Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

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相关量子物质的量子信息和算法

以电子和原子的强量子力学性质为特征的量子材料发现，揭示了由相关性产生的奇异特性。量子信息学对量子材料的希望与新的计算量子算法发现新的量子材料的潜力相叠加，这激发了本综述的灵感。我们预计，未来几年将被发现和开发的量子材料将改变包括通信，存储和计算在内的量子信息处理领域。同时，努力开发用于量子模拟的新量子算法方法和用于多体量子系统的高级计算方法，使功能性量子材料及其部署取得了重大进展。量子计算的出现带来了消除指数复杂性的新可能性，该复杂性阻碍了高性能经典计算机上相关量子系统的仿真。在这里，我们回顾了新的算法和计算方法，以预测和理解相关量子物质的行为。所涵盖主题的强烈跨学科性质要求使用通用语言来整合来自这些领域的想法。我们旨在提供这种通用语言，同时将电子结构理论，量子电动力学，算法设计和开放量子系统的各个领域编织在一起。我们的综述适时地向本领域介绍了具有非指数复杂性的算法，用于相关量子物质在大挑战问题中的应用。展望未来，