Digital simulation of zero-temperature spontaneous symmetry breaking in a superconducting lattice processor.

Quantum simulators are ideal platforms to investigate quantum phenomena that are inaccessible through conventional means, such as the limited resources of classical computers to address large quantum systems or due to constraints imposed by fundamental laws of nature. Here, through a digitized adiabatic evolution, we report an experimental simulation of antiferromagnetic (AFM) and ferromagnetic (FM) phase formation induced by spontaneous symmetry breaking (SSB) in a three-generation Cayley tree-like superconducting lattice. We develop a digital quantum annealing algorithm to mimic the system dynamics, and observe the emergence of signatures of SSB-induced phase transition through a connected correlation function. We demonstrate that the signature of a transition from classical AFM to quantum FM-like phase state happens in systems undergoing zero-temperature adiabatic evolution with only nearest-neighbor interacting systems, the shortest range of interaction possible. By harnessing properties of the bipartite Rényi entropy as an entanglement witness, we observe the formation of entangled quantum FM and AFM phases. Our results open perspectives for new advances in condensed matter physics and digitized quantum annealing.