Strong-to-Weak Spontaneous Symmetry Breaking Transitions on a Quantum Processor

Abstract

Mixed quantum states can exhibit unconventional forms of symmetry breaking without pure-state counterparts. A prominent example is strong-to-weak spontaneous symmetry breaking (SW-SSB), which cannot be diagnosed by observables linear in the density matrix. Here, we experimentally resolve finite-size critical signatures of SW-SSB transitions on a superconducting quantum processor. We develop a measurement protocol that combines quantum measurements with classical processing based on the known dephasing channel to reconstruct nonlinear mixed-state correlators. Using only two measurement settings, the protocol reconstructs fidelity, Rényi-2, and linear correlators, as well as string observables. Applying this approach to matrix-product states subjected to power-law-correlated dephasing, we observe finite-size crossings and scaling collapses in nonlinear correlators, accompanied by decaying linear correlations. We further map the estimated SW-SSB transition points across initial-state and channel parameters. Measurements of linear and Rényi-2 string observables further reveal signatures of mixed-state symmetry-protected topological (SPT) phases, with a nonlinear string-order crossover aligned with an independently estimated SW-SSB transition point. Our results establish a quantum-classical approach to probing SW-SSB critical behavior and mixed-state SPT order.