We propose an experimentally feasible scheme to achieve quantum computation based on a pair of orthogonal cyclic states. In this scheme, quantum gates can be implemented based on the total phase accumulated in cyclic evolutions. In particular, geometric quantum computation may be achieved by eliminating the dynamic phase accumulated in the whole evolution. Therefore, both dynamic and geometric operations for quantum computation are workable in the present theory. Physical implementation of this set of gates is designed for NMR systems. Also interestingly, we show that a set of universal geometric quantum gates in NMR systems may be realized in one cycle by simply choosing specific parameters of the external rotating magnetic fields. In addition, we demonstrate explicitly a multi-loop method to remove the dynamic phase in geometric quantum gates.

We explore theoretically the single-photon transport in a single-mode waveguide that is coupled to a hybrid atom-optomechanical system in a strong optomechanical coupling regime. Using a full quantum real-space approach, transmission and reflection coefficients of the propagating single-photon in the waveguide are obtained. The influences of atom-cavity detuning and the dissipation of atom on the transport are also studied. Intriguingly, the obtained spectral features can reveal the strong light-matter interaction in this hybrid system.

A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multi-loop approach is used to remove the dynamical phase accumulated in the operation process for geometric quantum gates. More intriguingly, we here illustrate in detail how to use a special single-loop method to remove the dynamical phase and thus to construct a set of universal quantum gates based on the nonadiabatic geometric phase shift. The present scheme is applicable to NMR systems and may be feasible in other physical systems.PACS numbers: 03.67. Lx, 03.65.Vf Quantum computers have been attracting more and more interests as they are illustrated to be capable of tackling efficiently certain problems that are intractable for classical computers [1]. Significant progress has recently been achieved in the field of quantum computing. Nevertheless, there are still many difficulties and challenges in physical implementation of quantum computation. The infidelity of quantum gates is one of them; to suppress the infidelity to a acceptable level is essential to construct workable quantum logical gates in a scalable quantum computer. Recently, a promising approach based on geometric phases[2, 3, 4] was proposed to achieve built-in fault-tolerant quantum gates with higher fidelities [5,6,7,8,9, 10] since the geometric phase depends only on the global feature of the evolution path and is believed to be robust against local fluctuations. The geometric quantum computation(GQC) and its physical implementation were addressed for NMR systems [8,9], Josephson junctions [6,10], and trapped ions [7].Theoretically, under the so-called adiabatic condition, one can construct a pure geometric phase quantum gate based on adiabatic geometric phase [8]. However, the adiabatic condition is not satisfied in many realistic cases because the long operation time is required, and thus it is hard to experimentally realize quantum computation with adiabatic evolutions, particularly for solid state systems whose decoherence time is quite short. To overcome this disadvantage, it was proposed to use the nonadiabatic cyclic geometric phase(AA phase) to construct geometric quantum gates [9,10]. These gates have not only the faster gate-operation time, but also intrinsic geometric features of the geometric phase. For a nonadiabatic cyclic evolution, the total phase difference between the final and initial states usually consists of both the geometric and dynamical phases. Therefore, to get the nonadiabatic geometric phase, we need to remove the * Electronic address: zwang@hkucc.hku.hk dynamical component. An interesting idea is to choose the cyclic evolution in dark states [7]: dark states have a zero energy eigenvalue for the effective Hamiltonian, and thus its dynamical phase will always be zero during the evolution. Another useful method to remove the dynamical phase is a so-called multi-loop scheme [8,10,11], in which the evolution is driven by the Hamiltonian along several closed loops. The dynamical phases accumulated ...