While quantum information processing by nuclear magnetic resonance (NMR) with
small number of qubits is well established, implementation of lengthy
computations have proved to be difficult due to decoherence/relaxation. In such
circumstances, shallow circuits (circuits using parallel computation) may prove
to be realistic. Parity and fanout gates are essential to create shallow
circuits. In this article we implement inversion-on-equality gate, followed by
parity gate and fanout gate in 3-qubit systems by NMR, using evolution under
indirect exchange coupling Hamiltonian.Comment: 24 pages, 7 figure