Approximate Toffoli Gate Originated from a Single Resonant Interaction of Cavity Dissipation and Atomic Spontaneous Emission

We propose a potentially practical scheme to implement an approximate three-qubit Toffoli gate by a single resonant interaction in dissipative cavity QED in which the cavity mode decay and atomic spontaneous emission are considered. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the approximate phase gate can be implemented by only a single dissipative resonant interaction of atoms with the cavity mode. Discussions are made for the advantages and the experimental feasibility of our scheme.     

A Scheme for Atomic Entangled States and Quantum Gate Operations in Cavity QED

We propose a scheme for controllably entangling the ground states of five-state W-type atoms confined in a cavity and realizing swap gate and phase gate operations. In this scheme the cavity is only virtually excited and the atomic excited states are almost not occupied, so the produced entangled states and quantum logic operations are very robust against the cavity decay and atomic spontaneous emission.     

Preparation of cluster state in large detuned cavity

An experimentally realizable physical scheme for preparing multiqubit cluster states from a large detuned atomcavity interaction is proposed. The scheme is free of any type of measurement and insensitive to the cavity decay, and the cavity field is only virtually excited so that there is no information exchanging between atom and cavity. The time required for the gate operations is very short, which is important for decoherence. We also discuss the experimental feasibility of our scheme.     

One-step implementing three-qubit phase gate via manipulating rf SQUID qubits in the decoherence-free subspace with respect to cavity decay

We present a scheme for implementing a three-qubit phase gate via manipulating rf superconducting quantum interference device (SQUID) qubits in the decoherence-free subspace with respect to cavity decay. Through appropriate changes of the coupling constants between rf SQUIDs and cavity, the scheme can be realized only in one step. A high fidelity is obtained even in the presence of decoherence.     

Efficient scheme of quantum SWAP gate and multi-atom cluster state via cavity QED

In this paper, we propose a physical scheme to realize quantum SWAP gate by using a large-detuned single-mode cavity field and two identical Rydberg atoms. It is shown that the scheme can also be used to create multi-atom cluster state. During the interaction between atom and cavity, the cavity is only virtually excited and thus the scheme is insensitive to the cavity field states and cavity decay. With the help of our scheme it is very simple to prepare the N-atom cluster state with perfect fidelity and probability. The practical feasibility of this method is also discussed.     

Efficient scheme of quantum SWAP gate and multi-atom cluster state via cavity QED

In this paper, we propose a physical scheme to realize quantum SWAP gate by using a large-detuned single-mode cavity field and two identical Rydberg atoms. It is shown that the scheme can also be used to create multi-atom cluster state. During the interaction between atom and cavity, the cavity is only virtually excited and thus the scheme is insensitive to the cavity field states and cavity decay. With the help of our scheme it is very simple to prepare the $N$-atom cluster state with perfect fidelity and probability. The practical feasibility of this method is also discussed.     

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.     

Two simple schemes for implementing Toffoli gate via atom--cavity field interaction in cavity quantum electrodynamics

This paper proposes two schemes for implementing three-qubit Toffoli gate with an atom (as target qubit) sent through a two-mode cavity (as control qubits). The first scheme is based on the large-detuning atom--cavity field interaction and the second scheme is based on the resonant atom-field interaction. Both the situations with and without cavity decay and atomic spontaneous emission are considered. The advantages and the experimental feasibility of these two schemes are discussed.     

Implementation of Controlled‐NOT Gate by Lyapunov Control

A scheme to implement the controlled‐NOT (CNOT) gate for quantum systems is proposed, which is based on Lyapunov control. The scheme does not require precise control of the interaction time since the system is stable when the control fields vanish. In particular, the control fields can be easily obtained by most initial states. As an example, the CNOT gate is realized for two atoms trapped in an optical cavity by exploiting two disturbance cases. Compared to continuous disturbance, the fidelity of the CNOT gate is higher under impulsive disturbance, however, interaction times are much longer. Numerical simulations indicate that the scheme is robust against variations of control parameters and decoherence caused by atomic spontaneous emission and cavity decay. Therefore, the scheme may provide useful applications in quantum computation.     

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 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 logic in SQUID-system.     

Scheme for implementing quantum logic gates for two atomstrapped in different cavities

A scheme is presented for realizing quantum logic gates for two atoms localized in two distant optical cavities. Our scheme works in a regime in which the atom--cavity coupling strength is smaller than the cavity decay rate. Thus the requirement on the quality factor of the cavities is greatly relaxed. Furthermore, the fidelity of our scheme is not affected by detection inefficiency and atomic decay. These advantages are important in view of experiment.     

