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The heart of the QAOA relies on the use of [[unitary operators]] dependent on <math> 2p </math> [[angle]]s, where <math> p>1 </math> is an input integer. These operators are iteratively applied on a state that is an equal-weighted [[quantum superposition]] of all the possible states in the computational basis. In each iteration, the state is measured in the computational basis and <math> C(z) </math> is calculated. After a sufficient number of repetitions, the value of <math> C(z) </math> is almost optimal, and the state being measured is close to being optimal as well.
 
In a paper<ref name=":0">{{Cite journal|last=Akshay|first=V.|last2=Philathong|first2=H.|last3=Morales|first3=M. E. S.|last4=Biamonte|first4=J. D.|date=2020-03-05|title=Reachability Deficits in Quantum Approximate Optimization|journal=Physical Review Letters|volume=124|issue=9|pages=090504|doi=10.1103/PhysRevLett.124.090504|arxiv=1906.11259}}</ref> published in [[Physical Review Letters]] on March 5, 2020 (pre-print<ref>{{cite journal|lastname=Akshay|first=V.|last2=Philathong|first2=H.|last3=Morales|first3=M.":0" E. S.|last4=Biamonte|first4=J.|title=Reachability Deficits in Quantum Approximate Optimization|journal=Physical Review Letters|volume=124|issue=9|pages=090504|arxiv=1906.11259|doi=10.1103/PhysRevLett.124.090504|year=2020}}</ref> submitted on 26 Jun 2019 to [[arXiv]]), the authors report that QAOA exhibits a strong dependence on the ratio of a problems constraint to variables (problem density) placing a limiting restriction on the algorithms capacity to minimize a corresponding objective function.
 
== See also ==