Variational Quantum Eigensolver (VQE)
A hybrid algorithm for noisy hardware: a short quantum circuit prepares a trial state and a classical optimizer tunes it toward a molecule's ground state.
The variational quantum eigensolver (VQE) is a hybrid algorithm designed for the hardware we actually have rather than the hardware we want. A quantum processor prepares a trial state with a short, tunable circuit and measures its energy; a classical computer adjusts the knobs and tries again, descending toward the lowest energy, typically the ground state of a molecule.
The division of labor is the point: the quantum chip does the one thing it's uniquely good at (representing entangled many-body states), while classical optimization absorbs the rest. Short circuits mean noise tolerance, which made VQE the signature algorithm of the NISQ era and the engine of nearly every 'quantum computer simulates molecule' headline of the past decade.
The open question, still, is whether VQE can beat the best classical chemistry methods on a problem anyone cares about before error-corrected machines make it obsolete.