# Quantum optimization with arbitrary connectivity using Rydberg atom arrays

**Authors:** Minh-Thi Nguyen, Jin-Guo Liu, Jonathan Wurtz, Mikhail D. Lukin, Sheng-Tao Wang, Hannes Pichler  
**arXiv:** [2209.03965](https://arxiv.org/abs/2209.03965)  
**Date:** 2022-09-08  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2209.03965v2/

## Key points

- Minh-Thi Nguyen, Jin-Guo Liu, Jonathan Wurtz, Mikhail D. Lukin, Sheng-Tao Wang, and Hannes Pichler explore programmable quantum systems based on Rydberg atom arrays for quantum optimization with arbitrary connectivity.
- The authors extend the capabilities of Rydberg arrays by developing explicit mappings from various problems to maximum weighted independent set problems on unit-disk graphs.
- This allows for efficient encoding of combinatorial optimization challenges including maximum weighted independent set on graphs with arbitrary connectivity and quadratic unconstrained binary optimization problems with diverse connectivity patterns.
- Numerical simulations show a strong correlation between the adiabatic time scale required to solve these mapped problems and their original counterparts.
- Utilizing Rydberg atom arrays can tackle a wide array of combinatorial optimization tasks beyond hardware geometry constraints.
- The study provides a blueprint for leveraging Rydberg arrays in solving complex optimization problems with arbitrary connectivity, advancing quantum computing capabilities in practical applications.

## Summary

In their recent work, Minh-Thi Nguyen, Jin-Guo Liu, Jonathan Wurtz, Mikhail D. Lukin, Sheng-Tao Wang, and Hannes Pichler explore the potential of programmable quantum systems based on Rydberg atom arrays for quantum optimization with arbitrary connectivity. The authors build upon previous research that demonstrated hardware-efficient testing of quantum optimization algorithms with hundreds of qubits. They extend the capabilities of Rydberg arrays by developing explicit mappings from a broad range of problems to maximum weighted independent set problems on unit-disk graphs. This expansion allows for efficient encoding of various combinatorial optimization challenges including maximum weighted independent set on graphs with arbitrary connectivity and quadratic unconstrained binary optimization problems with diverse connectivity patterns. Through numerical simulations conducted on small system sizes, the researchers observe a strong correlation between the adiabatic time scale required to solve these mapped problems and that of their original counterparts. This finding underscores the effectiveness of utilizing Rydberg atom arrays to tackle a wide array of combinatorial optimization tasks beyond the constraints imposed by hardware geometry. By providing a detailed blueprint for leveraging Rydberg arrays in solving complex optimization problems with arbitrary connectivity, this study opens up new possibilities for advancing quantum computing capabilities in practical applications requiring sophisticated problem-solving approaches.