Warm Starts, Cold States: Exploiting Adiabaticity for Variational Ground-States

TL;DR

This paper introduces an adiabatic-inspired iterative method for variational ground-state preparation in quantum computing, improving convergence by tracking the ground state through Hamiltonian deformation.

Contribution

It presents a novel stepwise Hamiltonian deformation strategy that enhances variational ground-state preparation by combining adiabatic principles with VQE, supported by theoretical and numerical validation.

Findings

Path-dependent tracking improves convergence to ground states.

Theoretical lower bound on loss variance ensures trainability.

Numerical simulations confirm robustness against shot noise.

Abstract

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.