Maximum-likelihood-estimate Hamiltonian learning via efficient and robust quantum likelihood gradient

Given the recent developments in quantum techniques, modeling physical Hamiltonian of a target many-body system is becoming an increasingly practical and vital research direction. Here, we propose efficient strategy combining maximum likelihood estimation, gradient descent, algorithms. measurement outcomes, optimize model density operator via series descents along gradient, which prove negative semi-definite with respect to negative-log-likelihood function. In addition such optimization efficiency, our maximum-likelihood-estimate learning respects locality given system, therefore, extends readily larger systems available Compared previous approaches, it also exhibits better accuracy overall stability toward noises, fluctuations, temperature ranges, demonstrate various examples.