论文标题
在变异算法中进行弹药优化的操作员采样
Operator Sampling for Shot-frugal Optimization in Variational Algorithms
论文作者
论文摘要
量子化学是量子计算机的近期应用。该应用可以通过变异量子古典算法（VQCA）促进，尽管对VQCA的关注是收敛所需的大量测量值，尤其是对于化学精度而言。在这里，我们介绍了一种通过随机采样操作员$ h_i $从整体汉密尔顿$ h = \ sum_i c_i c_i h_i $中随机采样$ h_i $来减少测量数（即镜头）的策略。特别是，我们采用加权采样，当$ C_I $非常均匀时，这很重要，而且化学典型也很重要。我们将该策略与我们小组最近开发的自适应优化器集成在一起，以构建一种改进的优化器Rosalin（随机操作员抽样，用于自适应学习，并单个拍摄数量）。 Rosalin在调整每个部分衍生物的射击噪声时实现随机梯度下降，并根据加权分布在$ H_I $之间随机分配镜头。我们实施此和其他优化器，以找到分子的基态h $ _2 $，lih和beh $ _2 $，而没有量子硬件噪声，而Rosalin在大多数情况下都优于其他优化器。
Quantum chemistry is a near-term application for quantum computers. This application may be facilitated by variational quantum-classical algorithms (VQCAs), although a concern for VQCAs is the large number of measurements needed for convergence, especially for chemical accuracy. Here we introduce a strategy for reducing the number of measurements (i.e., shots) by randomly sampling operators $h_i$ from the overall Hamiltonian $H = \sum_i c_i h_i$. In particular, we employ weighted sampling, which is important when the $c_i$'s are highly non-uniform, as is typical in chemistry. We integrate this strategy with an adaptive optimizer developed recently by our group to construct an improved optimizer called Rosalin (Random Operator Sampling for Adaptive Learning with Individual Number of shots). Rosalin implements stochastic gradient descent while adapting the shot noise for each partial derivative and randomly assigning the shots amongst the $h_i$ according to a weighted distribution. We implement this and other optimizers to find the ground states of molecules H$_2$, LiH, and BeH$_2$, without and with quantum hardware noise, and Rosalin outperforms other optimizers in most cases.
