How to construct Hamiltonian for combinatorial optimization problems and then convert into Pauli basis?

Suppose I have a portfolio optimization problem where I have to minimize, $$qx^T\sum x - \mu^Tx$$

where q is the maximum risk and x is {0,1}^n and $$\mu$$ are the expected returns.

Now I have to convert this problem into Hamiltonian and subsequently find the Pauli Basis for it. How can I do so?

• Are you going off a specific paper? Sep 18, 2020 at 15:33
• No not any paper Sep 19, 2020 at 16:11
• Ah, okay. Maybe look into general optimization problems? I'm not as familiar with creating Hamiltonians from general problems Sep 19, 2020 at 16:55