论文标题
关于贫瘠的高原和成本函数位置的变化量子算法
On barren plateaus and cost function locality in variational quantum algorithms
论文作者
论文摘要
变分量子算法依赖于基于梯度的优化来迭代地最大程度地减少通过测量量子处理器输出评估的成本函数。贫瘠的高原是在足够表达的参数化量子电路中成倍消失的梯度的现象。已经确定，贫瘠的高原制度的开始取决于成本功能，尽管仅针对某些类别的成本功能证明了特定行为。在这里，我们得出了梯度方差的下限，该方差主要取决于成本函数的Pauli分解中每个项的电路因果锥的宽度。我们的结果进一步阐明了贫瘠的高原发生的条件。
Variational quantum algorithms rely on gradient based optimization to iteratively minimize a cost function evaluated by measuring output(s) of a quantum processor. A barren plateau is the phenomenon of exponentially vanishing gradients in sufficiently expressive parametrized quantum circuits. It has been established that the onset of a barren plateau regime depends on the cost function, although the particular behavior has been demonstrated only for certain classes of cost functions. Here we derive a lower bound on the variance of the gradient, which depends mainly on the width of the circuit causal cone of each term in the Pauli decomposition of the cost function. Our result further clarifies the conditions under which barren plateaus can occur.
