From https://news.ycombinator.com/item?id=42030319 https://news.ycombinator.com/item?id=42030319 : > "Learning quantum Hamiltonians at any temperature in polyn

From https://news.ycombinator.com/item?id=42030319 https://news.ycombinator.com/item?id=42030319 : > "Learning quantum Hamiltonians at any temperature in polynomial time" (2024) https://arxiv.org/abs/2310.02243 https://arxiv.org/abs/2310.02243 re: the "relaxation technique" .. https://news.ycombinator.com/item?id=40396171 https://news.ycombinator.com/item?id=40396171 >> We fully resolve this problem, giving a polynomial time algorithm for learning H to precision ϵ from polynomially many copies of the Gibbs state at any constant β>0. >> Our main technical contribution is a new flat polynomial approximation to the exponential function, and a translation between multi-variate scalar polynomials and nested commutators. This enables us to formulate Hamiltonian learning as a polynomial system. We then show that solving a low-degree sum-of-squares relaxation of this polynomial system suffices to accurately learn the Hamiltonian. Relaxation (iterative method) https://en.wikipedia.org/wiki/Relaxation_(iterative_method) https://en.wikipedia.org/wiki/Relaxation_(iterative_method)