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arXiv:quant-ph/0608147 · Journal of Physics B Atomic Molecular and Optical Physics

Numerical simulation of a controlled–controlled-not (CCN) quantum gate in a chain of three interacting nuclear spins system

G V López, L Lara

Published Sep 12, 2006• 9 citations
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Abstract

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 $π$-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 ($J'/J$). We found that for $J'/J\ge 0.02$ we can have a well defined CCN quantum gate.

DOI
10.1088/0953-4075/39/18/019

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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 study the simulation of a single qubit rotation and Controlled-Not gate in a solid state one-dimensional chain of nuclear spins system interacting weakly through an Ising type of interaction with a modular component of the magnetic field in the z-direction, characterized by Bz(z,t)=Bo(z)cos⁡δtB_z(z,t)=Bo(z)\cosδtBz​(z,t)=Bo(z)cosδt. These qubits are subjected to electromagnetic pulses which determine the transition in the one or two qubits system. We use the fidelity parameter to determine the performance of the Not (N) gate and Controlled-Not (CNOT) gate as a function of the frequency parameter δδδ. We found that for ∣δ∣≤10−3MHz|δ|\le 10^{-3} MHz∣δ∣≤10−3MHz, these gates still have good fidelity.
We study the formation of an entangled state in a one-dimensional chain of three nuclear spins system which interact weakly through the Ising type of interaction and taking into account first and second neighbor interactions. We can get this entangled state using two pulses (π/2π/2π/2 and πππ pulses), and we study the efficiency of getting this entangled state 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≥0.04J'/J\ge 0.04J′/J≥0.04, the entangled state is well defined.
We study the simulation of a single qubit rotation and Controlled-Not gate in a solid state one-dimensional chain of nuclear spins system interacting weakly through an Ising type of interaction with a modular component of the magnetic field in the z-direction, characterized by Bz (z,t) = Bo(z) cos dt. These qubits are subjected to electromagnetic pulses which determine the transition in the one or two qubits system. We use the fidelity parameter to determine the performance of the Not (N) gate and Controlled-Not (CNOT) gate as a function of the frequency parameter S. We found that for |d| 10-3 MHz, these gates still have good fidelity.