标题： 量子优势的广阔世界 显示英文标题

标题： The vast world of quantum advantage

摘要： 寻找量子优势的历程是量子技术的核心。 虽然量子设备承诺了非凡的能力，从指数级的计算加速到前所未有的测量精度，但区分真正的优势与虚假的幻象仍然是一个艰巨的挑战。 在这个努力中，量子理论家就像先知一样试图预知未来，然而远见卓识与无根据幻想之间的界限却极为微妙。 在此观点下，我们审视我们的数学工具，以在计算、学习、传感和通信的广阔量子优势世界中进行导航。 我们探讨五个关键属性：可预测性、典型性、鲁棒性、可验证性和实用性，这些属性定义了一个理想的量子优势，并设想在量子技术普及的未来可能出现的新量子优势。 我们证明，一些量子优势仅使用经典资源是无法预测的，这表明其图景远比我们目前所能预见的要丰富得多。 尽管数学严谨性仍然是我们不可或缺的指南，但量子技术的最终力量可能来自于我们尚无法想象的优势。 显示英文摘要

摘要： The quest to identify quantum advantages lies at the heart of quantum technology. While quantum devices promise extraordinary capabilities, from exponential computational speedups to unprecedented measurement precision, distinguishing genuine advantages from mere illusions remains a formidable challenge. In this endeavor, quantum theorists are like prophets attempting to foretell the future, yet the boundary between visionary insight and unfounded fantasy is perilously thin. In this perspective, we examine our mathematical tools for navigating the vast world of quantum advantages across computation, learning, sensing, and communication. We explore five keystone properties: predictability, typicality, robustness, verifiability, and usefulness that define an ideal quantum advantage, and envision what new quantum advantages could arise in a future with ubiquitous quantum technology. We prove that some quantum advantages are inherently unpredictable using classical resources alone, suggesting a landscape far richer than what we can currently foresee. While mathematical rigor remains our indispensable guide, the ultimate power of quantum technologies may emerge from advantages we cannot yet conceive.