Variational ground-state quantum adiabatic theorem

TL;DR

This paper introduces a variational quantum adiabatic theorem showing that variational methods can reliably reach ground states even with complex intermediate states, especially for low-entanglement manifolds.

Contribution

It formulates a new variational quantum adiabatic theorem and demonstrates its effectiveness for low-entanglement variational manifolds targeting classical ground states.

Findings

Variational evolution converges to the target ground state.

Effective even with highly entangled intermediate states.

Theoretical analysis aligns with multiple example demonstrations.

Abstract

We present a variational quantum adiabatic theorem, which states that, under certain assumptions, the adiabatic dynamics projected onto a variational manifold follow the instantaneous variational ground state. We focus on low-entanglement variational manifolds and target Hamiltonians with classical ground states. Despite the presence of highly entangled intermediate states along the exact quantum annealing path, the variational evolution converges to the target ground state. We demonstrate this approach with several examples that align with our theoretical analysis.