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This study proves quantum advantages for learning quantum observables from classical data, a physically relevant task. It establishes boundaries for efficient classical learning versus scenarios needing quantum computation for data analysis in quantum many-body physics.

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Area of Science:

  • Quantum Computing
  • Machine Learning
  • Quantum Many-Body Physics

Background:

  • Classical machine learning can predict quantum system properties using classical data.
  • Previous quantum advantage claims were for non-physical tasks like cryptography.

Purpose of the Study:

  • To prove quantum advantages for learning quantum observables from classical data in physical scenarios.
  • To identify tasks where quantum computers are necessary for data analysis.

Main Methods:

  • Proved learning advantage for linear combinations of Pauli strings.
  • Extended results to unitarily parametrized observables.
  • Established classical hardness based on BQP simulation complexity.

Main Results:

  • Delineated sharp boundaries between classically learnable and quantum-necessary tasks.
  • Demonstrated a non-trivial quantum learning algorithm.
  • Showed quantum resources are useful for learning in quantum many-body physics.

Conclusions:

  • Quantum computers offer advantages for specific learning tasks in quantum physics.
  • Results guide practical applications of quantum learning.
  • Clarified the role of quantum resources in analyzing quantum many-body systems.