The Implementation Of Multi-qubit Logic Gate In Coupled Cavities

The realization of quantum computers will grandly improve the ability of human's computing and solve the problem which the traditional computers can't.Similar to traditional computers,quantum computers realizing computing tasks need a series of quantum logic gates operation,and how to implement quantum logic gates became hot spots of scientific research.Studies have shown that general single qubit gates and two qubits gates are enough to implement any quantum algorithm.However,considering the system's complexity and sensitivity to the environment,we need to use multi-qubit gates to simplify the system.This paper,based on the above facts,studies how to implement Fredkin gate and Toffoli gate.In this paper,the main content is as follows:The first chapter introduces the concept of quantum computer,and emphatically introduces the important parts of a quantum computer,quantum logic gates.At the end of this chapter we raises the research emphasis and the main content of this paper.The second chapter introduces the related basic knowledge of quantum information and quantum optics.Firstly,we introduce the coupled cavities system connected by optical fiber and the directly coupled cavities system,mainly talking about the advantages of these two systems.Then we introduce the quantum Zeno effect.In this part,we makes a simple introduction of the history of quantum Zeno effect first.The quantum Zeno effect on mathematical intuitive half-experience form is presented.Then the Misra-Sudashan theory and the quantum Zeno effect strict deduction in mathematics are shown.Through extension of Misra-Sudarshan theory,this chapter introduces the concept of quantum Zeno subspace.Then the quantum Zeno effect is introduced in detail in the unitary measurement applications.Finally we put forward the continuous coupling cases of quantum Zeno effect.At the last,the reason why the invariant-based inverse engineering appears and the mathmatical framework based on the Lewis-Riesenfeld theory are presented.Then we introduce applications of this method in a two-level atom or a three-level atom case to effectively achieve the population inversion.This type of population transfer driven by this method overcomes the limit of the adiabatic process of time-dependent interaction need long time,and can achieve the targeted state at any time theoretically.The third chapter studies the implementation Fredkin gate.Three atoms are trapped in three different but directly coupled cavities in this scheme.The strictly numerical simulations are given,and the influences of cavity decay and spontaneous emission on the gate operation are analyzed with master equation.The result shows that our scheme is robust against atomic spontaneous emission because of the large detuning.The forth chapter studies the realization of Toffoli gate.We put forward two methods to implement Toffoli gate in direct coupled cavity.In the first one,two classical laser fields with fixed Rabi frequency are used via quantum Zeno dynamics.While in the second scheme,the invariant-based inverse engineering is used to implement the Toffoli gate,which can drive the instantaneous eigenstates to evolve exactly under the Schrodinger equation.The strictly numerical simulations are given and the influences of cavity decay and spontaneous emission on the Toffoli gate operation are analyzed with master equation,proving that our scheme is robust against to the influence of environment.The end of the text makes a summary and looks into the future.