An upper bound on the Universality of the Quantum Approximate Optimization Algorithm

TL;DR

This paper establishes an upper bound on the universality of the Quantum Approximate Optimization Algorithm (QAOA) using Lie algebra, showing that a linear number of modifications suffices to approximate any universal gate set.

Contribution

It provides a theoretical upper bound on QAOA's ability to approximate universal gates, advancing understanding of its computational limits.

Findings

Upper bound for QAOA universality within O(n)

QAOA can approximate universal gates with linear complexity

Theoretical limits on QAOA's expressiveness

Abstract

Using lie algebra, this brief text provides an upper bound on the universality of QAOA. That is, we prove that the upper bound for the number of alterations of QAOA required to approximate a universal gate set is within O(n)