  In this paper, we consider the partial quantum consensus problem of a qubit
network in a distributed view. The local quantum operation is designed based on
the Hamiltonian by using the local information of each quantum system in a
network of qubits. We construct the unitary transformation for each quantum
system to achieve the partial quantum consensus, i.e., the directions of the
quantum states in the Bloch ball will reach an agreement. A simple case of
two-qubit quantum systems is considered first, and a minimum completing time of
reaching partial consensus is obtained based on the geometric configuration of
each qubit. Furthermore, we extend the approaches to deal with the more general
N-qubit networks. Two partial quantum consensus protocols, based on the
Lyapunov method for chain graphs and the geometry method for connected graphs,
are proposed. The geometry method can be utilized to deal with more general
connected graphs, while for the Lyapunov method, the global consensus can be
obtained. The numerical simulation over a qubit network is demonstrated to
verify the validity and the effectiveness of the theoretical results.
