Warm Starts, Cold States: Exploiting Adiabaticity for Variational Ground-States
This work addresses the challenge that variational quantum eigensolvers (VQE) often converge to local minima or suffer from barren plateaus in complex energy landscapes, hindering reliable preparation of many-body ground states. To overcome this, the authors propose an iterative strategy inspired by adiabatic evolution, which constructs a discretized deformation path of the Hamiltonian and tracks the ground-state manifold across a sequence of intermediate problems to guide VQE toward the target ground state. The method provides theoretical guarantees on trainability by avoiding regions where the spectral gap closes, thereby significantly enhancing the robustness and scalability of ground-state preparation. Numerical experiments demonstrate that the approach achieves stable convergence even in the presence of measurement noise, effectively circumventing the optimization pitfalls commonly encountered in conventional VQE implementations.