Quantum materials exhibit a wide array of exotic phenomena and practically useful properties. A better understanding of these materials can provide deeper insights into fundamental physics in the quantum realm as well as advance information processing technology and sustainability. The emergence of digital quantum computers (DQCs), which can efficiently perform quantum simulations that are otherwise intractable on classical computers, provides a promising path forward for testing and analyzing the remarkable, and often counter-intuitive, behavior of quantum materials. Equipped with these new tools, scientists from diverse domains are racing towards achieving physical quantum advantage (i.e. using a quantum computer to learn new physics with a computation that cannot feasibly be run on any classical computer). The aim of this review, therefore, is to provide a summary of progress made towards this goal that is accessible to scientists across the physical sciences. We will first review the available technology and algorithms, and detail the myriad ways to represent materials on quantum computers. Next, we will showcase the simulations that have been successfully performed on currently available DQCs, emphasizing the variety of properties, both static and dynamic, that can be studied with this nascent technology. Finally, we work through three examples of how to perform various materials simulation problems on DQCs, with full code included in the supplementary material (https://stacks.iop.org/QST/6/043002/mmedia). It is our hope that this review can serve as an organized overview of progress in the field for domain experts and an accessible introduction to scientists in related fields interested in beginning to perform their own simulations of quantum materials on DQCs.

量子材料表现出各种各样的奇异现象和实用的特性。更好地理解这些材料可以更深入地了解量子领域的基础物理学以及先进的信息处理技术和可持续性。数字量子计算机 (DQC) 的出现可以有效地执行在经典计算机上难以处理的量子模拟，为测试和分析量子材料的显着且通常违反直觉的行为提供了一条有前途的途径。配备了这些新工具，来自不同领域的科学家正在竞相实现物理量子优势（即使用量子计算机学习新物理，其计算无法在任何经典计算机上运行）。因此，本次审查的目的是 是对实现这一目标的进展进行总结，供物理科学领域的科学家使用。我们将首先回顾可用的技术和算法，并详细介绍在量子计算机上表示材料的无数方法。接下来，我们将展示在当前可用的 DQC 上成功执行的模拟，强调可以使用这种新兴技术研究的各种静态和动态特性。最后，我们通过三个示例来说明如何在 DQC 上执行各种材料模拟问题，完整代码包含在补充材料 (https://stacks.iop.org/QST/6/043002/mmedia) 中。