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Provably efficient machine learning for quantum many-body problems

Journal Article · · Science
 [1];  [2];  [3];  [4];  [5]
  1. Institute for Quantum Information and Matter and Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA.
  2. Institute for Integrated Circuits, Johannes Kepler University, Linz, Austria.
  3. AWS Center for Quantum Computing, Pasadena, CA, USA.
  4. Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, College Park, MD, USA.
  5. Institute for Quantum Information and Matter and Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA.; AWS Center for Quantum Computing, Pasadena, CA, USA.
+ Show Author Affiliations

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0020290; NA0003525
OSTI ID:
1980736
Journal Information:
Science, Vol. 377, Issue 6613; ISSN 0036-8075
Publisher:
AAAS
Country of Publication:
United States
Language:
English

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