论文标题
通过随机参数化量子电路的相关性大梯度
Large gradients via correlation in random parameterized quantum circuits
论文作者
论文摘要
变异量子算法对大问题大小的缩放需要有效地优化随机参数化量子电路。对于具有不相关参数的这样的电路，成本功能景观中呈指数消失的梯度的存在是通过梯度下降方法优化的障碍。在这项工作中，我们证明，通过利用包含空间或时间相关的栅极层的电路模块来降低参数空间的维度，可以使一个人可以避免消失的梯度现象。示例是根据基于量子交替运算符ANSATZ（QAOA）的Grover算法的随机分离电路和Grover算法的最佳最佳变异版本绘制的。在后一种情况下，我们对成本函数变化的界限意味着消失的梯度和有效的训练性之间的过渡，因为层的数量增加到了$ \ MATHCAL {O}（2^{n/2}）$，这是量子非结构性搜索的最佳甲骨文复杂性。
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 (QAOA). 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 $\mathcal{O}(2^{n/2})$, the optimal oracle complexity of quantum unstructured search.
