利用机器学习加速量子近似优化算法
Accelerating Quantum Approximate Optimization Algorithm using Machine Learning
摘要：
我们提出了一种基于机器学习的方法来加速量子近似优化算法（QAOA）的实现，这是一种很有前途的量子经典混合算法，以证明所谓的量子霸权。在QAOA中，参数量子电路和经典优化器在闭环中迭代以解决困难的组合优化问题。QAOA的性能随着量子电路中级数（深度）的增加而提高。然而，两个新的参数被引入到经典优化器的每个增加的阶段中，从而增加了优化循环迭代的次数。我们注意到较低深度和较高深度QAOA实现的参数之间的相关性，并通过开发机器学习模型来预测接近最佳值的门参数来利用它。结果，优化循环以较少的迭代次数收敛。本文以图的最大割问题为原型，采用QAOA进行求解.我们使用100个不同的QAOA实例执行特征提取例程，并开发具有13，860个最佳参数的训练数据集。我们提出了我们的分析，4种口味的回归模型和4种口味的经典优化。最后，我们表明，所提出的方法可以减少优化迭代次数平均44.9%（高达65.7%），从264口味的图进行分析。
英文摘要：
We propose a machine learning based approach to accelerate quantum approximate optimization algorithm (QAOA) implementation which is a promising quantum-classical hybrid algorithm to prove the so-called quantum supremacy. In QAOA, a parametric quantum circuit and a classical optimizer iterates in a closed loop to solve hard combinatorial optimization problems. The performance of QAOA improves with increasing number of stages (depth) in the quantum circuit. However, two new parameters are introduced with each added stage for the classical optimizer increasing the number of optimization loop iterations. We note a correlation among parameters of the lower-depth and the higher-depth QAOA implementations and, exploit it by developing a machine learning model to predict the gate parameters close to the optimal values. As a result, the optimization loop converges in a fewer number of iterations. We choose graph MaxCut problem as a prototype to solve using QAOA. We perform a feature extraction routine using 100 different QAOA instances and develop a training data-set with 13,860 optimal parameters. We present our analysis for 4 flavors of regression models and 4 flavors of classical optimizers. Finally, we show that the proposed approach can curtail the number of optimization iterations by on average 44.9% (up to 65.7%) from an analysis performed with 264 flavors of graphs.
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