Variational Forms (
In quantum mechanics, the variational method is one way of finding approximations to the lowest energy eigenstate, or ground state, and some excited states. This allows calculating approximate wave functions, such as molecular orbitals. The basis for this method is the variational principle.
The variational method consists of choosing a trial wave function, or variational form, that
depends on one or more parameters, and finding the values of these parameters for which the
expectation value of the energy is the lowest possible. The wave function obtained by fixing the
parameters to such values is then an approximation to the ground state wave function, and the
expectation value of the energy in that state is an upper bound to the ground state energy. Quantum
variational algorithms, such as
VQE, apply the variational method.
As such, they require a variational form.