Solving optimization problems with Rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks

TL;DR

This paper analyzes the requirements for Rydberg atom quantum computers to outperform classical algorithms in solving the Unit-Disk Maximum Independent Set problem, focusing on system size, noise levels, and coherence improvements.

Contribution

It provides quantitative estimates of system sizes and noise thresholds needed for quantum advantage using realistic noisy simulations and classical benchmarks.

Findings

Approximation ratio of 0.84 achievable with near-future noise levels.

Quantum advantage possible with ~8,000 atoms in 2 seconds.

Coherence improvements by a factor of 10 could enable quantum advantage at smaller scales.

Abstract

Platforms of Rydberg atoms have been proposed as promising candidates to solve some combinatorial optimization problems. Here, we compute quantitative requirements on the system sizes and noise levels that these platforms must fulfill to reach quantum advantage in approximately solving the Unit-Disk Maximum Independent Set problem. Using noisy simulations of Rydberg platforms of up to 26 atoms interacting through realistic van der Waals interactions, we compute the average approximation ratio that can be attained with a simple quantum annealing-based heuristic within a fixed temporal computational budget. Based on estimates of the correlation lengths measured in the engineered quantum state, we extrapolate the results to large atom numbers and compare them to a simple classical approximation heuristic. We find that approximation ratios of at least $\approx 0.84$ are within reach for near-future noise levels. Not taking into account further classical and quantum algorithmic improvements, we estimate that quantum advantage could be reached by attaining a number of controlled atoms of $\sim8,000$ for a time budget of 2 seconds, and $\sim 1,000-1,200$ for a time budget of 0.2 seconds, provided the coherence levels of the system can be improved by a factor 10 while maintaining a constant repetition rate.