Probing Entanglement Scaling Across a Phase Transition on a Quantum Computer

Entanglement is central to understanding quantum phase transitions, where quantum fluctuations drive complex behaviors that classical methods cannot fully capture. While quantum simulators have enhanced our understanding of near-critical systems, probing entanglement has remained costly due to limitations in measurement protocols, difficulties in preparing states near critical points and limited available system size. We address these challenges by using the multi-scale entanglement renormalization ansatz (MERA) on a digital fully-connected trapped-ion quantum computer. Our method accurately represents infinite systems and long-range correlations with few qubits, enabling efficient extraction of observables and entanglement properties. We efficiently simulate quantum ground states, observe quantum phase transitions with spontaneous symmetry breaking and reveal the evolution of detailed entanglement structure across the critical point. For the first time, we demonstrate log-law scaling of subsystem entanglement entropy at criticality on a digital quantum computer. Our demonstration establishes MERA's potential for advancing quantum many-body studies and marks a significant step towards a practical digital quantum simulation of many-body systems.