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Communications in Theoretical Physics

Effects of Unequal Couplings on Fidelity of a Quantum Controlled-Controlled-Not Gate

Yin‐Zhong Wu, Shi Cui-Hua, Tao Pan, Zhen‐Ya Li

Published Jun 1, 2009• 0 citations
Publisher

Abstract

By numerically solving the Schodinger equation of a three-nuclear-spin system, the effects of the non-uniform nearest-neighbor (NN) interaction on the fidelity of a quantum controlled-controlled-not (CCN) gate are investigated for a digital initial state and a superposition initial state respectively. It is found from our simulation that the ratio of the deviation of the NN coupling δJ to the NN coupling J should be smaller than 0.0005 to ensure a high fidelity of the quantum CCN gate.

DOI
10.1088/0253-6102/51/6/14

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By numerically solving the Schodinger equation of a three-nuclear-spin system, the effects of the non-uniform nearest-neighbor (NN) interaction on the fidelity of a quantum controlled-controlled-not (CCN) gate are investigated for a digital initial state and a superposition initial state respectively. It is found from our simulation that the ratio of the deviation of the NN coupling δJ to the NN coupling J should be smaller than 0.0005 to ensure a high fidelity of the quantum CCN 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.
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 develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperature which is unlikely to be measured, and at high dissipation there is a difference which is likely to be measured at any temperature.
We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperature which is unlikely to be measured, and at high dissipation there is a difference which is likely to be measured at any temperature.