Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although several theoretically appealing quantum algorithms have been proposed for this task, they typically require a black-box query model of the sparse Hamiltonian, rendering them impractical for near-term implementation on quantum devices. In this paper, we propose a technique named Hamiltonian embedding. This technique simulates a desired sparse Hamiltonian by embedding it into the evolution of a larger and more structured quantum system, allowing for more efficient simulation through hardware-efficient operations. We conduct a systematic study of this new technique and demonstrate significant savings in computational resources for implementing prominent quantum applications. As a result, we can now experimentally realize quantum walks on complicated graphs (e.g., binary trees, glued-tree graphs), quantum spatial search, and the simulation of real-space Schr\"odinger equations on current trapped-ion and neutral-atom platforms. Given the fundamental role of Hamiltonian evolution in the design of quantum algorithms, our technique markedly expands the horizon of implementable quantum advantages in the NISQ era.

翻译：许多有前景的量子应用依赖于对指数级稀疏哈密顿量的高效量子模拟，这一任务被称为稀疏哈密顿量模拟，在量子计算中具有根本重要性。尽管已有几种理论上吸引人的量子算法被提出用于此任务，但它们通常要求对稀疏哈密顿量采用黑盒查询模型，导致其难以在近期量子设备上实现。本文提出一种名为“哈密顿量嵌入”的技术。该技术通过将目标稀疏哈密顿量嵌入到更大且结构更规整的量子系统演化中，使得硬件高效操作能够实现更高效的模拟。我们对该新技术进行了系统研究，并证明了其在实现重要量子应用时可显著节省计算资源。基于此，我们如今能在当前离子阱和中性原子平台上实验实现复杂图（如二叉树、胶合树图）上的量子行走、量子空间搜索以及实空间薛定谔方程的模拟。鉴于哈密顿量演化在量子算法设计中的基础性作用，我们的技术显著拓展了NISQ时代可实现的量子优势的应用前景。