I am working with a tight binding model. I am looking for a way I can efficiently find the eigenvalues and eigenvectors of the Hamiltonian using a quantum algorithm. Can someone suggest some good resources?
I may proceed in the following two ways :
Generate the Hamiltonian classically and use a quantum algorithm to solve the big,sparse, hermitian matrix.
Use a ferimionic to spin transformation, directly implement this Hamiltonian on a quantum circuit and use some quantum algorithm to solve it.
Let me know if I'm thinking in the right direction or if there any other ways I can proceed. Resources/Algorithms for the suggested two ways would be highly appreciated. Thanks!