Improved algorithms for learning quantum Hamiltonians, via flat polynomials
<|reference_start|>Improved algorithms for learning quantum Hamiltonians, via flat polynomials: 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].<|reference_end|>
@article{narayanan2024improved,
    title={Improved algorithms for learning quantum Hamiltonians, via flat
  polynomials},
    author={Shyam Narayanan},
    journal={arXiv preprint arXiv:2407.04540},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.04540},
    primaryClass={quant-ph cs.DS cs.LG}
}