Variational Quantum Eigensolver (VQE)

Energy landscape ⟨ψ(θ)|H|ψ(θ)⟩ — gradient descent finds the ground state

0.050
0.08
E(θ) =
E_exact =
Step: 0
Δθ₁ =
Δθ₂ =
VQE algorithm:
θ ← θ − η∇E(θ)

Gradient via parameter-shift rule:
∂E/∂θ = [E(θ+π/2) − E(θ−π/2)]/2

Advantage over exact diag: exponentially fewer parameters