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Journal of Optics B Quantum and Semiclassical Optics

Numerical simulation of a quantum controlled-not gate implemented on four-spin molecules at room temperature

G V L pez, Jorge Ramon Vergara Quezada, G. P. Berman, G. D. Doolen, V. I. Tsifrinovich

Published Mar 31, 2003• 8 citations
Publisher

Abstract

We study numerically the non-resonant effects on four-spin molecules at room temperature with the implemented quantum controlled-not gate and using the 2π k method. The four nuclear spins in each molecule represent a four-qubit register. The qubits interact with each other through Ising-type interaction which is characterized by the coupling constant J a , b . We study the errors on the reduced density matrix as a function of the Rabi frequency, Ω, using the 2π k method and when all the coupling constants are equal or when one of them is different from the others.

DOI
10.1088/1464-4266/5/2/311

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We study numerically the non-resonant effects on four-spin molecules at room temperature with the implemented quantum controlled-not gate and using the 2π k method. The four nuclear spins in each molecule represent a four-qubit register. The qubits interact with each other through Ising-type interaction which is characterized by the coupling constant J a , b . We study the errors on the reduced density matrix as a function of the Rabi frequency, Ω, using the 2π k method and when all the coupling constants are equal or when one of them is different from the others.
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We present the study of a quantum Controlled-Controlled-Not gate, implemented in a chain of three nuclear spins weakly Ising interacting between all of them, that is, taking into account first and second neighbor spin interactions. This implementation is done using a single resonant pi\\pipi-pulse on the initial state of the system (digital and superposition). The fidelity parameter is used to determine the behavior of the CCN quantum gate as a function of the ratio of the second neighbor interaction coupling constant to the first neighbor interaction coupling constant (J′/JJ'/JJ′/J). We found that for J′/Jge0.02J'/J\\ge 0.02J′/Jge0.02 we can have a well defined CCN quantum gate.
We present the study of a quantum Controlled-Controlled-Not gate, implemented in a chain of three nuclear spins weakly Ising interacting between all of them, that is, taking into account first and second neighbor spin interactions. This implementation is done using a single resonant πππ-pulse on the initial state of the system (digital and superposition). The fidelity parameter is used to determine the behavior of the CCN quantum gate as a function of the ratio of the second neighbor interaction coupling constant to the first neighbor interaction coupling constant (J′/JJ'/JJ′/J). We found that for J′/J≥0.02J'/J\ge 0.02J′/J≥0.02 we can have a well defined CCN quantum gate.
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We implement Grover's quantum search algorithm on a nuclear spin-chain quantum computer, taking Ising-type interactions between nearest and second-nearest neighbours into account. The performance of this implementation is studied by numerical simulations with four spins. We determine the temporal behaviour of the fidelity during the algorithm, and we compute the final fidelity as a function of the Rabi frequency. For the latter, we obtain pronounced maxima at frequencies which fulfil the condition of the 2π k -method with respect to the second-nearest- neighbour interactions.