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Edward Farhi's paper on the Quantum Approximate Optimization Algorithm introduces a way for gate model quantum computers to solve combinatorial optimization algorithms. However, D-Wave style quantum annealers have focused on combinatorial optimization algorithms for some time now. What is gained by using QAOA on a gate model quantum computer instead of using a Quantum Annealer?

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One of the advantages, as stated in the paper you linked, is that with QAOA you can increase the precision arbitrarily, whereas QA will only find the solution with probability 1 as $T \to \infty$ which is impractical. In addition if $T$ is too long you're likely to not find the solution as the probability is not monotonic. I believe an example of this can be found in a fair-sampling paper by Matsuda et al. Figure 4 shows that for large $\tau$, using quantum annealing on a 5-qubit system, you only likely to find 2 of the 3 possible states.

[arXiv:0808.0365v3] Ground-state statistics from annealing algorithms: Quantum vs classical approaches - Matsuda et al.

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  • $\begingroup$ Yes, you can increase the precision arbitrarily with QAOA, but you do that by increasing the integer $p$. When $p\rightarrow \infty$ then you find the solution with probability $1$. $\endgroup$ – Turbotanten Mar 30 at 13:35
  • $\begingroup$ What is an intuitive or mathematical reason behind better result with increasing p? $\endgroup$ – Abdullah Ash- Saki Apr 20 at 3:22

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