Probing entanglement in a 2D hard-core Bose–Hubbard lattice

Entanglement and its propagation are central to understanding many physical properties of quantum systems1–3. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behaviour4–7. 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 systems8–14. 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. By emulating a 2D hard-core Bose–Hubbard lattice using a controllable 4 × 4 array of superconducting qubits, volume-law entanglement scaling as well as area-law scaling at different locations in the energy spectrum are observed.