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.     

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.     

Implementing Two-Qubit SWAP Gate with SQUID Qubits in a Microwave Cavity via Adiabatic Passage Evolution

We presented a scheme to implement SWAP gate in a microwave cavity. In our scheme, two superconducting quantum interference device (SQUID) qubits are coupled to a single-mode microwave cavity field by adiabatic passage method for their manipulation. This process of implementing SWAP gate is in the range of present experiments. The scheme can be easily obtained only by three steps, which does not require perform any operation. In the scheme, the operations only involve three lowest flux states of the SQUIDs, and the excited states would not be excited; therefore, the decoherence due to spontaneous emission of the SQUIDs’ levels would not affect the operations. In addition, during the whole procedure the cavity field is not necessary to be excited because it does not require transfer quantum information between the SQUID’s and the cavity field. Thus, the cavity decay is suppressed. Therefore our scheme may be realized in superconducting systems.     

Simultaneous implementation of n SWAP gates using superconducting charge qubits coupled to a cavity

Based on superconducting quantum interference devices (SQUIDs) coupled to a cavity, we propose a scheme for implementing n SWAP gates simultaneously. In our scheme, the SQUID works in the charge regime, the quantum logic gate operations are performed in the subspace spanned by two charge states |0〉 and |1〉. The interaction between the qubits and the cavity field can be achieved by turning the gate voltage and the external flux. Especially, the gate operation time is independent of the number of the qubits, and the gate operation is insensitive to the initial state of the cavity mode. We also analyze the experimental feasibility that the conditions of the large detuning can be achieved by adjusting the frequency of the cavity mode, and the operation time satisfies the requirement for the designed experiment by choosing suitable detuning and the quality factor of the cavity. Based on the simple operation, our scheme may be realized in this solid-state system, and our idea may be realized in other systems.     

Three-qubit quantum-gate operation with an SQUID in a cavity

We propose a method of realizing a three-qubit quantum gate with a superconducting quantum interference device(SQUID) in a cavity.In this proposal,the gate operation involves the SQUID ground-states and the Fock states of cavity modes b and c.The two field-modes act as the controlling qubits,and the two SQUID states form the target qubit.Since only the metastable lower levels are involved in the gate operation,the gate is not affected by the SQUID decay rates.     

Unconventional Geometric Quantum Gate in Circuit QED

We propose a scheme to implement an unconventional geometric phase gate in circuit QED, i.e. two superconducting charge qubits inside a superconducting transmission line resonator. The quantum operation depends only on global geometric features, and thus is insensitive to the state of the cavity mode.     

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.     

Scheme for Generating Cluster States with Charge Qubits in a Cavity

Based on superconducting charge qubits （SCCQs） coupled to a single-mode microwave cavity, we propose a scheme for generating charge cluster states. For all SCCQs, the controlled gate voltages are all in their degeneracy points, the quantum information is encoded in two logic states of charge basis. The generation of the multi-qubit cluster state can be achieved step by step on a pair of nearest-neighbor qubits. Considering effective long-rang coupling, we provide an efficient way to one-step generating of a highly entangled cluster state, in which the qubit-qubit coupling is mediated by the cavity mode. Our quantum operations are insensitive to the initial state of the cavity mode by removing the influence of the cavity mode via the periodical evolution of the system. Thus, our operation may be against the decoherence from the cavity.     

Deterministic geometric quantum phase gates for two atoms in decoherence-free subspace

We propose a scheme for realizing conventional geometric quantum phase gates in the context of cavity QED. During the operation neither the atomic system nor the cavity mode is excited, which is important in view of decoherence. The scheme does not require detection of photons, so the gate operation is deterministic and the influence of photodetection imperfection is eliminated. Taking advantage of the geometric manipulation, the phase gate is resilient to fluctuations of experimental parameters.     

One-step implementation of the Toffoli gate via quantum Zeno dynamics

Based on the quantum Zeno dynamics, we present a scheme for one-step implementation of a Toffoli gate via manipulating three rf superconducting quantum interference device (SQUID) qubits to resonantly interact with a superconducting cavity. The effects of decoherence such as spontaneous emission and the loss of cavity are also considered.     

