The Variational Quantum Eigensolver, or VQE, is an algorithm for finding the ground-state energy of a quantum system, which is its lowest possible energy configuration. This is a fundamental problem in chemistry and materials science, since the ground-state energy governs how molecules bond, react, and behave.
VQE is a hybrid algorithm. A quantum computer runs a series of variational circuits and returns measurement results, which are fed into a classical optimisation routine. The classical optimiser then updates the circuit parameters, and the process repeats until it converges on the optimal set of parameters and the lowest energy estimate. Like QAOA, this structure keeps the quantum circuits shallow enough to run on near-term hardware.
VQE is one of the most studied algorithms for quantum chemistry and is a natural target application for scalable quantum processors.