  Quantum teleportation enables networking participants to move an unknown
quantum state between the nodes of a quantum network, and hence constitutes an
essential element in constructing large-sale quantum processors with a quantum
modular architecture. Herein, we propose two protocols for teleporting qubits
through an N-node quantum network in a highly-entangled box-cluster state or
chain-type cluster state. The proposed protocols are systematically scalable to
an arbitrary finite number N and applicable to arbitrary size of modules. The
protocol based on a box-cluster state is implemented on a 14-qubit IBM quantum
computer for N up to 12. To identify faithful networking teleportation, namely
that the elements on real devices required for the networking teleportation
process are all qualified for achieving teleportation task, we quantify
quantum-mechanical processes using a generic classical-process model through
which any classical strategies of mimicry of teleportation can be ruled out.
From the viewpoint of achieving a genuinely quantum-mechanical process, the
present work provides a novel toolbox consisting of the networking
teleportation protocols and the criteria for identifying faithful teleportation
for universal quantum computers with modular architectures and facilitates
further improvements in the reliability of quantum-information processing.
