An Approximate Algorithm for Quantum Hamiltonian Identification with Complexity Analysis

Identification of the Hamiltonian is vital for characterizing the dynamical evolution of a quantum system. The dimension of a multi-qubit system increases exponentially with the qubit number, which usually leads to daunting computational complexity for general Hamiltonian identification algorithms. In this paper, we design an efficient quantum Hamiltonian identification method based on periodical sampling. The computational complexity is O(M² + MN²), where M is the number of unknown parameters to be identified in the Hamiltonian and N is the length of the sampling data. Numerical results with different data lengths demonstrate the effectiveness of the proposed identification algorithm.