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Journal of Sichuan University

Realization of Universal Single Qubit Logic Gate

Shun-Jin Wang

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The auathors investigate a particle with spin-1/2 moving in a time-dependent magnetic field. The system has an SU(2) algebraic structure. Using algebraic dynamical method, authors have obtained the rigorous analytical solution to the time dependent Schroedinger equation. Based on the analytical solution, authors have realize the universal single qubit logic gate controlled by the amplitude and frequency of magnetic field and the six special single qubit gates are realized as well.

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Chinese Physics Letters•Mar 1, 2008•2 citations
The auathors investigate a particle with spin-1/2 moving in a time-dependent magnetic field. The system has an SU(2) algebraic structure. Using algebraic dynamical method, authors have obtained the rigorous analytical solution to the time dependent Schroedinger equation. Based on the analytical solution, authors have realize the universal single qubit logic gate controlled by the amplitude and frequency of magnetic field and the six special single qubit gates are realized as well.
We investigate an annular spin cluster made of three particles with anisotropic Heisenberg-chain controlled by a time-dependent magnetic field. The system has an SU(2) algebraic structure. Using algebraic dynamical method, we have obtained the exact analytical solution to the time dependent Schrdinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and consequently six special single qubit logic gates can be realized.
We investigate an anisotropic Heisenberg spin cluster with five particles controlled by a time-dependent magnetic field. With the algebraic dynamical method, we obtain the exact analytical solution to the time dependent Schrödinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and the six special single qubit logic gates can be realized physically. We also discuss the anti-decoherence property of the qubit and its logic gates resulted from particle coupling effect and collectivity of the cluster.
We study the low energy states of one-dimensional spin chain clusters consisting of three spin-1/2 Heisenberg particles. When applying an external magnetic field on the spin chain cluster, the ground state doublet will generate Zeeman splitting. As a two-level quantum system, the split ground state doublet can be defined as a new 'spin cluster qubit'. The cluster quibit is shown to be more robust with a smaller decoherence rate. We realize universal single-qubit gates with the algebraic dynamical method, by applying a time-dependent magnetic field on the spin cluster. We also investigate a two-qubit system made up of two such Heisenberg spin chain clusters which interact through a tunable Heisenberg coupling. In the two-qubit product basis, the controlled quantum phase gates can be generated by applying a magnetic field along the z-axis on the system of the two clusters. One can realize the controlled-NOT gate through a three-step time evolution by adjusting the corresponding physical parameters. Our scheme involves two kinds of dynamically distinct operations, which is much simpler and more feasible.
Based on the semi-classical theory of the interaction between light and matter, we propose an effective scheme for describing the realization of single quantum gates. The rigorous analytical solution for the resonant system, in which the double ultra-short powerful laser pulses with accurately controllable relative phase difference will interact with the atoms, is obtained by solving the time-dependent Schrödinger equation. According to the corresponding solution, we deduce the systematic matrix expression of unitary transformation. Universal quantum logic gates are all implemented theoretically by means of regulating properly the laser pulses' intensity and its relative phase difference as well as the optic detuning. This method also proves practical in terms of its comparably easier manipulation.
We investigate a Heisenberg spin cluster with two particles controlled by a time-dependent magnetic field. The system is controlled by tuning the amplitude, frequency, and interaction time of the three-step time-dependent magnetic field. Then we solve the time-dependent Schrödinger equation of the two-particle system, and obtain the time evolution operator. By the three-timestep interaction, the wavefunction evolves from the initial state to the final state, and the total evolution operator can be expressed as a product of the three evolution operators. By adjusting the physical parameters, the key two-qubit logic gate, the C-Not gate, can be realized physically.