Geometric quantum computation using fictitious spin-½ subspaces of strongly dipolar coupled nuclear spins

Gopinath, T. ; Anil Kumar, (2006) Geometric quantum computation using fictitious spin-½ subspaces of strongly dipolar coupled nuclear spins Physical Review A, 73 (2). 022326. ISSN 1050-2947

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Official URL: http://pra.aps.org/abstract/PRA/v73/i2/e022326

Related URL: http://dx.doi.org/10.1103/PhysRevA.73.022326

Abstract

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-½ 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 2π 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.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:72659
Deposited On:29 Nov 2011 03:57
Last Modified:29 Nov 2011 03:57

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