Optimal learning of quantum Hamiltonians from high-temperature Gibbs states

Jeongwan Haah, Robin Kothari, Ewin Tang

We study the problem of learning a Hamiltonian $H$ to precision $\epsilon$, supposing we are given copies of its Gibbs state $\rho =\exp (-\beta H)/\mathrm{Tr}(\exp (-\beta H))$ at a know…