| Quantum computer, following the laws of quantum mechanics, is a physical devicewhich can be used to carry out high-speed math and logic operations, quantum informa-tion storage and processing. Quantum logic gate is the basic operation unit of quantumcomputer. By using quantum logic gate, quantum computer can control and operate theevolution and transmission of quantum state in the process of quantum information pro-cessing. In physical realization of quantum logic gate, a lot of substantial research workhas been done, and a considerable number of experimental results have been made. How-ever, these experiments are carried out in small-scale range, there is still a lot of workto do in realizing a large-scale effective quantum computing (quantum logic network).Therefore, researching on the suitable physical systems to perform quantum logic opera-tions effectively is the key for realization of quantum computer. In this paper, we studythe physical systems for realization of quantum computer theoretically. In ion-trap sys-tem, cavity QED system and ion trap-optical cavity system, we propose some theoreticalschemes to construct an important quantum logic gate - quantum phase gate. The feasi-bility of the proposed schemes is demonstrated by discussing fidelity, success probabilityand generation time.In ion-trap system, we propose two schemes for generation of unconventional geo-metric phase gate. The first scheme is based on the interaction of the trapped ions withtwo laser beams of different frequencies. Generation time t=2π/δonly depends on pa-rameterδ, a shorter generation time can be obtained by selecting parameterδto satisfy theconditionδ>>2π. The second scheme is based on resonance interaction of the trappedions with a standing-wave laser. Generation time t= 2π/v is only dependent of the fre-quency of the vibrational mode v. Under the same conditions, generation time for thesecond scheme is shorter than that based on non-resonance interaction of a standing-wavelaser with the ions[Phys. Rev. A, 2006, 74(3): 032322]. Due to the frequency of vibra-tional mode is at the magnitude of 109, generation time required in the second schemeis much shorter than that in the scheme for generation of geometric phase gate based onatomic resonance coupling with classical field in cavity QED system[Phys. Rev. A, 2006,73(3): 032344]. Therefore the second scheme possess some characteristics, such as a shorter generation time, a higher efficiency, a smaller impact of decoherence, and so on.In cavity QED, we propose a scheme for generation of an approximate multi-bitquantum phase gate based on nonidentical coupling of the three-level atoms with the cav-ity. Generation time doesn't rise with the increase of the number of qubits. Moreover,the generation time can be much shorter than atomic radiative lifetime and photon life-time by choosing some appropriate parameters. The atoms interact with a highly detunedcavity-field mode, quantum information doesn't transfer between atoms and cavity field,thus the in?uence of cavity decay is negligible. In the previous scheme that based onatom-cavity resonance interaction[Phys. Rev. A, 2007, 75(3): 034307], only when thecoupling constants satisfy the condition ??1 ? ??, a satisfied fidelity and success proba-bility can be obtained. While in our scheme, with the choice of a smaller odd number?? = ??2/??12(related to atoms-cavity coupling constants), the phase gate can be generatedwith a higher fidelity and a higher success probability in a shorter time. Therefore, ourscheme loosens the requirements for atoms-cavity coupling constants. Furthermore, anoutstanding feature of our scheme is the universal expressions of the fidelity and the suc-cess probability. Using the universal expressions we research on the factors that impacton the fidelity and success probability. The results show that different atoms-cavity cou-pling constants directly affect on generation time, fidelity and success probability whenthe number of qubits is fixed. Therefore we can construct a multi-bit quantum phase gatewith a shorter generation time, higher fidelity and higher success probability by control-ling different atoms-cavity coupling constants. We also study the in?uence of the numberof qubits ?? on fidelity and success probability. When the number of qubits ?? exceedscertain small values, the fidelity and success probability rise slowly with the increase ofthe number of qubits N. When N→∞, the fidelity and success probability infinitelyapproach 1, but never exceed 1. This is to say, the present scheme is suitable for gen-eration of a phase gate with more qubits. Implementing multi-qubit gates directly areessential in construction of quantum-computing networks in view of shortening gate timeand reducing the operation complexity. Especially for a larger number of qubits, the pro-cedure for implementation of many elementary gates in obtaining a multi-qubit gate isextraordinarily complicated and a longer gate time is required.In ion trap-optical cavity system, we propose a scheme to generate an unconven-tional geometric phase via the interaction of the trapped ions with the lasers and the quan- tized cavity field. Generation time is expressed as t = 2π/Δ= 2π/(ω0-ωc-v). Wecan tune ion transition frequencyω0, cavity mode frequencyωc, and vibrational modefrequency v, appropriately, to ensure that not only the restrictive condition v,ωc>>Δ,Ω,and g is satisfied but also the value forΔis large enough so that the generation time isshorter than the coherence time of qubits and decay time of the optical cavity. Thereforethe influences of ion decoherence and decay of optical cavity are negligible. The inno-vation of our scheme is that we use creation operators and elimination operators of ionvibrational mode and cavity mode to construct a two-mode squeezed operator and use thesqueezed operator to generalize unconventional geometric phase shift. Compared withusual scheme based on displacement operator, the present scheme possesses some advan-tages in reducing quantum noise of a quantum system due to squeezed operator can lowerquantum fluctuations of a quadrature component below vacuum level in phase space ofsqueezed parameters. Therefore the present scheme plays an important role in exploringof the physics systems for quantum computing with a small impact of decoherence.
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