Abstract
We demonstrate how one can use machine learning techniques to bypass the technical difficulties of designing an experiment and translating its outcomes into concrete claims about fundamental features of quantum fields. In practice, all measurements of quantum fields are carried out through local probes. Despite measuring only a small portion of the field, such local measurements have the capacity to reveal many of the field’s global features. This is because, when in equilibrium with their environments, quantum fields store global information locally, albeit in a scrambled way. We show that neural networks can be trained to unscramble this information from data generated from a very simple one-size-fits-all local measurement protocol. To illustrate this general claim we will consider three non-trivial features of the field as case studies: a) how, as long as the field is in a stationary state, a particle detector can learn about the field’s boundary conditions even before signals have time to propagate from the boundary to the detector, b) how detectors can determine the temperature of the quantum field even without thermalizing with it, and c) how detectors can distinguish between Fock states and coherent states even when the first and second moments of all their quadrature operators match. Each of these examples uses the exact same simple fixed local measurement protocol and machine-learning ansatz successfully. This supports the claim that the framework proposed here can be applied to nearly any kind of local measurement on a quantum field to reveal nearly any of the field’s global properties in a one-size-fits-all manner.
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Acknowledgments
The authors would like to thank Luis J. Garay for enlightening discussions. DG acknowledges support by NSERC through a Vanier Scholarship. JPG acknowledges support by a Mike and Ophelia Lazaridis Fellowship. JPG also acknowledges the support of a fellowship from “La Caixa” Foundation (ID 100010434, code LCF/BQ/AA20/11820043). EMM acknowledges support through the Discovery Grant Program of the Natural Sciences and Engineering Research Council of Canada (NSERC). EMM also acknowledges support of his Ontario Early Researcher award. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Industry Canada and by the Province of Ontario through the Ministry of Colleges and Universities. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET:www.sharcnet.ca) and Compute/Calcul Canada.
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Grimmer, D., Melgarejo-Lermas, I., Polo-Gómez, J. et al. Decoding quantum field theory with machine learning. J. High Energ. Phys. 2023, 31 (2023). https://doi.org/10.1007/JHEP08(2023)031
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DOI: https://doi.org/10.1007/JHEP08(2023)031