Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Numerical simulation of a Controlled-Controlled-Not (CCN) quantum gate in a chain of three interacting nuclear spins system

Gustavo V. López, Lorena Lara

Published Jan 1, 2006• 13 citations
OpenAlex

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 $\\pi$-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.

Related papers

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

G V López, L Lara

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.

arXiv:quant-ph/0608147•Journal of Physics B Atomic Molecular and Optical Physics•Sep 12, 2006•9 citations

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

Yin‐Zhong Wu, Shi Cui-Hua, Tao Pan +1 more

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.

Communications in Theoretical Physics•Jun 1, 2009•0 citations

Modular magnetic field on the z-direction on a chain of nuclear spin system and quantum Not and Controlled-Not gates

Gustavo V. López, Manuél Ávila

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 $B_z(z,t)=Bo(z)\cosδt$. 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 $δ$. We found that for $|δ|\le 10^{-3} MHz$, these gates still have good fidelity.

arXiv:1205.6449•Mar 2, 2012•0 citations

Effects on the quantum not and controlled-not gates of a modular magnetic field in the z-direction in a chain of nuclear spin system

Gustavo V. López, Manuél Ávila

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.

Revista Mexicana de Física•Aug 15, 2011•0 citations

Dynamics of a Control-Not gate for a quantum system of two weakly interacting spins

G. P. Berman, David K Campbell, G. D. Doolen +2 more

Abstract We present the results of computer simulations of dynamics of the quantum Control-Not gate for the system of two spins connected by a weak Ising interaction. It is demonstrated that, for both “digital” and “superposition” initial conditions, 3 resonant π-pulse can provide an adequate implementation of the quantum Control-Not gate. We also consider the influence of slightly non-resonant π-pulse and noise on the dynamics of the quantum Control-Not gate.

Physica B Condensed Matter•Sep 1, 1997•10 citations

Simulation of an entangled state in a chain of three nuclear spins system

Gustavo V. López, Lorena Lara

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 ($π/2$ and $π$ 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 ($J'/J$). We found that for $J'/J\ge 0.04$, the entangled state is well defined.

arXiv:quant-ph/0608191•Aug 24, 2006•0 citations
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.
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 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.
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.