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A 1,968-node coupled ring oscillator circuit for combinatorial optimization problem solving

Nature Electronics volume 5, pages 310–317 (2022)Cite this article

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Abstract

Computational architectures that are optimized to solve non-deterministic polynomial-time hard or complete problems are of use in the development of machine learning, logistical planning and pathfinding. A range of quantum-, optical- and spintronic-based approaches have been explored for solving such combinatorial optimization problems, but they remain complicated to build and to scale. Here we report a scalable ring-oscillator-based integrated circuit for optimization problem solving. Our 1,968-node King’s graph ring oscillator array has five levels of coupling strengths and can achieve up to 95% accuracy for randomly generated combinatorial optimization problems. The measured average power consumption of the Ising chip is 0.042 W and it takes less than 50 oscillation cycles to resolve to the ground state. Our device is resilient to environmental and variation effects. By using a multi-phase phase measurement circuit, we also capture the true phase behaviour within a coupled-oscillator integrated circuit.

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Fig. 1: Computation steps and operating principle of the coupled-oscillator-based Ising machine.
Fig. 2: Schematic of a coupled oscillator and 1,968-node Ising chip layout.
Fig. 3: Unit-tile oscillator and support circuits.
Fig. 4: Phase-sampling circuit, measured raw phase maps and post-processing steps.
Fig. 5: Measured results from the 1,968 oscillator chips.

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Data availability

The problem set and test data presented in this paper are available at https://figshare.com/projects/A_1_968_node_coupled_ring_oscillator_circuit_for_combinatorial_optimization_problem_solving/134594.

Code availability

The code used to generate the optimal Hamiltonians is available at https://figshare.com/projects/A_1_968_node_coupled_ring_oscillator_circuit_for_combinatorial_optimization_problem_solving/134594.

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Acknowledgements

I.A. and C.H.K. acknowledges the initial support of the project from the National Science Foundation under ECCS 1739635 and the Semiconductor Research Corporation (SRC) under 2759.007. For the chip testing and data analysis works, W.M. and C.H.K. have been supported in part by the SRC under 3024.001. We would like to thank SRC’s industry liaisons for their technical feedback.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA

    William Moy, Ibrahim Ahmed, Po-wei Chiu, John Moy, Sachin S. Sapatnekar & Chris H. Kim

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  1. William Moy
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Contributions

W.M., I.A., P.-W.C., S.S.S. and C.H.K. participated in the circuit and architecture design of the integrated circuit. W.M., I.A. and P.-W.C. created the layout for the fabrication of the integrated circuit. W.M. and C.H.K. performed the testing and measurement of the chip. J.M. created the cloud-testing interface and testing automation setup for the chip.

Corresponding author

Correspondence to Chris H. Kim.

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Competing interests

The authors declare the following competing interest: US patent application 17/213,396 (Probabilistic compute engine using coupled ROSCs).

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Nature Electronics thanks Michael Huang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Raw phase map data with post-processed results.

Raw phase maps are shown for uniform, chequerboard, and random pattern graphs. A lightweight post-processing method that emphasizes the relative phase difference between adjacent nodes can eliminate non-ideal effects and produce the expected spin value maps on the right. The weights and spin values are colour coded and overlaid for better visualization. ROSCs are indexed from 1 (upper left corner) to 1,968 (lower right corner), with ROSC 1 being directly above ROSC 42.

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Moy, W., Ahmed, I., Chiu, Pw. et al. A 1,968-node coupled ring oscillator circuit for combinatorial optimization problem solving. Nat Electron 5, 310–317 (2022). https://doi.org/10.1038/s41928-022-00749-3

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