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Entanglement and its propagation are central to understanding a multitude of physical properties of quantum systems. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behavior, yet a universal understanding remains challenging due 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. Here, we use a controllable $4 \times 4$ array of superconducting qubits to emulate a two-dimensional hard-core Bose-Hubbard 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 center of the spectrum and a crossover to the onset of area-law scaling near its edges.

Quantum information processing relies on precise control of non-classical states in the presence of many uncontrolled environmental degrees of freedom -- requiring careful orchestration of how the relevant degrees of freedom interact with that environment. These interactions are often viewed as detrimental, as they dissipate energy and decohere quantum states. Nonetheless, when controlled, dissipation is an essential tool for manipulating quantum information: Dissipation engineering enables quantum measurement, quantum state preparation, and quantum state stabilization. The progress of quantum device technology, marked by improvements of characteristic coherence times and extensible architectures for quantum control, has coincided with the development of such dissipation engineering tools which interface quantum and classical degrees of freedom. This Review presents dissipation as a fundamental aspect of the measurement and control of quantum devices and highlights the role of dissipation engineering for quantum error correction and quantum simulation that enables quantum information processing on a practical scale., Review article: 28 pages, 4 figures, 2 boxes. Comments welcome