Generation of four-atom cluster states in thermal cavity and implementing remote controlled not gate

We propose an experimentally feasible scheme for preparing a four-atom cluster state in a thermal cavity. In the scheme, the cavity field is only virtually excited and the photon-number-dependent part in the effective Hamiltonian is cancelled so that the system is insensitive to the cavity decay and the thermal field. At the same time, the scheme can be generalized to prepare n-atom cluster states with the success probability 100\%. In addition, using the four-atom cluster state, we also propose a simpler scheme for implementing a remote--controlled not gate (CNOT) without the Bell states measurement.     

Generation of an N-qubit phase gate via atom--cavity nonidentical coupling

A scheme for approximate generation of an N-qubit phase gate is proposed in cavity QED based on nonidentical coupling between the atoms and the cavity. The atoms interact with a highly detuned cavity-field mode, but quantum information does not transfer between the atoms and cavity field, and thus the cavity decay is negligible. The gate time does not rise with an increase in the number of qubits. With the choice of a smaller odd number l （related to atom-cavity coupling constants）, the phase gate can be generated with a higher fidelity and a higher success probability in a shorter time （the gate time is much shorter than the atomic radiative lifetime and photon lifetime）. When the number of qubits N exceeds certain small values, the fidelity and success probability rise slowly with an increase in the number of qubits N. When N→∞, the fidelity and success probability infinitely approach 1, but never exceed 1.     

Realization of Toffoli gate operation using four-level atoms in cavity QED system

This paper proposes a scheme for realization of a three-qubit Toffoli gate operation using three four-level atoms by a selective atom--field interaction in a cavity quantum electrodynamics system. In the proposed protocol, the quantum information is encoded on the stable ground states of atoms, and atomic spontaneous emission is negligible as the large atom--cavity detuning effectively suppresses the spontaneous decay of the atoms. The influence of the dissipation on fidelity and success probability of the three-qubit Toffoli gate is also discussed. The scheme can also be applied to realize an N-qubit Toffoli gate and the interaction time required does not rise with increasing the number of qubits.     

Quantum logic gates operation using SQUID qubits in bimodal cavity

We present a scheme to realize the basic two-qubit logic gates such as the quantum phase gate and SWAP gate using a detuned microwave cavity interacting with three-level superconducting-quantum-interference-device (SQUID) qubit(s), by placing SQUID(s) in a two-mode microwave cavity and using adiabatic passage methods. In this scheme, the two logical states of the qubit are represented by the two lowest levels of the SQUID, and the cavity fields are treated as quantized. Compared with the previous method, the complex procedures of adjusting the level spacing of the SQUID and applying the resonant microwave pulse to the SQUID to create transformation are not required. Based on superconducting device with relatively long decoherence time and simplified operation procedure, the gates operate at a high speed, which is important in view of decoherence.     

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.     

Quantum Logic Gates and Cluster States with Four-level Atoms in Cavity QED

We propose a model to implement the two-qubit quantum logic gates, i.e., the quantum phase gate and the Controlled-NOT gate, and generate the atomic qubits cluster states with a large detuned interaction between four-level atoms and a single-mode cavity field. In the presented protocol, the quantum information is encoded on the stable ground states of the atoms, and the effect of decoherence from atomic spontaneous emission is negligible. In addition, the interaction between atoms and the cavity is large detuned, and the cavity is only virtually excited. Therefore, the scheme is insensitive to the cavity decay. The experimental feasibility of our proposal is also discussed.     

Scheme for Remote Implementation of Partially Unknown Quantum Operation of Two Qubits in Cavity QED

By constructing the recovery operations of the protocol of remote implementation of partially unknown quantum operation of two qubits [An-Min Wang: Phys. Rev. A 74 (2006) 032317] with two-qubit Cnot gate and single qubit logic gates, we present a scheme to implement it in cavity QED. Long-lived Rydberg atoms are used as qubits, and the interaction between the atoms and the field of cavity is a nonresonant one. Finally, we analyze the experimental feasibility of this scheme.     

Quantum teleportation of an arbitrary superposition of atomic states

This paper proposes a scheme to teleport an arbitrary multi-particle two-level atomic state between two parties or an arbitrary zero- and one-photon entangled state of multi-mode between two high-Q cavities in cavity QED. This scheme is based on the resonant interaction between atom and cavity and does not involve Bell-state measurement. It investigates the fidelity of this scheme and find out the case of this unity fidelity of this teleportation. Considering the practical case of the cavity decay, this paper finds that the condition of the unity fidelity is also valid and obtains the effect of the decay of the cavity on the successful probability of the teleportation.     

Generation of Entangled Multi-atom Dicke States in Cavity Quantum Electrodynamics

We propose a scheme to generate two-atom maximally entangled state in cavity quantum electrodynamies （QED）. The scheme can 5e extended to generation of entangled multi-atom Dicke states if we control the interaction time of atoms with cavity modes. We use adiabatically state evolution under large atom-cavity detuning, so the scheme is insensitive to atomic spontaneous decay. The influence of cavity decay on fidelity and success probability is discussed.