Unconventional Geometric Phase Gate with Superconducting Quantum Interference Device Qubits in Cavity QED

In the system with superconducting quantum interference devices （SQUID） in cavity, a scheme for constructing two-qubit quantum phase gate via a conventional geometric phase-shift is proposed by using a quantized cavity field and classical microwave pulses. In this scheme, the gate operation is realized in the subspace spanned by the two lower flux states of the SQUID system mud the population operator of the excited state has no effect on it. Thus the effect of decoherence caused from the levels of the SQUID system is possible to minimize. Under cavity decay, our strictly numerical simulation shows that it is also possible to realize the unconventional geometric phase gate. The experimental feasibility is discussed in detail.     

Nonlocal Gate of a Quantum Network via Cavity Quantum Electrodynamics

We propose an experimentally feasible scheme to realize the nonlocal gate between two different nodes of a quantum network. With an entanglement-qubit acts as a quantum channel, our scheme is resist to actual environment noise and can get a high fidelity in current cavity quantum electrodynamics （C-QED） system.     

Unconventional Geometric Phase-Shift Gates Based on Superconducting Quantum Interference Devices Coupled to a Single-Mode Cavity

We present a scheme to realize geometric phase-shift gate for two superconducting quantum interference device （SQUID） qubits coupled to a single-mode microwave field. The geometric phase-shift gate operation is performed in two lower flux states, and the excited state [2〉 would not participate in the procedure. The SQUIDs undergo no transitions during the gate operation. Thus, the docoherence due to energy spontaneous emission based on the levels of SQUIDs are suppressed. The gate is insensitive to the cavity decay throughout the operation since the cavity mode is displaced along a circle in the phase space, acquiring a phase conditional upon the two lower flux states of the SQUID qubits, and the cavity mode is still in the original vacuum state. Based on the SQUID qubits interacting with the cavity mode, our proposed approach may open promising prospects for quantum iogic in SQUID-system.     

Implementation of a Controlled-Phase Gate and Deutsch-Jozsa Algorithm with Superconducting Charge Qubits in a Cavity

Based on superconducting quantum interference devices （SQUIDs） coupled to a cavity, we propose a scheme for implementing a quantum controlled-phase gate （QPG） and Deutsch-Jozsa （D J） algorithm by a controllable interaction. In the present scheme, the SQUID works in the charge regime, and the cavity field is ultilized as quantum data-bus, which is sequentially coupled to only one qubit at a time. The interaction between the selected qubit and the data bus, such as resonant and dispersive interaction, can be realized by turning the gate capacitance of each SQUID. Especially, the bus is not excited and thus the cavity decay is suppressed during the implementation of DJ algorithm. For the QPG operation, the mode of the bus is unchanged in the end of the operation, although its mode is really excited during the operations. Finally, for typical experiment data, we analyze simply the experimental feasibility of the proposed scheme. Based on the simple operation, our scheme may be realized in this solid-state system, and our idea may be realized in other systems.     

Resonant interaction scheme for GHZ state preparation and quantum phase gate with superconducting qubits in a cavity

A scheme is proposed to generate GHZ state and realize quantum phase gate for superconducting qubits placed in a microwave cavity. This scheme uses resonant interaction between the qubits and the cavity mode, so that the interaction time is short, which is important in view of decoherence. In particular, the phase gate can be realized simply with a single interaction between the qubits and the cavity mode. With cavity decay being considered, the fidelity and success probability are both very close to unity.     

Efficient Scheme for Entanglement and Quantum Information Processing with Two Superconducting Quantum-Interference Devices in Cavity QED

In this paper, a scheme is proposed to create the entanglement of two superconducting quantum-interference devices （SQUIDs） and implement a two-quhit quantum phase gate between two SQUIDs in cavity. The scheme only requires resonant interactions. Thus the scheme is very simple and the quantum dynamics operation can he realized at a high speed, which is important in view of decoherence.     

One-step Implementation of Two-qubit logic Gates

We propose a simple scheme for realizing the basic two-qubit logic gates with an atom inside a bimodal cavity. In the scheme, a two-qubit quantum phase gate （QPG） and a SWAP gate are performed by only one step. In addition, the controlled-NOT gate （CNOT） can also be implemented from a QPG. Our scheme is based on resonant interaction of an atom with cavity modes. In consideration of atomic spontaneous emission and cavity decay, the quantum logic gates still operate successfully, thus our scheme is insensitive to the decoherence..     

Remote interactions between two d-dimensional distributed quantum systems： nonlocal generalized quantum control-NOT gate and entanglement swapping

We present a systematic simple method to implement a generalized quantum control-NOT （CNOT） gate on two d-dimensional distributed systems. First, we show how the nonlocal generalized quantum CNOT gate can be implemented with unity fidelity and unity probability by using a maximally entangled pair of qudits as a quantum channel. We also put forward a scheme for probabilistically implementing the nonlocal operation with unity fidelity by employing a partially entangled qudit pair as a quantum channel. Analysis of the scheme indicates that the use of partially entangled quantum channel for implementing the nonlocal generalized quantum CNOT gate leads to the problem of ＇the general optimal information extraction＇. We also point out that the nonlocal generalized quantum CNOT gate can be used in the entanglement swapping between particles belonging to distant users in a communication network and distributed quantum computer.[第一段]     

Universal Quantum Cloning Machine in Circuit Quantum Electrodynamics

We propose a scheme for realizing the 1 → 2 universal quantum cloning machine （UQCM） with superconducting quantum interference device （SQUID） qubits in circuit quantum electrodynamics （circuit QED）. In this scheme, in order to implement UQCM, we only need phase shift gate operation on SQUID qubits and the Raman transitions. The cavity number we need is only one. Thus our scheme is simple and has advantages in the experimental realization. Furthermore, both the cavity and the SQUID qubits are virtually excited, so the decoherence can be neglected.     

