Abstract Abstract—The Quantum Approximate Optimization Al-gorithm (QAOA) is a hybrid quantum-classical algorithmto solve binary-variable optimization problems. Due to theshort circuit depth and its expected robustness to systematicerrors it is a promising candidates likely to run on near-term quantum devices. We simulate the performance ofQAOA applied to the Max-Cut problem and compareit with some of the best classical alternatives. Whencomparing solvers, their performance is characterized bythe computational time taken to achieve a given qualityof solution. Since QAOA is based on sampling, we utilizeperformance metrics based on the probability of observinga sample above a certain quality. In addition, we show thatthe QAOA performance varies significantly with the graphtype. In particular for 3-regular random graphs, QAOAperformance shows improvement by up to 2 orders of mag-nitude compared to previous estimates, strongly reducingthe performance gap with classical alternatives. This waspossible by reducing the number of function evaluationsper iteration and optimizing the variational parameterson small graph instances and transferring to large viatraining.Because QAOA’s performance guarantees areonly known for limited applications and contexts, we utilizea framework for the search for quantum advantage whichincorporates a large number of problem instances and allthree classical solver modalities: exact, approximate, andheuristic.

中文翻译：

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基于单个样本的近似比评估 QAOA

摘要 摘要：量子近似优化算法（QAOA）是一种解决二元变量优化问题的混合量子经典算法。由于短路深度及其对系统错误的预期鲁棒性，它是可能在近期量子设备上运行的有希望的候选者。我们模拟了应用于 Max-Cut 问题的 QAOA 的性能，并将其与一些最好的经典替代方案进行比较。在比较求解器时，它们的性能以达到给定质量的解所花费的计算时间为特征。由于 QAOA 是基于抽样的，因此我们利用基于观察到高于特定质量的样本的概率的性能指标。此外，我们表明 QAOA 性能随图形类型而显着变化。特别是对于 3 正则随机图，与之前的估计相比，QAOA 性能显示出高达 2 个数量级的改进，大大缩小了与经典替代方案的性能差距。这可以通过减少每次迭代的函数评估次数和优化小图实例的变分参数并通过训练转移到大图来实现。因为 QAOA 的性能保证仅适用于有限的应用和上下文，我们利用一个框架来搜索量子优势，该框架包含大量问题实例和所有三种经典求解器模式：精确、近似和启发式。与之前的估计相比，QAOA 性能显示出高达 2 个数量级的改进，大大缩小了与经典替代方案的性能差距。这可以通过减少每次迭代的函数评估次数和优化小图实例的变分参数并通过训练转移到大图来实现。因为 QAOA 的性能保证仅适用于有限的应用和上下文，我们利用一个框架来搜索量子优势，该框架包含大量问题实例和所有三种经典求解器模式：精确、近似和启发式。与之前的估计相比，QAOA 性能显示出高达 2 个数量级的改进，大大缩小了与经典替代方案的性能差距。这可以通过减少每次迭代的函数评估次数和优化小图实例的变分参数并通过训练转移到大图来实现。因为 QAOA 的性能保证仅适用于有限的应用和上下文，我们利用一个框架来搜索量子优势，该框架包含大量问题实例和所有三种经典求解器模式：精确、近似和启发式。