VQE

VQE (Variational Quantum Eigensolver) is a hybrid quantum-classical algorithm designed for NISQ devices. It finds the minimum eigenvalue (ground state energy) of a Hamiltonian — critical for quantum chemistry and materials science. VQE uses a parameterized quantum circuit (ansatz) to prepare a trial quantum state |ψ(θ)⟩, measures the expectation value ⟨ψ(θ)|H|ψ(θ)⟩ on the QPU, then uses a classical optimizer (COBYLA, BFGS) to update the parameters θ to minimize the energy. This variational loop continues until convergence. VQE can approximate molecular ground state energies that are intractable for classical computers. PennyLane, Qiskit, and HLQuantum all provide VQE implementations. Limitations include barren plateaus (flat optimization landscapes) and circuit expressibility.