The Variational Quantum Eigensolver prepares a parameterized quantum state |ψ(θ)⟩ using a circuit ansatz,
then classically minimizes ⟨ψ(θ)|H|ψ(θ)⟩ to find the ground state energy.
This hybrid quantum-classical algorithm exploits the variational principle: any trial state gives an upper bound on the true ground energy.