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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 :

  1. Generate the Hamiltonian classically and use a quantum algorithm to solve the big,sparse, hermitian matrix.

  2. 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!

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Please see chapter 6 of Preskill's review: https://arxiv.org/abs/2106.10522. You might also find something useful in chapters 2 and 3 of Pablo Antonio Moreno Casares's thesis: https://arxiv.org/pdf/2301.08057.pdf

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  • $\begingroup$ Thanks! That was a good overview of dealing with hamiltonians and finding their eigenvalues. However, this mostly contained methods for when eigenstates are known or if you have a good estimate of the ground state. Are there any resources which solve lattice model Hamiltonians in other ways? I can only think of designing a variational quantum algorithm for now. $\endgroup$
    – Cheshta Joshi
    Jul 12 at 10:17
  • $\begingroup$ I added another possibly useful link to the answer, take a look on it $\endgroup$
    – Yaron Jarach
    Jul 12 at 10:49

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