We review the variational quantum eigensolver (VQE) as a near-term route to estimating molecular ground-state energies, formalise the variational principle it rests on, and analyse how the choice of ansatz and the measurement cost of a Pauli-decomposed Hamiltonian govern its practicality. A hybrid classical/quantum optimisation loop is described, and the conditions under which barren plateaus erase the method's advantage are made explicit.
Papers & preprints.
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