Optimization, sampling and machine learning are topics of broad interest that have inspired significant developments and new approaches in quantum computing. One such approach is quantum annealing (QA). In this Review, we assess the prospects for algorithms within the general framework of QA to achieve a quantum speedup relative to classical state-of-the-art methods. We argue for continued exploration in the QA framework on the basis that improved coherence times and control capabilities will enable the near-term exploration of several heuristic quantum optimization algorithms. These continuous-time Hamiltonian computation algorithms rely on control protocols that are more advanced than those in traditional ground-state QA, while still being considerably simpler than those used in gate-model implementations. The inclusion of coherent diabatic transitions to excited states results in a generalization we refer to collectively as diabatic quantum annealing, which we believe is the most promising route to quantum enhancement within this framework. Other promising variants of traditional QA include reverse annealing, continuous-time quantum walks and analogues of parameterized quantum circuit ansatzes for machine learning. Most of these algorithms have no known efficient classical simulations, making them worthy of further investigation with quantum hardware in the intermediate-scale regime.

优化、采样和机器学习是广泛关注的主题，激发了量子计算的重大发展和新方法。一种这样的方法是量子退火（QA）。在这篇评论中，我们评估了在 QA 的一般框架内实现相对于经典最先进方法的量子加速的算法的前景。我们主张在 QA 框架中继续探索，因为改进的相干时间和控制能力将使近期探索几种启发式量子优化算法成为可能。这些连续时间哈密顿计算算法依赖于比传统基态 QA 中的那些更先进的控制协议，同时仍然比门模型实现中使用的那些简单得多。包含相干非绝热跃迁到激发态导致了我们统称为非绝热量子退火的概括，我们认为这是该框架内量子增强的最有希望的途径。传统 QA 的其他有前途的变体包括反向退火、连续时间量子行走和用于机器学习的参数化量子电路 ansatze 的类似物。这些算法中的大多数都没有已知的有效经典模拟，这使得它们值得在中尺度范围内使用量子硬件进行进一步研究。连续时间量子行走和用于机器学习的参数化量子电路 ansatze 的类似物。这些算法中的大多数都没有已知的有效经典模拟，这使得它们值得在中尺度范围内使用量子硬件进行进一步研究。连续时间量子行走和用于机器学习的参数化量子电路 ansatze 的类似物。这些算法中的大多数都没有已知的有效经典模拟，这使得它们值得在中尺度范围内使用量子硬件进行进一步研究。