A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem
Abstract
We apply our recent Quantum Approximate Optimization Algorithm to the combinatorial problem of bounded occurrence Max E3LIN2. The input is a set of linear equations each of which contains exactly three boolean variables and each equation says that the sum of the variables mod 2 is 0 or is 1. Every variable is in no more than D equations. A random string will satisfy 1/2 of the equations. We show that the level one QAOA will efficiently produce a string that satisfies $\left(\frac{1}{2} + \frac{1}{101 D^{1/2}\, l n\, D}\right)$ times the number of equations. A recent classical algorithm achieved $\left(\frac{1}{2} + \frac{constant}{D^{1/2}}\right)$. We also show that in the typical case the quantum computer will output a string that satisfies $\left(\frac{1}{2}+ \frac{1}{2\sqrt{3e}\, D^{1/2}}\right)$ times the number of equations.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.6062
 Bibcode:
 2014arXiv1412.6062F
 Keywords:

 Quantum Physics
 EPrint:
 This version contains a tighter analysis that leads to stronger results on the performance of the quantum algorithm