Ensemble quantum-information processing by NMR: implementation of gates and the creation of pseudopure states using dipolar coupled spins as qubits

Abstract

Quantum-information processing is carried out using dipolar coupled spins and high-resolution nuclear magnetic resonance (NMR). The systems chosen are the dipolar coupled methyl protons of CH₃CN partially oriented in a liquid crystalline matrix yielding a two-qubit system and dipolar coupled ¹³C and methyl protons of ¹³CH₃CN also partially oriented in the liquid crystalline matrix, yielding a three-qubit system. The dipolar coupled protons of oriented CH₃ group are chemically and magnetically identical and their eigenstates can be divided into a set of quartet states (symmetric A) and a pair of doublet (E) states. We describe here a method for selectively retaining the magnetization of the symmetric states, yielding two and three qubit systems. We create pseudopure states using single-quantum-transition selective pulses and implement two- and three-qubit gates using one- and two-dimensional NMR.