论文标题
系统研究暖量量子近似优化算法对近似溶液的依赖性
Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions
论文作者
论文摘要
量子近似优化算法（QAOA）是在嘈杂的中间尺度量子计算机时代解决组合优化问题的一种有希望的杂种量子古典算法。最近，已经提出了热烈启动的方法来改善QAOA的性能，在该方法中，通过经典算法提前获得了近似的解决方案，并将其纳入初始状态和/或统一ANSATZ。在这项工作中，我们详细研究了近似解决方案的准确性如何影响温暖的QAOA（WS-QAOA）的性能。我们从数值上发现，在典型的最大切割问题中，WS-QAOA倾向于优于QAOA，因为大约解决方案在锤距离方面变得更接近确切的解决方案。我们揭示这可以定量地归因于ANSATZ的初始状态。我们还通过WS-QAOA解决了通过QAOA获得的近似解决方案的最大切割问题，其结果比QAOA更好，尤其是当电路相对较浅时。我们认为，我们的研究可能会加深对WS-QAOA性能的了解，并为近似解决方案的必要质量提供指南。
Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently warm-start approaches have been proposed to improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affect the performance of the warm-start QAOA (WS-QAOA). We numerically find that in typical MAX-CUT problems, WS-QAOA tends to outperform QAOA as approximate solutions become closer to the exact solutions in terms of the Hamming distance. We reveal that this could be quantitatively attributed to the initial state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having a better result than QAOA especially when the circuit is relatively shallow. We believe that our study may deepen understanding of the performance of WS-QAOA and also provide a guide as to the necessary quality of approximate solutions.
