Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays

TL;DR

This paper demonstrates quantum algorithms implemented on Rydberg atom arrays to solve the Maximum Independent Set problem, showing potential quantum speedup over classical methods for certain complex graphs.

Contribution

It introduces a hardware-efficient encoding for quantum optimization using Rydberg blockade and experimentally benchmarks quantum algorithms against classical approaches.

Findings

Superlinear quantum speedup observed on hardest graphs

Quantum algorithms outperform classical simulated annealing in deep circuit regime

Problem hardness linked to solution degeneracy and local minima

Abstract

Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.