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Rydberg quantum wires for maximum independent set problems


One application of near-term quantum computing devices1,2,3,4 is to solve combinatorial optimization problems such as non-deterministic polynomial-time hard problems5,6,7,8. Here we present an experimental protocol with Rydberg atoms to determine the maximum independent set of graphs9, defined as an independent set of vertices of maximal size. Our proposal is based on a Rydberg quantum wire scheme, which exploits auxiliary atoms to engineer long-ranged networks of qubits. We experimentally test the protocol on three-dimensional Rydberg atom arrays, overcoming the intrinsic limitations of two-dimensional arrays for tackling combinatorial problems and encode high-degree vertices. We find the maximum independent set solutions with our programmable quantum-wired Rydberg simulator for Kuratowski subgraphs10 and a six-degree graph, which are paradigmatic examples of non-planar and high-degree graphs, respectively. Our protocol provides a way to engineer the complex connections of high-degree graphs through many-body entanglement, taking a step towards the demonstration of quantum advantage in combinatorial optimization.

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Fig. 1: The graph representation of a Rydberg atom array.
Fig. 2: Experimental tests of Rydberg quantum wires.
Fig. 3: Experimental construction of Kuratowski subgraphs.
Fig. 4: Vertex-splitting demonstration.

Data availability

The data that support the findings of this study are available from Figshare, the public data repository at Source data are provided with this paper.

Code availability

The computer codes used to analyse the data of this study are available from Figshare, the public data repository at


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This research was supported by the Samsung Science and Technology Foundation (SSTF-BA1301-52) and the National Research Foundation of Korea (NRF) (2017R1E1A1A01074307, 2019M3E4A1080411, 2020R1A4A3079707 and 2021R1A2C4001847).

Author information

Authors and Affiliations



J.A. designed the project. M.K. and K.K. performed most of the experiments. M.K., K.K., J.H. and J.A. analysed and validated the data. E.-G.M. and J.A. wrote the manuscript. All authors have read, discussed and contributed to the manuscript.

Corresponding author

Correspondence to Jaewook Ahn.

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The authors declare no competing interests.

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Nature Physics thanks Davide Venturelli and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Discussion, Figs. 1 and 2, and Tables 1 and 2.

Supplementary Video 1

Visualization of a 3D atom array of the quantum-wired K5 graph.

Supplementary Video 2

Visualization of a 3D atom array of the quantum-wired K3,3 graph.

Source data

Source Data Fig. 2

Experimental data of Fig. 2.

Source Data Fig. 3

Experimental data of Fig. 3.

Source Data Fig. 4

Experimental data of Fig. 4.

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Kim, M., Kim, K., Hwang, J. et al. Rydberg quantum wires for maximum independent set problems. Nat. Phys. 18, 755–759 (2022).

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