Variational quantum eigensolver

Variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm that finds the smallest eigenvalue (and corresponding eigenvector) of a given Hamiltonian. One of the main applications of the algorithm is finding ground state energy of molecules. It has a big advantage over IQPE (iterative quantum phase estimation) and QPE (quantum phase estimation) algorithms, that also can be used for finding the ground state energy of a molecule. The main advantage is that VQE uses much smaller circuit depths (or gates) then IQPE and QPE, what is very important for NISQ (Noisy Intermediate-Scale Quantum) era quantum computation. In the NISQ era (now!) we are working with qubits that are very noisy because they are not isolated from the environment well enough. Thus, there is small and finite time to work with qubits until they will be "spoiled", because of the environment, imperfect gates and etc. This restriction gives a big advantage to those algorithms (like VQE) that are using small depth circuits..