16

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?

glS
  • 24,708
  • 5
  • 34
  • 108
hopefully coherent
  • 697
  • 6
  • 14

1 Answers1

7

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.

Andrew O
  • 1,749
  • 1
  • 15
  • 21
  • 1
    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 $1$. – Turbotanten Mar 30 '19 at 13:35
  • What is an intuitive or mathematical reason behind better result with increasing p? – Edifice Apr 20 '19 at 03:22