Applying the Quantum Alternating Operator Ansatz to the Graph Matching Problem
Abstract
The Quantum Alternating Operator Ansatz (QAOA+) framework has recently gained attention due to its ability to solve discrete optimization problems on noisy intermediatescale quantum (NISQ) devices in a manner that is amenable to derivation of worstcase guarantees. We design a technique in this framework to tackle a few problems over maximal matchings in graphs. Even though maximum matching is polynomialtime solvable, most counting and sampling versions are #Phard. We design a few algorithms that generates superpositions over matchings allowing us to sample from them. In particular, we get a superposition over all possible matchings when given the empty state as input and a superposition over all maximal matchings when given the W states as input. Our main result is that the expected size of the matchings corresponding to the output states of our QAOA+ algorithm when ran on a 2regular graph is greater than the expected matching size obtained from a uniform distribution over all matchings. This algorithm uses a W state as input and we prove that this input state is better compared to using the empty matching as the input state.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 arXiv:
 arXiv:2011.11918
 Bibcode:
 2020arXiv201111918C
 Keywords:

 Quantum Physics;
 Computer Science  Data Structures and Algorithms
 EPrint:
 9 pages, 3 figures, 3 charts