Speaker
Description
Quantum Imaginary Time Evolution (QITE) has recently received increasing attention as a pathway for ground state preparation on quantum hardware. However, the efficiency of this approach is frequently compromised by energy plateau, dynamical regimes characterized by vanishing energy reduction where the system stagnates near some metastable states. In this work, we dissect the anatomy of these stagnation periods, identifying them as saddle-point-like features arising when the dynamical trajectory traverses the vicinity of intermediate energy eigenstates. We demonstrate that the local energy relaxation rate is characterized by the spectral geometry of these saddle points, specifically the gaps separating the trapping eigenstate from its nearest eigenstates. By reducing the dynamics to an effective three-level system, we show that this minimal model captures the essential local structure of these metastable transients. We derive rigorous analytical upper and lower bounds on the plateau duration, connecting the algorithmic runtime to the initial state overlap and the relevant spectral gaps and degenerate subspace structures. Furthermore, we provide a geometric characterization of these trajectories within the probability simplex and discuss the implications of our bounds for average-case convergence in generic many-body systems.