Warm Starts, Cold States: Exploiting Adiabaticity for Variational Ground-States
This work addresses the challenge of variational training in quantum computing for applications like chemistry and materials modeling, offering an incremental improvement over existing methods.
The paper tackles the problem of reliably preparing many-body ground states in quantum computing by introducing an iterative strategy based on Hamiltonian deformation, which complements the Variational Quantum Eigensolver with adiabatic principles to avoid local minima and barren plateaus, demonstrating consistent convergence to the target ground state in numerical simulations.
Reliable preparation of many-body ground states is an essential task in quantum computing, with applications spanning areas from chemistry and materials modeling to quantum optimization and benchmarking. A variety of approaches have been proposed to tackle this problem, including variational methods. However, variational training often struggle to navigate complex energy landscapes, frequently encountering suboptimal local minima or suffering from barren plateaus. In this work, we introduce an iterative strategy for ground-state preparation based on a stepwise (discretized) Hamiltonian deformation. By complementing the Variational Quantum Eigensolver (VQE) with adiabatic principles, we demonstrate that solving a sequence of intermediate problems facilitates tracking the ground-state manifold toward the target system, even as we scale the system size. We provide a rigorous theoretical foundation for this approach, proving a lower bound on the loss variance that suggests trainability throughout the deformation, provided the system remains away from gap closings. Numerical simulations, including the effects of shot noise, confirm that this path-dependent tracking consistently converges to the target ground state.