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First of all, QAOA can be regarded as an application of VQE. (Take a look at this answer.) Therefore, we can consider their performance to be similar enough to talk about them together. Although for some particular cases, a quantum computer isn't even needed for QAOA, but let's consider only the cases in which quantum circuits are used. Briefly, it is not ...


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In QAOA you do not implement Hamiltonian $H$ itself but gate defined as $U = \mathrm{e}^{iHt}$. Since Hamiltonian $H$ is always Hermitian, operator $U$ is always unitary. You can see proof of this here. Concerning implementation of QAOA circuits, I would recommed this article. It contains discussion how to convert QUBO to Hamiltonian and in the appendix, ...


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There was an issue that was fixed with QAOA https://github.com/Qiskit/qiskit-aqua/pull/1316 whereby using all zeros as an initial point was changed since the optimizer could easily get stuck there. Given the version you have the easiest way to change things would just be to pass an initial point that is non-zero. I.e. instead of [0,0] which it uses with the ...


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Probably the easiest way to understand this is to pretend that the mixer is NOT there and see what happens. So, let's assume you have some initial state $\lvert \psi \rangle = \sum_x \psi_x \lvert x \rangle$ and you want to use QAOA to find the ground state of some cost Hamiltonian $H_C$. I'm using the notation $\big\{\lvert x \rangle : x \in \{\pm 1\}^n \...


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