  Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ)
entangled state, we show that GHZ states of N-group qubits distributed in N
cavities can be created via a 3-step operation. The GHZ states of the N-group
qubits are generated by using N-group qutrits placed in the N cavities. Here,
"qutrit" refers to a three-level quantum system with the two lowest levels
representing a qubit while the third level acting as an intermediate state
necessary for the GHZ state creation. This proposal does not depend on the
architecture of the cavity-based quantum network and the way for coupling the
cavities. The operation time is independent of the number of qubits. The GHZ
states are prepared deterministically because no measurement on the states of
qutrits or cavities is needed. In addition, the third energy level of the
qutrits during the entire operation is virtually excited and thus decoherence
from higher energy levels is greatly suppressed. This proposal is quite general
and can in principle be applied to create GHZ states of many qubits using
different types of physical qutrits (e.g., atoms, quantum dots, NV centers,
various superconducting qutrits, etc.) distributed in multiple cavities. As a
specific example, we further discuss the experimental feasibility of preparing
a GHZ state of four-group transmon qubits (each group consisting of three
qubits) distributed in four one-dimensional transmission line resonators
arranged in an array.
