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.     

Unconventional geometric quantum phase gates with two SQUIDs in a cavity

We present a potential scheme to implement two-qubit quantum phase gates through an unconventional geometric phase shift with two four-level SQUIDs in a cavity. The SQUID qubits undergo no transitions during the gate operation, while the cavity mode is displaced along a circle in the phase space, acquiring a geometric phase depending conditionally upon the SQUIDs’ states. Under certain conditions, the SQUID qubits are disentangled with the cavity mode and the SQUIDs’ states remain in their ground states during the gate operation, thus the gate is insensitive to both the SQUIDs’ “spontaneous emission” and the cavity decay.     

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.     

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.     

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.     

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.     

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.     

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.     

腔QED中利用超导量子干涉仪实现Toffoli门

基于腔量子电动力学技术,提出了利用三能级超导量子干涉仪实现Toffoli门的理论方案.利用超导量子干涉仪与腔场发生耦合,以及与外加经典脉冲发生共振跃迁来实现量子态的演化控制.该方案可以拓展到N比特Toffoli门的实现.最后,讨论了逻辑门的实验可行性,四比特Toffoli门的作用时间约为30 nm,它远小于腔衰减时间和较高能级的能量驰豫时间,从而足以实现量子态的操控.并且随着比特数的增多,Toffoli门作用时间的增幅较慢.     

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.     

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.     

基于新型超导电荷量子比特的几何量子门

超导量子系统被认为是最可能用于实现大规模量子计算、量子信息、以及量子存储等的物理系统之一.本文在一种特别设计的超导电荷比特的基础上,通过微波腔与超导比特的相互作用,探讨了在此系统中实现几何相单门以及非常规几何相两量子门的途径,并讨论了制备多量子比特最大纠缠态的方法.     

Scalable geometric quantum computing with Cooper-pair box qubits in circuit QED

We theoretically present a scheme to realize the scalable geometric quantum computing with Cooper-pair box (CPB) qubits in circuit QED. A one-dimensional transmission line resonator in circuit QED acting as quantum data bus generates a common cavity mode and interacts with each CPB. It is found that the interqubit couplings between any pair of qubits are switchable by individually adjusting the gate pulses applied to the selected CPBs. In this proposed scheme, we can both controllably and selectively address logic gates in geometric scenarios, which opens the possibility to implement the scalable fault-tolerant quantum computing with Josephson qubits.     

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.     

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.     

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.     

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.     

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.     

Effect of Multiphoton Processes on Geometric Quantum Computation in Superconducting Circuit QED

We study the influence of multi-photon processes on the geometric quantum computation in the systems of superconducting qubits based on the displacement-like and the general squeezed operator methods. As an example, we focus on the question about how to implement a two-qubit geometric phase gate using superconducting circuit quantum electrodynamics with both single- and two-photon interaction between the qubits and the cavity modes. We find that the multiphoton processes are not only controllable but also improve the gating speed. The comparison with other physical systems and experimental feasibility are discussed in detail.