# QAOA for Max-Cut requires hundreds of qubits for quantum speed-up

## TL;DR

This paper argues that noisy intermediate-scale quantum computers need to have hundreds of qubits to achieve practical quantum speed-up for solving combinatorial problems using hybrid algorithms like QAOA.

## Contribution

The study provides realistic simulations showing that quantum speedup for Max-Cut via QAOA requires hundreds of qubits, highlighting the scale needed for practical quantum advantage.

## Key findings

- Quantum speedup for Max-Cut with QAOA requires hundreds of qubits.
- Simulations indicate current noisy devices are insufficient for practical advantage.
- Hybrid quantum-classical algorithms need large-scale quantum computers for effectiveness.

## Abstract

Computational quantum technologies are entering a new phase in which noisy intermediate-scale quantum computers are available, but are still too small to benefit from active error correction. Even with a finite coherence budget to invest in quantum information processing, noisy devices with about 50 qubits are expected to experimentally demonstrate quantum supremacy in the next few years. Defined in terms of artificial tasks, current proposals for quantum supremacy, even if successful, will not help to provide solutions to practical problems. Instead, we believe that future users of quantum computers are interested in actual applications and that noisy quantum devices may still provide value by approximately solving hard combinatorial problems via hybrid classical-quantum algorithms. To lower bound the size of quantum computers with practical utility, we perform realistic simulations of the Quantum Approximate Optimization Algorithm and conclude that quantum speedup will not be attainable, at least for a representative combinatorial problem, until several hundreds of qubits are available.