Symmetry‐Protected Quantum Adiabatic Evolution in Spontaneous Symmetry‐Breaking Transitions

Abstract

AbstractQuantum adiabatic evolution describes the dynamical evolution of a slowly driven Hamiltonian. In most systems undergoing spontaneous symmetry‐breaking transitions, the symmetry‐protected quantum adiabatic evolution can still appear, even when the two lowest eigenstates become degenerate. Here, a general derivation to revisit the symmetry‐dependent transition and the symmetry‐dependent adiabatic condition (SDAC) is given. Further, based on the SDAC, an adiabatic‐parameter‐fixed sweeping scheme is used for achieving fast adiabatic evolution, which is more efficient than the linear sweeping scheme. In the limit of small adiabatic parameter, an analytic inequality is obtained for the ground state fidelity only dependent on the adiabatic parameter. The general statements are then demonstrated via two typical systems. Besides, the robustness of the symmetry‐dependent adiabatic evolution against weak symmetry‐breaking sources is studied. The findings can be tested via the techniques in quantum annealing and may provide promising applications in practical quantum technologies.