Observation of critical entanglement and quantum phase transitions on a quantum computer*

The simulation of strongly-correlated quantum matter poses a significant challenge due to the curse of dimensionality and complex entanglement structures. This complexity is especially pronounced in the critical regime, where quantum fluctuations occur at all length scales and low-energy states are highly entangled. The (Trotterized) multiscale entanglement renormalization ansatz - a special type of tensor networks with narrow causal cones - makes it possible to study large many-body systems on noisy intermediate-scale quantum (NISQ) devices. Here we report on experimental results using ion-trap systems. In particular, we demonstrate a quantum phase transition with spontaneous symmetry breaking in the thermodynamic limit and we measure bipartite entanglement entropies, which scale according to an area law for gapped systems and according to a log-area law at the critical point. The experimental demonstration of the (Trotterized) multiscale entanglement renormalization ansatz approach with pre-optimized states is a pivotal step towards a full-fledged and practicable digital simulation of many-body systems on quantum computers.