论文标题
量子近似优化算法的自动深度优化
Automatic Depth Optimization for Quantum Approximate Optimization Algorithm
论文作者
论文摘要
量子近似优化算法（QAOA）是一种混合算法，其控制参数经典优化。除了变分参数外，正确的超参数选择对于改善任何优化模型的性能至关重要。控制深度或变分参数的数量被认为是QAOA最重要的超参数。在本文中，我们使用基于近端梯度下降的自动算法研究对照深度选择。自动算法的性能在7节点和10节点最大切割问题上证明，这表明在迭代过程中可以显着降低控制深度，同时达到足够的优化精度。有了理论收敛的保证，提出的算法可以用作选择适当的控制深度作为替代随机搜索或经验规则的有效工具。此外，减小对照深度将导致电路中量子门的数量显着减少，从而提高了QAOA在嘈杂的中间尺度量子（NISQ）设备上的适用性。
Quantum Approximate Optimization Algorithm (QAOA) is a hybrid algorithm whose control parameters are classically optimized. In addition to the variational parameters, the right choice of hyperparameter is crucial for improving the performance of any optimization model. Control depth, or the number of variational parameters, is considered as the most important hyperparameter for QAOA. In this paper we investigate the control depth selection with an automatic algorithm based on proximal gradient descent. The performances of the automatic algorithm are demonstrated on 7-node and 10-node Max-Cut problems, which show that the control depth can be significantly reduced during the iteration while achieving an sufficient level of optimization accuracy. With theoretical convergence guarantee, the proposed algorithm can be used as an efficient tool for choosing the appropriate control depth as a replacement of random search or empirical rules. Moreover, the reduction of control depth will induce a significant reduction in the number of quantum gates in circuit, which improves the applicability of QAOA on Noisy Intermediate-scale Quantum (NISQ) devices.
