量子电路合成问题的背景下表现出时间优势控制的增强，以便沿着与低维度多数量系统相关的谎言组流形近似地理学（以及最小的电路），例如SU（SU（2），SU（2），SU（4），SU（4）和SU（8）。我们展示了Greybox模型的卓越性能，该模型将传统的黑框算法与先前的量子力学知识结合在一起，作为学习基础量子电路分布的方法。我们的结果表明，几何控制技术如何用于（a）验证几何合成的量子电路在多大程度上沿着测量，因此时间优化，路线和（b）合成这些电路。我们的结果对量子控制和量子信息理论的研究人员感兴趣，以期将机器学习和几何技术结合起来，以解决时间优势控制问题。
The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches to solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with prior domain knowledge of quantum mechanics, as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
