Observation and Modulation of the Quantum Mpemba Effect on a Superconducting Quantum Processor

In non-equilibrium quantum many-body systems, the quantum Mpemba effect (QME) emerges as a counterintuitive phenomenon: systems exhibiting greater initial symmetry breaking restore symmetry faster than those with less. While theoretical exploration of QME has surged, experimental studies on its multidimensional modulation remain limited. Here, we report the observation and control of QME using a superconducting processor featuring a unique fully connected, tunable-coupling architecture that enables precise modulation from short- to long-range interactions. This platform allows independent manipulation of coupling regimes, on-site potentials, and initial states, elucidating their roles in QME. To quantify symmetry restoration, we employ entanglement asymmetry (EA) -- the relative entropy between a subsystem reduced density matrix and its symmetric projection -- as a sensitive probe of symmetry breaking. In strong short-range coupling regimes, EA crossovers during quenches from tilted N\'{e}el states confirm the presence of QME. In contrast, in intermediate coupling regimes, synchronized EA and entanglement entropy dynamics reveal the suppression of QME. Remarkably, QME reemerges with the introduction of on-site linear potentials or quenches from tilted ferromagnetic states, the latter proving robust against on-site disorder. Our study provides the first demonstration of flexible QME modulation on a superconducting platform with multiple controllable parameters, shedding light on quantum many-body non-equilibrium dynamics and opening avenues for quantum information applications.