Improved algorithms for learning quantum Hamiltonians, via flat polynomials

Shyam Narayanan
7/5/2024
quant-phcs.DScs.LG

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Abstract

We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample complexity and runtime dependence to singly exponential in the inverse-temperature parameter, as opposed to doubly exponential. Our main technical contribution is a new flat polynomial approximation to the exponential function, with significantly lower degree than the flat polynomial approximation used in [BLMT24].

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Cite this paper

@article{narayanan2024improved,
  title  = {Improved algorithms for learning quantum Hamiltonians, via flat polynomials},
  author = {Shyam Narayanan},
  year   = {2024},
  eprint = {2407.04540},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2407.04540v1}
}

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