Learning quantum Hamiltonians at any temperature in polynomial time with Chebyshev and bit complexity
<|reference_start|>Learning quantum Hamiltonians at any temperature in polynomial time with Chebyshev and bit complexity: We consider the problem of learning local quantum Hamiltonians given copies of their Gibbs state at a known inverse temperature, following Haah et al. [2108.04842] and Bakshi et al. [arXiv:2310.02243]. Our main technical contribution is a new flat polynomial approximation of the exponential function based on the Chebyshev expansion, which enables the formulation of learning quantum Hamiltonians as a polynomial optimization problem. This, in turn, can benefit from the use of moment/SOS relaxations, whose polynomial bit complexity requires careful analysis [O'Donnell, ITCS 2017]. Finally, we show that learning a $k$-local Hamiltonian, whose dual interaction graph is of bounded degree, runs in polynomial time under mild assumptions.<|reference_end|>
@article{wodecki2024learning,
    title={Learning quantum Hamiltonians at any temperature in polynomial time with
  Chebyshev and bit complexity},
    author={Ales Wodecki and Jakub Marecek},
    journal={arXiv preprint arXiv:2402.05552},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.05552},
    primaryClass={quant-ph cs.LG math.OC}
}