Variational quantum algorithms (VQAs) promise efficient use of near-term quantum computers. However, training VQAs often requires an extensive amount of time and suffers from the barren plateau problem where the magnitude of the gradients vanishes with increasing number of qubits. Here, we show how to optimally train VQAs for learning quantum states. Parameterized quantum circuits can form Gaussian kernels, which we use to derive adaptive learning rates for gradient ascent. We introduce the generalized quantum natural gradient that features stability and optimized movement in parameter space. Both methods together outperform other optimization routines in training VQAs. Our methods also excel at numerically optimizing driving protocols for quantum control problems. The gradients of the VQA do not vanish when the fidelity between the initial state and the state to be learned is bounded from below. We identify a VQA for quantum simulation with such a constraint that thus can be trained free of barren plateaus. Finally, we propose the application of Gaussian kernels for quantum machine learning.
翻译:变化量算法(VQAs)可以保证高效使用短期量子计算机。然而,培训VQA往往需要大量的时间,并且受到高原问题的影响,因为高原的梯度随着qubits的数量而消失。在这里,我们展示了如何最佳地训练VQAs学习量子状态。参数量子电路可以形成高萨内核,我们用它来得出梯度上升的适应性学习率。我们引入了通用量子自然梯度,其特征是稳定性和在参数空间的优化移动。两种方法加在一起,均优于培训VQAs的其他优化常规。我们的方法也优于量子控制问题的数字优化驱动程序。当初始状态和所学状态的正轨离下方时,VQA的梯度不会消失。我们为量子模拟确定了一个VQA,其约束性因此可以培养出无贫性高原。最后,我们建议应用高斯内核来学习量子机器。