Algorithm implementation in quadrupole systems

Ermakov and Fung [19] reported an implementation of a continuous version of the Grover search algorithm in a system of / = 3/2 nuclei. 

Quantum simulation is one of the most promising and interesting area of quantum information. The proposal is to map the Hamiltonian of the system to be simulated onto the Hamiltonian of the system where the simulation will take place. There has been a number of reports on quantum simulations by NMR. The idea is to apply a sequence of radiofrequency pulses which transform the natural NMR Hamiltonian to simulate a different dynamics. In this section some implementations of simulations of interesting physical systems performed using NMR quantum computers are discussed. 

In 1999 Somaroo et al. [21] reported the first NMR implementation of a quantum simulation experiment a truncated harmonic oscillator. This is a classical problem, with many applications in physics. The quantum harmonic oscillator Hamiltonian is described by  

The authors used as qubits the two protons of 2,3-dibromothiophene. The first four levels of the harmonic oscillator are mapped to the spin energy levels as  

Tseng et al. [22] reported the NMR quantum simuiation of the non-physical three-body interaction problem. This involves a Hamiltonian of the type which can be 

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