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Quantum state transfer is a very important process in building a quantumnetwork when information from flying Qubit is transferred to the stationaryQubit in a node via a quantum state transfer. NV centers due to their longcoherence time and the presence of nearby $13_C$ nuclear spin is an excellentcandidate for multi-Qubit quantum memory. Here we propose a theoreticaldescription for such a quantum state transfer from a cavity to a nearestneighbour $13_C$ nuclear spin of a single Nitrogen vacancy center in diamond;it shows great potential in realizing scalable quantum networks and quantumsimulation. The full Hamiltonian was considered with the zeroth-order andinteraction terms in the Hamiltonian and the theory of effective hamiltoniantheory was applied. We study the time evolution of the combined cavity-$13_C$state through analytical calculation and simulation using QuTip. Graphs forstate transfer and fidelity measurement are presented here. We show that ourtheoretical description verifies a high fidelity quantum state transfer fromthe cavity to $13_C$ center by choosing suitable system parameters.

Quantum State Transfer Between NV Center -- $13_C$ System Coupled To A CPW Cavity