Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover’s algorithm based on the quantum alternating operator ansatz. In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward , the optimal oracle complexity of quantum unstructured search.

将变分量子算法缩放到大问题规模需要对随机参数化量子电路进行有效的优化。对于具有不相关参数的此类电路，成本函数格局中指数级消失的梯度的存在是通过梯度下降方法进行优化的障碍。在这项工作中，我们证明了通过利用包含时空相关的栅极层的电路模块来减小参数空间的维数，可以使人们避免消失的梯度现象。例子来自随机可分电路和基于量子交替算子ansatz的Grover算法的渐近最优变式。在后一种情况下，，量子非结构化搜索的最佳预言复杂度。