variational quantum eigensolver

The Variational Quantum Eigensolver (VQE) is primarily used in quantum chemistry to estimate the ground state energy of a given molecule. By finding this minimum energy, researchers can predict chemical properties that are too complex for classical computers to calculate.

VQE is hybrid because it relies on a continuous feedback loop between a quantum computer and a classical computer. The quantum processor evaluates a parameterized quantum circuit, while the classical processor uses a mathematical optimizer to update the parameters.

In VQE, the Hamiltonian is a mathematical operator that describes the total energy of the molecular system being studied. The entire goal of the algorithm is to find the lowest possible eigenvalue of this operator, which represents the system's ground state energy.

VQE is highly suited for the Noisy Intermediate-Scale Quantum (NISQ) era because it relies on shallow quantum circuits that are resilient to noise. Because the circuits are short and constantly optimized by the classical computer, they avoid the heavy error accumulation that plagues deep quantum algorithms.