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For QAOA it is known that in the large $p$ limit, the algorithm finds the minimum/maximum (see article A Quantum Approximate Optimization Algorithm).

Is there in general a proof for VQE starting from, let's say, uniform superposition state? Is there a standard construction of a circuit (ansatz preparation? not sure about the terminology) that the algorithm converges in some limit?

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    $\begingroup$ I guess that depending on the problem. For certain chemistry problems, it is possible to guarantee convergence if you use says the UCCSD ansaz. I also feel like the classical optimizer plays a huge role whether you can reach convergence or not as well... $\endgroup$
    – KAJ226
    Commented Mar 7, 2021 at 17:41
  • $\begingroup$ I have seen that as well in the literature. A related question is whether QAOA works non-combinatorial optimizations over binary variables or only combinatorial ones? I mean that the cost function is $C(z) = \sum_\alpha \beta_\alpha C_\alpha(z)$ where $\beta_\alpha$ may be real values, and $C_\alpha$ are clauses. $\endgroup$
    – creet
    Commented Mar 7, 2021 at 19:10

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