论文标题
通过梯度下降学习单位
Learning Unitaries by Gradient Descent
论文作者
论文摘要
我们通过梯度下降在交替的操作员序列的时间参数上学习$ u（d）$中学习单一转换的硬度。我们提供的数值证据表明，尽管损失格局的非凸性性质，但当序列包含$ d^2 $或更多参数时，梯度下降总是会收敛于目标统一。收敛速率表示“计算相变”。在少于$ d^2 $参数的情况下，梯度下降会收敛到亚最佳解决方案，而使用$ d^2 $参数超过$ d^2 $参数，梯度下降将指数收敛于最佳解决方案。
We study the hardness of learning unitary transformations in $U(d)$ via gradient descent on time parameters of alternating operator sequences. We provide numerical evidence that, despite the non-convex nature of the loss landscape, gradient descent always converges to the target unitary when the sequence contains $d^2$ or more parameters. Rates of convergence indicate a "computational phase transition." With less than $d^2$ parameters, gradient descent converges to a sub-optimal solution, whereas with more than $d^2$ parameters, gradient descent converges exponentially to an optimal solution.
