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Learning models of quantum systems from experiments

Nature Physics volume 17, pages 837–843 (2021)Cite this article

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Abstract

As Hamiltonian models underpin the study and analysis of physical and chemical processes, it is crucial that they are faithful to the system they represent. However, formulating and testing candidate Hamiltonians for quantum systems from experimental data is difficult, because one cannot directly observe which interactions are present. Here we propose and demonstrate an automated protocol to overcome this challenge by designing an agent that exploits unsupervised machine learning. We first show the capabilities of our approach to infer the correct Hamiltonian when studying a nitrogen-vacancy centre set-up. In preliminary simulations, the exact model is known and is correctly inferred with success rates up to 59%. When using experimental data, 74% of protocol instances retrieve models that are deemed plausible. Simulated multi-spin systems, characterized by a space of 1010 possible models, are also investigated by incorporating a genetic algorithm in our protocol, which identifies the target model in 85% of instances. The development of automated agents, capable of formulating and testing modelling hypotheses from limited prior assumptions, represents a fundamental step towards the characterization of large quantum systems.

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Fig. 1: Overview of the QMLA protocol and its principal subroutines.
Fig. 2: QMLA results for simulated and experimental data, describing a NV centre system.
Fig. 3: QMLA applied to systems composed of several interacting spins implementing various exploration strategies.

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Data availability

Data and analysis scripts are available at https://figshare.com/s/caf2581da7eb2414fc7f. The data are presented in CSV format with analysis in Python using Pandas and NumPy libraries.

Code availability

Our code, written in Python and implemented via the Portable Batch System for parallel processing, is available at https://github.com/flynnbr11/QMLA, with documentation at https://quantum-model-learning-agent.readthedocs.io/en/latest/.

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Acknowledgements

We thank C. Bonato, F. Jelezko, F. Marquardt, T. Fösel, C. Woods, J. Wang, M. G. Thompson, A. Paiement, A. Cimarelli, P. Yard and J. Bulmer for useful discussions and feedback. A.A.G., S.K., S.P. and R.S. acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC), programme grant no. EP/L024020/1. B.F. acknowledges support from Airbus and EPSRC grant EP/P510427/1. N.W. was funded by a grant from Google Quantum AI, the NQI center for Quantum Co-Design, the Pacific Northwest National Laboratory LDRD programme and the ‘Embedding Quantum Computing into Many-Body Frameworks for Strongly Correlated Molecular and Materials Systems’ project, funded by the US Department of Energy (DOE). J.G.R. acknowledges support from EPSRC (EP/M024458/1). A.L. acknowledges fellowship support from EPSRC (EP/N003470/1). This work is supported by the UK Hub in Quantum Computing and Simulation, part of the UK National Quantum Technologies Programme with funding from UKRI EPSRC grant no. EP/T001062/1, and by the European project QuCHIP (Quantum Simulation on a Photonic Chip; grant agreement no. 641039). This work was carried out using the computational facilities of the Advanced Computing Research Centre, University of Bristol (http://www.bristol.ac.uk/acrc/).

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Author notes

  1. These authors contributed equally: Antonio A. Gentile, Brian Flynn, Sebastian Knauer, Raffaele Santagati.

Authors and Affiliations

  1. Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, Bristol, UK

    Antonio A. Gentile, Brian Flynn, Sebastian Knauer, Stefano Paesani, John G. Rarity, Raffaele Santagati & Anthony Laing

  2. Qu & Co BV, Amsterdam, The Netherlands

    Antonio A. Gentile

  3. Quantum Engineering Centre for Doctoral Training, University of Bristol, Bristol, UK

    Brian Flynn

  4. Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, New South Wales, Australia

    Sebastian Knauer

  5. Department of Physics, University of Washington, Seattle, WA, USA

    Nathan Wiebe

  6. Pacific Northwest National Laboratory, Richland, WA, USA

    Nathan Wiebe

  7. Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA, USA

    Christopher E. Granade

  8. International Iberian Nanotechnology Laboratory (INL), Braga, Portugal

    Raffaele Santagati

  9. Boehringer-Ingelheim Quantum Lab, Wien, Austria

    Raffaele Santagati

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Contributions

R.S., A.A.G. and N.W. conceived the methodology. B.F., A.A.G. and R.S. performed simulations with support from N.W., S.P. and C.E.G. S.K. built the set-up and performed the experiments under the guidance of J.G.R. A.A.G., R.S., B.F. and S.P. analysed and interpreted the data with support from N.W., S.K. and C.E.G. A.A.G., R.S., B.F., S.K., N.W., S.P., C.E.G. and A.L. wrote the manuscript. R.S. and A.L. supervised the project.

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Correspondence to Raffaele Santagati.

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Peer review information Nature Physics thanks Dong-Ling Deng and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Figs. 1–7, discussion and analysis, Tables 1 and 2.

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Gentile, A.A., Flynn, B., Knauer, S. et al. Learning models of quantum systems from experiments. Nat. Phys. 17, 837–843 (2021). https://doi.org/10.1038/s41567-021-01201-7

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