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Learning interpretable representations of entanglement in quantum optics experiments using deep generative models

Nature Machine Intelligence volume 4, pages 544–554 (2022)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Quantum physics experiments produce interesting phenomena such as interference or entanglement, which are the core properties of numerous future quantum technologies. The complex relationship between the setup structure of a quantum experiment and its entanglement properties is essential to fundamental research in quantum optics but is difficult to intuitively understand. We present a deep generative model of quantum optics experiments where a variational autoencoder is trained on a dataset of quantum optics experiment setups. In a series of computational experiments, we investigate the learned representation of our quantum optics variational autoencoder (QOVAE) and its internal understanding of the quantum optics world. We demonstrate that QOVAE learns an interpretable representation of quantum optics experiments and the relationship between the experiment structure and entanglement. We show QOVAE is able to generate novel experiments for highly entangled quantum states with specific distributions that match its training data. QOVAE can learn to generate specific entangled states and efficiently search the space of experiments that produce highly entangled quantum states. Importantly, we are able to interpret how QOVAE structures its latent space, finding curious patterns that we can explain in terms of quantum physics. The results demonstrate how we can use and understand the internal representations of deep generative models in a complex scientific domain. QOVAE and the insights from our investigations can be immediately applied to other physical systems.

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Fig. 1: Data representation and model.
Fig. 2: Comparison with training data.
Fig. 3: Interpolations.
Fig. 4: QOVAE latent spaces.
Fig. 5: More QOVAE latent spaces.

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Data availability

The training data are available via GitHub at https://github.com/danielflamshep/qovae/blob/main/setups.smi (ref. 79).

Code availability

The code is available via GitHub at https://github.com/danielflamshep/qovae (ref. 79). The source code for the Melvin algorithm is available via GitHub at https://github.com/XuemeiGu/MelvinPython.

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Acknowledgements

A.A.-G. acknowledges support from the Canada 150 Research Chairs Program, the Canada Industrial Research Chair Program and from Google in the form of a Google Focused Award. M.K. acknowledges support from the FWF (Austrian Science Fund) via Erwin Schrödinger Fellowship no. J4309.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Toronto, Toronto, Ontario, Canada

    Daniel Flam-Shepherd, Tony C. Wu, Alba Cervera-Lierta, Mario Krenn & Alán Aspuru-Guzik

  2. Vector Institute for Artificial Intelligence, Toronto, Ontario, Canada

    Daniel Flam-Shepherd, Mario Krenn & Alán Aspuru-Guzik

  3. Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, China

    Xuemei Gu

  4. Department of Chemistry, University of Toronto, Toronto, Ontario, Canada

    Alba Cervera-Lierta, Mario Krenn & Alán Aspuru-Guzik

  5. Max Planck Institute for the Science of Light (MPL), Erlangen, Germany

    Mario Krenn

  6. Canadian Institute for Advanced Research, Toronto, Ontario, Canada

    Alán Aspuru-Guzik

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Contributions

D.F.-S. conceived the overall project, developed the approach and wrote the paper. D.F.-S. and T.W. designed and performed the investigations. A.C.-L. provided the technical advice. X.G. provided the technical advice and wrote the entanglement calculation code. M.K. built the dataset, provided technical advice and helped design the interpretability investigation and analysed the experiments. A.A.-G. led the project and provided the overall directions. All the authors participated in preparing the manuscript.

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Correspondence to Daniel Flam-Shepherd, Mario Krenn or Alán Aspuru-Guzik.

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Nature Machine Intelligence thanks Michael Hartmann, Sohaib Alam and Patrick Huembeli for their contribution to the peer review of this work.

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Supplementary Discussion, Table 1 and Figs. 1–8.

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Flam-Shepherd, D., Wu, T.C., Gu, X. et al. Learning interpretable representations of entanglement in quantum optics experiments using deep generative models. Nat Mach Intell 4, 544–554 (2022). https://doi.org/10.1038/s42256-022-00493-5

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