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

arXiv:quant-ph/9802013

Generalized Quantum Control-Not Gate in Two-Spin Ising System

G. P. Berman, Gary D. Doolen, Gustavo V. López, V. I. Tsifrinovich

Published Feb 3, 1998• 5 citations
arXivHTMLPDF

Abstract

The physical implementation of the quantum Control-Not gate for a two-spin system is investigated numerically. The concept of a generalized quantum Control-Not gate, with arbitrary phase shift, is introduced. It is shown that a resonant $π$-pulse provides a simple example of a generalized quantum Control-Not gate.

DOI
10.48550/arxiv.quant-ph/9802013

Related papers

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

Dynamics of a quantum control-not gate for an ensemble of four-spin molecules at room temperature

G. P. Berman, Gary D. Doolen, Gustavo V. López +1 more

We investigate numerically a single-electromagnetic-pulse implementation of a quantum control-not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time evolution of the density matrix for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of a quantum CN gate in this system at finite temperature, using a single electromagnetic \ensuremath{\pi} pulse. We also study the quantum dynamics of creating entangled states in a macroscopic paramagnetic spin system at low temperatures, and compare the related quantum and corresponding classical dynamics. In the quantum case, one can create entangled states using a resonant interaction between the spin system and the electromagnetic \ensuremath{\pi} pulse. In the classical limit, the interaction of the spin system with the same pulse becomes nonresonant and the corresponding classical dynamics differs significantly from the quantum dynamics. This difference in the behavior of the macroscopic magnetization can be used in experiments as an indication of the existence of entangled states.

arXiv:quant-ph/9802016•Physical review. B, Condensed matter•Nov 1, 1998•4 citations

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

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

Gustavo V. López, Lorena 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 $\\pi$-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.

•Jan 1, 2006•13 citations

Universal quantum control in zero-field nuclear magnetic resonance

Ji Bian, Min Jiang, Jiangyu Cui +7 more

This paper describes a general method for the manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spin-spin couplings. For spin-$\frac{1}{2}$ nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary single-qubit gates and a two-qubit controlled-not gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology, quantum information processing, and fundamental physics.

arXiv:1705.02064•Physical Review A•May 23, 2017•23 citations

NON-ADIABATIC ARBITRARY GEOMETRIC PHASE GATE IN 2-QUBIT SPIN MODEL

YU TONG

We study a 2-qubit spin model for the possibility of realizing an arbitrary geometric quantum phase gate in terms of a single coherent magnetic pulse with multi-harmonic frequency. Using resonant transition approximation, the time-dependent Hamiltonian of two coupled spins can be solved analytically. The time evolution of the wave function is obtained without adiabatic approximation. The parameters of magnetic pulse, such as the frequency, amplitude, phase of each harmonic part as well as the time duration of the pulse are determined for achieving an arbitrary non-adiabatic geometric phase gate. The requirement of materials for realizing such a gate is analyzed. As a result, the non-adiabatic geometric controlled phase gates and A–A phase are also addressed.

arXiv:quant-ph/0607041•Modern Physics Letters B•Jun 20, 2007•0 citations
The physical implementation of the quantum Control-Not gate for a two-spin system is investigated numerically. The concept of a generalized quantum Control-Not gate, with arbitrary phase shift, is introduced. It is shown that a resonant πππ-pulse provides a simple example of a generalized quantum Control-Not gate.
We investigate numerically a single-electromagnetic-pulse implementation of a quantum control-not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin ``molecules'' we simulate the time evolution of the density matrix for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of a quantum CN gate in this system at finite temperature, using a single electromagnetic \ensuremath{\pi} pulse. We also study the quantum dynamics of creating entangled states in a macroscopic paramagnetic spin system at low temperatures, and compare the related quantum and corresponding classical dynamics. In the quantum case, one can create entangled states using a resonant interaction between the spin system and the electromagnetic \ensuremath{\pi} pulse. In the classical limit, the interaction of the spin system with the same pulse becomes nonresonant and the corresponding classical dynamics differs significantly from the quantum dynamics. This difference in the behavior of the macroscopic magnetization can be used in experiments as an indication of the existence of entangled states.
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.
This paper describes a general method for the manipulation of nuclear spins in zero magnetic field. In the absence of magnetic fields, the spins lose the individual information on chemical shifts and inequivalent spins can only be distinguished by nuclear gyromagnetic ratios and spin-spin couplings. For spin-12\frac{1}{2}21​ nuclei with different gyromagnetic ratios (i.e., different species) in zero magnetic field, we describe the scheme to realize a set of universal quantum logic gates, e.g., arbitrary single-qubit gates and a two-qubit controlled-not gate. This method allows for universal quantum control in systems which might provide promising applications in materials science, chemistry, biology, quantum information processing, and fundamental physics.
We study a 2-qubit spin model for the possibility of realizing an arbitrary geometric quantum phase gate in terms of a single coherent magnetic pulse with multi-harmonic frequency. Using resonant transition approximation, the time-dependent Hamiltonian of two coupled spins can be solved analytically. The time evolution of the wave function is obtained without adiabatic approximation. The parameters of magnetic pulse, such as the frequency, amplitude, phase of each harmonic part as well as the time duration of the pulse are determined for achieving an arbitrary non-adiabatic geometric phase gate. The requirement of materials for realizing such a gate is analyzed. As a result, the non-adiabatic geometric controlled phase gates and A–A phase are also addressed.