量子近似优化算法中最优参数识别的无监督策略
Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm
摘要：
由于组合优化是量子计算的主要应用之一，许多基于参数化量子线路的方法正在被开发。通常，调整一组参数以优化量子线路输出的成本函数。这些算法之一，量子近似优化算法脱颖而出，作为一个有前途的方法来解决组合问题。然而，找到合适的参数是一项艰巨的任务。虽然QAOA具有浓度特性，但它们可以依赖于可能不容易识别的实例特征，但仍然可以提供有用的信息来找到好的参数。在这项工作中，我们研究了无监督的机器学习方法来设置这些参数而无需优化。我们使用角度值和实例编码（使用实例特征或变分图自动编码器的输出）进行聚类，并比较不同的方法。当利用QAOA作为子例程时，这些角度发现策略可以用于减少对量子线路的调用。我们在递归QAOA中展示了它们，直到深度$3$，其中每次迭代使用的QAOA参数的数量仅限于$3$，对于$200$上的MaxCut，实现了$0.94$的中值近似比。我们获得了类似的性能的情况下，我们广泛优化的角度，从而节省了大量的电路调用。
英文摘要：
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.
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