Physics

Qubit

Degeneracy (biology)

Mathematics

Bioinformatics

Biology

Quantum annealing

Algorithm

Rydberg atom

Geodesy

Quantum algorithm

Mathematical analysis

Parallel computing

Benchmark (surveying)

Maxima and minima

Geography

Ionization

Computer science

Quantum computer

Quantum mechanics

Speedup

Rydberg formula

Quantum

Science

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.

Quantum optimization of maximum independent set using Rydberg atom arrays