Practical algorithm for determining Hamiltonian identifiability

We demonstrate a practical algorithm for determining the identifiability of Hamiltonian parameters with local accessibility. We consider the problem of estimating the parameters of the Hamiltonian of one-dimensional spin chain systems with nearest-neighbor interaction and assume that we only have access to a single quantum probe coupled to the target system. We demonstrate a practical implementation of Hamiltonian identifiability by the eigensystem realization algorithm and Gröbner basis. Furthermore, we also provide a practical code to estimate the Hamiltonian parameters from the experimental results. XH and RG equally contributed to this work.