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Journal of Magnetic Resonance (1969)

Magnetic Double Resonance of a System of Two Spin- nuclei

Pietro Bucci, M Martinelli, S. Santucci, A.M Serra

Published Mar 1, 1972• 10 citations
Publisher
DOI
10.1016/0022-2364(72)90101-1

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Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1 , are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover’s algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1 and quadrupolar spin 3 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.
A quantum computer can be constructed from nuclear spins in a crystal lattice of a rare-earth monophosphide such as cerium-monophosphide (CeP). The 12 spin of a 31P nucleus can be used to represent a quantum bit (‘qubit’) with a relatively long relaxation time. In a CeP crystal lattice, 31P nuclei are periodically situated in three dimensions at distances of about 12Å. The application of a static magnetic field gradient in one direction causes differences in the Zeeman frequencies of separate nuclei. This allows thousands of distinct qubits to be individually addressed. Initializations of the qubits can be done efficiently by the Pound-Overhauser double resonance effect on the nuclear spins and the antiferromagnetically ordered 4f electron spins of cerium ions. Logic operations can be performed by simple pulse sequences, and computational results after logic operations can be measured by the nuclear magnetic resonance of neighboring nuclei, or the electron resonance of neighboring 4f electrons of cerium ions.