Multiqubit logic gates in NMR quantum computing
Mark D. Price, Timothy F. Havel, David G. Cory · New Journal of Physics · 2000
Much of the current understanding of logic gates for quantum computation relies on the application of one- and two-qubit gates in order to implement a universal set of logic gates, as well as other gates. Such ideas stem from the notion that the Hamiltonians available for quantum computation are one or two-body processes. However, present day NMR implementations of quantum information processing (QIP) rely on the internal Hamiltonian of a liquid state system in which there are many two-body processes that occur simultaneously. Such use of the internal Hamiltonian allows for the creation of `multiqubit' logic gates, i.e. logic gates that operate on many qubits simultaneously and are more efficient than a sequence of one- and two-qubit rotations that effect the same operation. Such larger qubit operations offer a universal set of gates (even when not all couplings within the internal Hamiltonian are readily accessible) as well as more convenient and efficient implementations of the Hadamard transform, the controlled-NOT gate, and a quantum Fourier transform that scales linearly (assuming all couplings can be turned on and off at will).