Although we are currently in the era of noisy intermediate scale quantum devices, several studies are being conducted with the aim of bringing machine learning to the quantum domain. Currently, quantum variational circuits are one of the main strategies used to build such models. However, despite its widespread use, we still do not know what are the minimum resources needed to create a quantum machine learning model. In this article, we analyze how the expressiveness of the parametrization affects the cost function. We analytically show that the more expressive the parametrization is, the more the cost function will tend to concentrate around a value that depends both on the chosen observable and on the number of qubits used. For this, we initially obtain a relationship between the expressiveness of the parametrization and the mean value of the cost function. Afterwards, we relate the expressivity of the parametrization with the variance of the cost function. Finally, we show some numerical simulation results that confirm our theoretical-analytical predictions.
翻译:虽然我们目前正处于超声中间量子装置时代,但目前正在进行若干研究,目的是将机器学习带入量子域。目前,量子变换电路是用来建立这种模型的主要战略之一。然而,尽管使用范围很广,我们仍然不知道创建量子机器学习模型所需的最低资源是什么。在本篇文章中,我们分析了超音速化的表达性如何影响成本功能。我们分析表明,对称化的表达性越强,成本功能就越倾向于集中于一个既取决于所选择的可观测值,又取决于所使用的qubits数量的价值。为此,我们最初获得了对准化的表达性与成本函数的平均值之间的关系。随后,我们把对称化的表达性与成本函数的差异联系起来。最后,我们展示了一些数字模拟结果,证实了我们的理论分析预测。