Approximating maximum independent set on Rydberg atom arrays using local detunings

Abstract: Rydberg atom arrays operated by a quantum adiabatic principle are among the most promising quantum simulating platforms due to their scalability and long coherence time. From the perspective of combinatorial optimization, they offer an efficient solution for an intrinsic maximum independent set problem because of the resemblance between the Rydberg Hamiltonian and the cost function of the maximum independent set problem. In this study, a strategy is suggested to approximate maximum independent sets by adjusting local detunings on the Rydberg Hamiltonian according to each vertex's vertex support, which is a quantity that represents connectivity between vertices. By doing so, the strategy successfully reduces the error rate three times for the checkerboard graphs with defects when the adiabaticity is sufficient. In addition, the strategy decreases the error rate for random graphs even when the adiabaticity is relatively insufficient. Moreover, it is shown that the strategy helps to prepare a quantum many-body ground state by raising the fidelity between the evolved quantum state and a 2D cat state on a square lattice. Finally, the strategy is combined with the non-abelian adiabatic mixing and this approach is highly successful in finding maximum independent sets compared to the conventional adiabatic evolution with local detunings.