# Benchmarking the Quantum Approximate Optimization Algorithm

## TL;DR

This paper benchmarks the quantum approximate optimization algorithm across various problem instances, comparing its performance on simulators, real quantum hardware, and quantum annealers, revealing instance-dependent results.

## Contribution

It provides a comprehensive performance evaluation of QAOA on different hardware and problem types, highlighting its strengths and limitations.

## Key findings

- D-Wave quantum annealer outperforms QAOA on tested instances.
- QAOA performance varies significantly with problem instance.
- QAOA's success depends heavily on the specific problem structure.

## Abstract

The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation ratio. The set of problem instances studied consists of weighted MaxCut problems and 2-satisfiability problems. The Ising model representations of the latter possess unique ground states and highly-degenerate first excited states. The quantum approximate optimization algorithm is executed on quantum computer simulators and on the IBM Q Experience. Additionally, data obtained from the D-Wave 2000Q quantum annealer is used for comparison, and it is found that the D-Wave machine outperforms the quantum approximate optimization algorithm executed on a simulator. The overall performance of the quantum approximate optimization algorithm is found to strongly depend on the problem instance.