Exploring Quantum Phase Transitions Beyond Landau Theory on a Quantum Processor

Direct continuous quantum phase transitions between phases that break distinct symmetries challenge the conventional Landau-Ginzburg-Wilson paradigm and provide a framework for deconfined quantum criticality. Here, we investigate a Landau-forbidden ferromagnetic-to-valence-bond-solid (FM-VBS) transition in a frustrated one-dimensional spin chain using superconducting quantum processors. Combining matrix-product-state-assisted circuit preparation with quantum-hardware measurements, we resolve the suppression of long-range ferromagnetic correlations and the redistribution of competing-order fluctuations across the transition. Distance-resolved correlations and finite-size analyses reveal signatures consistent with critical behavior. We further extend our investigation to nonequilibrium dynamics, directly preparing dimerized states and tracking the evolution of VBS order and joint FM-VBS fluctuations under local unitary interactions. Our results establish a versatile quantum-hardware framework for probing competing orders, critical correlations, and many-body dynamics beyond conventional Landau theory.