Entanglement and its propagation are central to understanding many physical properties of quantum systems^1,2,3. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behaviour^4,5,6,7. However, a universal understanding remains challenging owing to the non-integrability and computational intractability of most large-scale quantum systems. Quantum hardware platforms provide a means to study the formation and scaling of entanglement in interacting many-body systems^{8,9,10,11,12,13,14}. Here we use a controllable 4 × 4 array of superconducting qubits to emulate a 2D hard-core Bose–Hubbard (HCBH) lattice. We generate superposition states by simultaneously driving all lattice sites and extract correlation lengths and entanglement entropy across its many-body energy spectrum. We observe volume-law entanglement scaling for states at the centre of the spectrum and a crossover to the onset of area-law scaling near its edges.

纠缠及其传播对于理解量子系统的许多物理特性至关重要^1,2,3。值得注意的是，在封闭量子多体系统中，纠缠被认为会产生涌现的热力学行为^4,5,6,7。然而，由于大多数大规模量子系统的不可积性和计算​​困难性，普遍理解仍然具有挑战性。量子硬件平台提供了一种研究交互多体系统中纠缠的形成和扩展的方法^{8,9,10,11,12,13,14}。在这里，我们使用可控的 4 × 4 超导量子位阵列来模拟 2D 硬核 Bose-Hubbard (HCBH) 晶格。我们通过同时驱动所有晶格位点来生成叠加态，并提取其多体能谱上的相关长度和纠缠熵。我们观察到光谱中心状态的体积定律纠缠标度以及其边缘附近的面积定律标度的交叉。