# Reachability Deficits in Quantum Approximate Optimization

## TL;DR

This paper reveals that the Quantum Approximate Optimization Algorithm (QAOA) faces fundamental limitations related to problem density, affecting its ability to effectively solve certain optimization problems, even beyond known barren plateau issues.

## Contribution

It identifies and characterizes reachability deficits in QAOA related to problem density, highlighting limitations not previously understood or documented.

## Key findings

- QAOA's effectiveness depends strongly on problem density.
- Reachability deficits occur even without barren plateau effects.
- These limitations are outside previously known QAOA restrictions.

## Abstract

The quantum approximate optimization algorithm (QAOA) has rapidly become a cornerstone of contemporary quantum algorithm development. Despite a growing range of applications, only a few results have been developed towards understanding the algorithms ultimate limitations. Here we report that QAOA exhibits a strong dependence on a problem instances constraint to variable ratio$-$this problem density places a limiting restriction on the algorithms capacity to minimize a corresponding objective function (and hence solve optimization problem instances). Such $reachability~deficits$ persist even in the absence of barren plateaus [McClean et al., 2018] and are outside of the recently reported level-1 QAOA limitations [Hastings 2019]. These findings are among the first to determine strong limitations on variational quantum approximate optimization.