Encoding computationally hard problems in triangular Rydberg atom arrays

TL;DR

This paper introduces a new encoding scheme for Rydberg atom arrays arranged in triangular lattices, significantly improving the accuracy of quantum optimization by reducing violations and minimizing post-processing, thus advancing quantum computing capabilities.

Contribution

The authors develop a universal encoding method for triangular lattices that outperforms previous approaches like King's subgraphs, enhancing the physical realism and efficiency of quantum optimization.

Findings

Reduces independence-constraint violations by about two orders of magnitude.

Improves encoding accuracy for Rydberg atom arrays on triangular lattices.

Decreases reliance on post-processing in quantum optimization experiments.

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 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: the 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 post-processing 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 quantum optimization on triangular lattices reduces independence-constraint violations by approximately two orders of magnitude compared to King's subgraphs, substantially alleviating the need for post-processing in experiments.