Repeat-until-success measurement-based scheme for controlled phase gates in a cavity

We propose a new repeat-until-success （RUS） measurement-based scheme to implement quantum controlled phase gates according to the effect of dipole-induced-transparency （DIT） in a cavity and single-photon interference at a 50：50 beam-splitter. In our scheme, the DIT effect can appropriately attach a photon to the state of the dipoles according to their initial state, and in this way, a suitably encoded dipole-photon state is thus prepared. The measurement of the photon after it passing through a 50：50 beam-splitter can project the encoded matter-photon state to either a desired phase gate operation for the matter qubits or to their initial states. The recurrence of the initial state permits us to implement the desired entangling gate in a RUS way.     

Laser-polarization-dependent spontaneous emission of the zero phonon line from single nitrogen vacancy center in diamond

We investigate spontaneous emission properties and control of the zero phonon line （ZPL） from a diamond nitrogen- vacancy （NV） center coherently driven by a single ellipfically polarized control field. We use the Schrrdinger equation to calculate the probability amplitudes of the wave function of the coupled system and derive analytical expressions of the spontaneous emission spectra. The numerical results show that a few interesting phenomena such as enhancement, narrowing, suppression, and quenching of the ZPL spontaneous emission can be realized by modulating the polarization- dependent phase, the Zeeman shift, and the intensity of the control field in our system. In the dressed-state picture of the control field, we find that multiple spontaneously generated coherence arises due to three close-lying states decaying to the same state. These results are useful in real experiments.     

Quantum Controlled-Not Gate Operation and Complete Bell-State Analysis Using Hybrid Quantum Circuits

Here we propose a hybrid quantum circuit for achieving the quantum controlled-not (CNOT) gate operation on a photon-spin hybrid state. The hybrid quantum circuit consists of a nitrogen-vacancy (N-V) center and microtoroidal resonator coupling system, and a single photon waveguide. We implement the complete Bell state analysis using the proposed circuit. This proposed hybrid quantum circuit could enable a high fidelity of qubit manipulation and allows the feasible with the current experimental technologies.     

A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.     

Symmetry Reduction and Cauchy Problems for a Class of Fourth-Order Evolution Equations

We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations to Cauchy problems for systems of ordinary differential equations （ODEs）. We classify a class of fourth-order evolution equations which admit certain higher-order generalized conditional symmetries （GCSs） and give some examples to show the main reduction procedure. These reductions cannot be derived within the framework of the standard Lie approach, which hints that the technique presented here is something essential for the dimensional reduction of evolution equations.     

Classification and Approximate Solutions to Perturbed Nonlinear Diffusion-Convection Equations

This paper studies the perturbed nonlinear diffusion-convection equation with source term via the approximate generalized conditional symmetry （A GCS）. Complete classification of those perturbed equations which admit certain types of AGCSs is derived. Some approximate invariant solutions to the resulting equations can also be obtained.     

Variable Separation for （1 ＋ 1）-Dimensional Nonlinear Evolution Equations with Mixed Partial Derivatives

We present basic theory of variable separation for （1 ＋ 1）-dimensional nonlinear evolution equations with mixed partial derivatives. As an application, we classify equations uxt = A（u, ux）uxxx ＋ B（u, ux） that admits derivativedependent functional separable solutions （DDFSSs） and illustrate how to construct those DDFSSs with some examples.     

New Exact Solutions and Evolution of Solitons in Background Waves for （2＋1）-Dimensional Modified Dispersive Water-Wave System

With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.     

Solutions and Conditional Lie-Backlund Symmetries of Quasi-linear Diffusion-Reaction Equations

New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.     

Structure and Connectivity Analysis of Financial Complex System Based on G-Causality Network

The recent financial crisis highlights the inherent weaknesses of the financial market. To explore the mechanism that maintains the financial market as a system, we study the interactions of U.S. financial market from the network perspective. Applied with conditional Granger causality network analysis, network density, in-degree and out-degree rankings are important indicators to analyze the conditional causal relationships among financial agents, and further to assess the stability of U.S. financial systems. It is found that the topological structure of G-causality network in U.S. financial market changed in diferent stages over the last decade, especially during the recent global financial crisis. Network density of the G-causality model is much higher during the period of 2007–2009 crisis stage, and it reaches the peak value in 2008, the most turbulent time in the crisis. Ranked by in-degrees and out-degrees, insurance companies are listed in the top of 68 financial institutions during the crisis. They act as the hubs which are more easily influenced by other financial institutions and simultaneously influence others during the global financial disturbance.     

Non-Geometric Conditional Phase Gate by Quantum Zeno Dynamics in Laser-Excited Nitrogen-Vacancy Centers

Based on the quantum Zeno dynamics,we propose a two-qubit non-geometric conditional phase gate between two nitrogen-vacancy centers coupled to a whispering-gallery mode cavity.The varying phases design of periodic laser can be used for realizing non-geometric conditional phase gate,and the cavity mode is virtually excited during the gate operation.Thus,the fidelity of the gate operation is insensitive to cavity decay and the fluctuation of the preset laser intensity.The numerical simulation with a realistic set of experimental parameters shows that the gate fidelity 0.987 can be within reached in the near future.