Demonstration of quantum logic gates in liquid crystal nuclear magnetic resonance

¹H-¹³C heteronuclear dipolar couplings are used to produce the NMR (nuclear magnetic resonance) version of a two bit controlled-NOT quantum logic gate. This gate is coupled with the Hadamard gate to complete a circuit which generates the Einstein-Podolsky-Rosen (EPR) state which is the maximally entangled state of a pair of spins. The EPR state is crucial for the potential exponential speed advantage of quantum computers over their classical counterparts. We sample the deviation density matrix of the two spin system to verify the presence of the EPR state. EPR state lifetimes are also measured with this technique, thereby demonstrating the viability of liquid crystals as a platform for quantum computing.