Variational Quantum Eigensolver

Classically optimize a quantum ansatz circuit to find the ground state energy of H₂

VQE Controls

⟨H⟩ = —

Ansatz Circuit

|ψ(θ)⟩ = CNOT·Ry(θ₂)·Ry(θ₁)|00⟩

Physics: H₂ Molecule

The H₂ Hamiltonian in minimal basis (STO-3G) has energy:
E(R) depends on bond length R.
Ground state energy ≈ −1.137 Hartree at R=0.74Å.

Variational principle: ⟨ψ|H|ψ⟩ ≥ E_ground for all |ψ⟩.

The quantum circuit prepares a trial state, the classical optimizer adjusts θ to minimize ⟨H⟩. The optimum is the ground state.