Efficient Hamiltonian Engineering for Adiabatic MIS Algorithms

TL;DR

This paper introduces a hybrid adiabatic algorithm using Rydberg atom arrays for efficiently solving maximum independent set problems, improving success rates and reducing error decay.

Contribution

It develops local control techniques that accelerate convergence and suppress trap states, outperforming traditional global control methods.

Findings

Higher success probabilities than traditional methods

25% reduction in fidelity decay rate with increased problem hardness

Accelerated convergence to the MIS state

Abstract

We present a hybrid adiabatic algorithm for maximum independent set (MIS) using Rydberg atom arrays. We engineer local controls that preferentially excite atoms with few neighbors, which represent graph nodes with small degrees. Numerical simulations show that the designed pulses accelerate convergence to the MIS state and suppress population in trap states. We obtain higher success probabilities than traditional global controls and a $25\%$ reduction in fidelity decay rate as problem hardness increases.