TY - JOUR
T1 - Geometric quantum computation using fictitious spin- 1 2 subspaces of strongly dipolar coupled nuclear spins
AU - Gopinath, T.
AU - Kumar, Anil
PY - 2006
Y1 - 2006
N2 - Geometric phases have been used in NMR to implement controlled phase shift gates for quantum-information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems by using nonadiabatic geometric phases, obtained by evolving the magnetization of fictitious spin- 1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete 2Ï€ rotation. A detailed theoretical explanation of nonadiabatic geometric phases in NMR is given by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm, and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.
AB - Geometric phases have been used in NMR to implement controlled phase shift gates for quantum-information processing, only in weakly coupled systems in which the individual spins can be identified as qubits. In this work, we implement controlled phase shift gates in strongly coupled systems by using nonadiabatic geometric phases, obtained by evolving the magnetization of fictitious spin- 1/2 subspaces, over a closed loop on the Bloch sphere. The dynamical phase accumulated during the evolution of the subspaces is refocused by a spin echo pulse sequence and by setting the delay of transition selective pulses such that the evolution under the homonuclear coupling makes a complete 2Ï€ rotation. A detailed theoretical explanation of nonadiabatic geometric phases in NMR is given by using single transition operators. Controlled phase shift gates, two qubit Deutsch-Jozsa algorithm, and parity algorithm in a qubit-qutrit system have been implemented in various strongly dipolar coupled systems obtained by orienting the molecules in liquid crystal media.
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U2 - 10.1103/PhysRevA.73.022326
DO - 10.1103/PhysRevA.73.022326
M3 - Article
AN - SCOPUS:33144463302
SN - 1050-2947
VL - 73
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 2
M1 - 022326
ER -