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.     

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.     

Multipartite entanglement in the interaction system between a single-mode microwave cavity field and superconducting charge qubits

This paper proposes a method of generating multipartite entanglement through using d.c. superconducting quantum interference devices (SQUID) inside a standing wave cavity. In this scheme, the d.c. SQUID works in the charge region. It is shown that, a large number of important multipartite entangled states can be generated by a controllable interaction between a cavity field and qubits. It is even possible to produce entangled states involving different cavity modes based on the measurement of charge qubits states. After such superpositions states are created, the interaction can be switched off by the classical magnetic field through the SQUID, and there is no information transfer between the cavity field and the charge qubits.     

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.     

Geometric Phase Gate Based on Both Displacement Operator and Squeezed Operators with a Superconducting Circuit Quantum Electrdynamics

We give the brief review on the related definition of the geometric phase independent of specific physical system based on the displacement opreator and
the sqeezed operator, then show how the displacement operator and the squeezed operator can induce the general geometric phase. By means of the displacement operator and the squeezed operator concerning the circuit cavity mode state along a closed path in the phase space, we discuss specifically how to implement a two-qubit geometric phase gate in circuit quantum electrodynamics with both single photon interaction and two-photon interaction between the superconducting qubits and the circuit cavity modes. The experimental feasibility is discussed in detail.     

Realization of Three-Qubit Controlled-Phase Gate Operation with Atoms in Cavity QED System

We propose a scheme for realization of three-qubit controlled-phase gate via passing two three-level atoms through a high-Q optical cavity in a cavity QED system. In the presented protocol, the two stable ground states of the atoms act as the two controlling qubits and the zero- and one-photon Fock states of the cavity-field form the target qubit, and no auxiliary state or any measurement is required. The numerical simulation shows that the gate fidelities remain at a high level under the influence of the atomic spontaneous emission, the decay of the cavity mode and deviation of the coupling strength. The experimental feasibility of our proposal is also discussed.     

腔QED中超导量子干涉仪概率克隆机的物理实现

提出一个量子概率克隆机的物理实现方案,该方案首先将高Q腔中的两个超导量子干涉仪分别作为初始比特和目标比特,腔模作为测量比特,通过腔模和经典微波脉冲与超导量子干涉仪的多种相互作用实现量子概率克隆机的幺正演化;然后将腔模态映射到另一个超导量子干涉仪上,通过对该超导量子干涉仪磁通量的测量完成状态坍缩,从而以最优的成功概率实现量子态的精确克隆.本方案采用双光子拉曼共振过程加快单比特门的操作速率,并且总操作时间远小于自发辐射和腔模衰变时间,因而在实验上是可行的.     

Scheme for n phase gates operation and one-step preparation of highly entangled cluster state

In the system with superconducting quantum interference devices (SQUIDs) in a cavity, we propose a scheme for simultaneous implementing n phase gates and one step preparing the highly entangled cluster states based on the two-channel Raman interaction. In our scheme, the system is independent to the photon number of the cavity field, the cavity field can be initially in an arbitrary state, which is convenient for the experimental operation. The n phase gates operation and the cluster state generation are realized by using only the two lower flux states of the SQUID and the excited state would not be excited so that the influence of the decoherence due to spontaneous emission of the SQUID’s levels is possible to minimize. More importantly, the operation time of the phase gates is independent of the number n of the qubits. Finally, the experimental feasibility is also discussed in detail.     

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.     

Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity

We analyze a new scheme for quantum information processing, with superconducting charge qubits coupled through a cavity mode, in which quantum manipulations are insensitive to the state of the cavity. We illustrate how to physically implement universal quantum computation as well as multiqubit entanglement based on unconventional geometric phase shifts in this scalable solid-state system. Some quantum error-correcting codes can also be easily constructed using the same technique. In view of the gate dependence on just global geometric features and the insensitivity to the state of cavity modes, the proposed quantum operations may result in high-fidelity quantum information processing.