Theoretical Framework for Quantum Information Processing Using Nitrogen-Vacancy Centres in Diamond Synthesised from Nigerian Carbon Sources

Nitrogen-vacancy centres in diamond are among the most promising qubit candidates for room-temperature quantum computing, quantum sensing, and quantum communication due to their long spin coherence times and optical addressability. Nigeria's coal and petroleum coke resources from the North East and South South regions offer potential feedstocks for chemical vapour deposition diamond synthesis, creating a pathway for domestic quantum materials production. This study develops a theoretical framework for quantum information processing using NV centres in diamond, focusing on coherent spin manipulation, entanglement generation, and decoherence mechanisms relevant to the specific nitrogen and 13C isotopic compositions achievable from Nigerian carbon feedstocks. The spin Hamiltonian including hyperfine, zero-field splitting, and Zeeman interactions is solved analytically under dynamic decoupling pulse sequences. A Lindblad master equation incorporating spectral density functions characterising phonon-induced decoherence is solved numerically to predict T1 and T2 coherence times as a function of isotopic purity and NV centre density. Optimal control theory is applied to design microwave pulse shapes maximising gate fidelity under realistic decoherence conditions. Results show that 12C isotopic enrichment above 99.8 percent achievable from petroleum coke feedstock should enable T2 coherence times exceeding 1 millisecond, sufficient for multi-qubit gate operation. Keywords: nitrogen-vacancy centre, diamond, quantum computing, coherence time, carbon feedstock