Orbit consensus of quantum networks based on interaction design

For a general quantum network system with a non-zero Hamiltonian H composed of n identical m-level quantum subsystems, any symmetric consensus state in the interaction picture exactly corresponds to an orbit in the Schrödinger picture, which is called the H-orbit of the symmetric consensus state. By using the interaction picture transformation and the tool of the LaSalle invariance principle, this paper analyzes the orbit consensus of this quantum network and designs the corresponding swapping operators such that the system converges to the H-orbit of the target symmetric consensus state that exists in the interaction picture. In particular, we prove the convergence of the quantum network to the H-orbit when the quantum interaction graph is connected and the system Hamiltonian is permutation invariant. The orbit consensuses of a four-qubit network system and a quantum network of three identical three-level subsystems are achieved numerically, which verifies the correctness of our theoretical results and the effectiveness of the designed swapping operators.