论文标题
无监督的策略,用于识别量子近似优化算法中的最佳参数
Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm
论文作者
论文摘要
由于组合优化是主要的量子计算应用程序之一,因此正在开发许多基于参数化量子电路的方法。通常,正在调整一组参数,以优化量子电路输出中的成本函数。这些算法之一,量子近似优化算法是解决组合问题的有前途的方法。但是,找到适当的参数是一项艰巨的任务。尽管QAOA具有浓度属性,但它们可以取决于可能不容易识别的实例特征,但仍可提供有用的信息来找到良好的参数。在这项工作中,我们研究了无监督的机器学习方法,用于设置这些参数而无需优化。我们使用角度值执行聚类,但也可以进行实例编码(使用实例功能或变异图自动编码器的输出),并比较不同的方法。当利用QAOA作为子例程时,这些角度调查策略可用于减少对量子电路的调用。我们将它们在递归-QAOA中展示至深度$ 3 $,其中迭代使用的QAOA参数数量限制为$ 3 $,MAXCUT的中位数近似值为$ 0.94 $,超过$ 200 $ 200 $ERDőS-ERDőS-rényi图。我们获得与广泛优化角度的情况相似的表演,从而节省了许多电路调用。
As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of the quantum circuit output. One of these algorithms, the Quantum Approximate Optimization Algorithm stands out as a promising approach to tackling combinatorial problems. However, finding the appropriate parameters is a difficult task. Although QAOA exhibits concentration properties, they can depend on instances characteristics that may not be easy to identify, but may nonetheless offer useful information to find good parameters. In this work, we study unsupervised Machine Learning approaches for setting these parameters without optimization. We perform clustering with the angle values but also instances encodings (using instance features or the output of a variational graph autoencoder), and compare different approaches. These angle-finding strategies can be used to reduce calls to quantum circuits when leveraging QAOA as a subroutine. We showcase them within Recursive-QAOA up to depth $3$ where the number of QAOA parameters used per iteration is limited to $3$, achieving a median approximation ratio of $0.94$ for MaxCut over $200$ Erdős-Rényi graphs. We obtain similar performances to the case where we extensively optimize the angles, hence saving numerous circuit calls.