4 - Introduction to NMR quantum computing

Abstract

This chapter discusses nuclear magnetic resonance (NMR) implementations of one- and two-qubit gates. This relies on the idea that a universal set of logical gates can be constructed only using one- and two-qubit gates. It means that only individual pair of qubits can be used to implement all necessary logic gates for quantum information processing (QIP) because the absence of three body interactions in nature prohibits the implementation of true multiqubit gates (logic gates that act in many qubits simultaneously). Deustch has demonstrated the existence of a set of universal three-qubit gates and it would be interesting to simulate such multiqubit gates. This can be achieved if there is a many particle system coupled by means of two-body interactions acting simultaneously. This is the case of NMR multi-spin system, where there are many spins interacting in pairs through direct dipolar couplings. The presence of such simultaneous two-body interactions can be further exploited to construct simulations of multiqubit gates that are more efficient than sets of one- and two-qubit gates. One example of such gates is the NMR implementation of the Toffoli gate, which uses much less pulses than the same operation constructed by combination of two-qubit operations.