How quantum complexity reveals hidden symmetries at phase transitions

A quantum system's complexity—how hard it is to build its ground state from simple operations—behaves in surprising ways near phase transitions. Using Bloch sphere geometry, researchers found that this complexity diverges logarithmically when crossing topological boundaries in the SSH model, and they proved complexity changes are always bounded by a quantity measuring quantum fragility (fidelity susceptibility). The result reveals an unexpected non-unitary symmetry linking topological and trivial phases, suggesting complexity could serve as a new probe of quantum criticality.