A proof is given that two-bit quantum gates are sufficient to construct any general quantum circuit, demonstrating their universality. This contrasts with previous results showing the universality of three-bit gates. The paper discusses the challenges of quantum computing, including the need for long quantum phase coherence times and the difficulty of isolating quantum systems from environmental interference. A "quantum gearbox" is proposed, which uses atomic-force microscope principles to enable two-bit gates with long coherence times. The paper also explores the feasibility of implementing two-bit gates using nuclear spins and magnetic resonance techniques. It shows that two-bit gates can be used to simulate three-bit operations, and that the Lie algebra of quantum gates can be generated using two-bit operations. The paper concludes that while two-bit gates are sufficient for universal quantum computation, practical implementation remains a challenge. The work highlights the importance of quantum coherence and the potential for new physics experiments in quantum computing.A proof is given that two-bit quantum gates are sufficient to construct any general quantum circuit, demonstrating their universality. This contrasts with previous results showing the universality of three-bit gates. The paper discusses the challenges of quantum computing, including the need for long quantum phase coherence times and the difficulty of isolating quantum systems from environmental interference. A "quantum gearbox" is proposed, which uses atomic-force microscope principles to enable two-bit gates with long coherence times. The paper also explores the feasibility of implementing two-bit gates using nuclear spins and magnetic resonance techniques. It shows that two-bit gates can be used to simulate three-bit operations, and that the Lie algebra of quantum gates can be generated using two-bit operations. The paper concludes that while two-bit gates are sufficient for universal quantum computation, practical implementation remains a challenge. The work highlights the importance of quantum coherence and the potential for new physics experiments in quantum computing.