Quantum optimization of maximum independent set using Rydberg atom arrays

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 that the problem hardness is controlled by the solution degeneracy and number of local minima, and we 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. Description Solving hard graph problems Realizing quantum speedup for solving practical, computationally hard problems is the central challenge in quantum information science. Ebadi et al. used Rydberg atom arrays composed of up to 289 coupled qubits in two spatial dimensions to investigate quantum optimization algorithms for solving the maximum independent set, a paradigmatic nondeterministic polynomial time–hard combinatorial optimization problem (see the Perspective by Schleier-Smith). A hardware-efficient encoding protocol associated with Rydberg blockade was used to realize a closed-loop optimization method to test several variational algorithms and subsequently apply them to systematically explore a class of nonplanar graphs with programmable connectivity. The results demonstrate the potential of quantum machines as a tool for the discovery of new promising algorithm classes. —ISO Rydberg atom arrays provide quantum speed-up for solving computationally hard optimization problems.