Encoding computationally hard problems in triangular Rydberg atom arrays
Phys. Rev. A 114, 022623 – Published 31 August, 2026
DOI: https://doi.org/10.1103/kh98-chtn
Abstract
Rydberg atom arrays are a promising platform for quantum optimization, encoding computationally hard problems by reducing them to independent set problems with unit-disk graph topology. In the work of Nguyen et al., PRX Quantum 4, 010316 (2023), a systematic and efficient strategy was introduced to encode multiple problems into a special unit-disk graph: King's subgraph. However, King's subgraphs are not the optimal choice in two dimensions. Due to the power-law decay of Rydberg interaction strengths, the approximation to unit-disk graphs in real devices is poor, necessitating postprocessing that lacks physical interpretability. In this work we develop an encoding scheme that can universally encode computationally hard problems on triangular lattices, based on our innovative automated gadget search strategy. Numerical simulations demonstrate that, for a benchmark instance, quantum optimization on triangular lattices reduces independence-constraint violations by nearly two orders of magnitude compared to King's subgraphs, substantially alleviating the need for postprocessing in experiments.
