Transferring entangled states of photonic cat-state qubits in circuit QED

We propose a method for transferring quantum entangled states of two photonic cat-state qubits(cqubits)from two microwave cavities to the other two microwave cavities.This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit.Because of using four cavities with different frequencies,the inter-cavity crosstalk is significantly reduced.Since only one coupler qutrit is used,the circuit resource is minimized.The entanglement transfer is completed with a singlestep operation only,thus this proposal is quite simple.The third energy level of the coupler qutrit is not populated during the state transfer,therefore decoherence from the higher energy level is greatly suppressed.Our numerical simulations show that high-fidelity transfer of two-cqubit entangled states from two transmission line resonators to the other two transmission line resonators is feasible with current circuit QED technology.This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems,such as four microwave or optical cavities,which are coupled to a natural or artificial three-level atom.     

Transferring quantum entangled states between multiple single-photon-state qubits and coherent-state qubits in circuit QED

We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto ncoherent-state (CS) qubits, by employing 2nmicrowave cavities coupled to a superconducting flux qutrit. The two logic states of a SPS qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CS qubit are encoded with two coherent states of a cavity. Because of using only one superconducting qutrit as the coupler, the circuit architecture is significantly simplified. The operation time for the state transfer does not increase with the increasing of the number of qubits. When the dissipation of the system is negligible, the quantum state can be transferred in a deterministic way since no measurement is required. Furthermore, the higher-energy intermediate level of the coupler qutrit is not excited during the entire operation and thus decoherence from the qutrit is greatly suppressed. As a specific example, we numerically demonstrate that the high-fidelity transfer of a Bell state of two SPS qubits onto two CS qubits is achievable within the present-day circuit QED technology. Finally, it is worthy to note that when the dissipation is negligible, entangled states of n CS qubits can be transferred back onto n SPS qubits by performing reverse operations. This proposal is quite general and can be extended to accomplish the same task, by employing a natural or artificial atom to couple 2nmicrowave or optical cavities.     

Speeding up the Generation of Entangled State between a Superconducting Qubit and Cavity Photons via Counterdiabatic Driving

Optimal generation of entangled states is of critical significance for robust quantum information processing. An effective scheme is presented for speeding up the generation of an entangled state between a superconducting qubit and microwave photons via counterdiabatic driving. At a magic bias point, the first three levels of a charge-phase quantum circuit constitute an effective qutrit. An entangled state based on adiabatic population transfer is first achieved. By the technique of shortcuts to adiabaticity, a counterdiabatic driving is applied to the qutrit, which then accelerates the entanglement generation significantly. Moreover, with the accessible decoherence rates, the rapid operations in a shortcut way are highly robust when compared with adiabatic manipulations. The scheme could offer a promising approach toward optimal preparation of entangled states with superconducting artificial atoms in circuit quantum electrodynamics, experimentally.     

Efficient scheme for realizing a multiplex-controlled phase gate with photonic qubits in circuit quantum electrodynamics

We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only one step of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encoded with a vacuum state and an arbitrary non-vacuum state |φ> (e.g., a Fock state, a superposition of Fock states, a cat state, or a coherent state, etc.) which is orthogonal or quasi-orthogonal to the vacuum state. The scheme has some additional advantages: because only two levels of the coupler are used, i.e., no auxiliary levels are utilized, decoherence from higher energy levels of the coupler is avoided; the gate operation time does not depend on the number of qubits; and the gate is implemented deterministically because no measurement is applied. As an example, we numerically analyze the circuit-QED based experimental feasibility of implementing a three-qubit MCP gate with photonic qubits each encoded via a vacuum state and a cat state. The scheme can be applied to accomplish the same task in a wide range of physical system, which consists of multiple microwave or optical cavities coupled to a two-level coupler such as a natural or artificial atom.     

Decoherence in solid-state qubits

The interaction of solid-state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid-state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review, we discuss how decoherence affects two of the most successful realizations of solid-state qubits, namely, spin qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented by confining the electron spin in a semiconductor quantum dot. Superconducting devices show quantum behaviour at low temperatures, and the qubit is encoded in the two lowest energy levels of a superconducting circuit. The electron spin in a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted relaxation channel, due to the presence of a spin–orbit interaction, and a (non-Markovian) spin bath constituted by the spins of the nuclei in the quantum dot that interact with the electron spin via the hyperfine interaction. In a superconducting qubit, decoherence takes place as a result of fluctuations in the control parameters, such as bias currents, applied flux and bias voltages, and via losses in the dissipative circuit elements.     

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.     

超导量子比特的耦合研究进展

超导量子比特以其在可控性、低损耗以及可扩展性等方面的优势被认为是最有希望实现量子计算机的固态方式之一.量子比特之间的相干可控耦合是实现大规模的量子计算的必要条件.本文介绍了超导量子比特耦合方式的研究进展,包括利用电容或电感实现量子比特的局域耦合,着重介绍一维传输线谐振腔作为量子总线实现多个量子比特的可控耦合的电路量子电动力学体系,并对最新的三维腔与超导量子比特的耦合结构的研究进展进行了论述.对各种耦合体系的哈密顿量进行了比较详细的分析,并按照局域性和可控性对不同耦合机制进行了分类.     

One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED

We propose a single-step implementation of a muti-target-qubit controlled phase gate with one catstate qubit (cqubit) simultaneously controlling n–1 target cqubits. The two logic states of a cqubit are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.     

Entanglement reciprocation between two charge qubits and two-cavity field

We propose a simple scheme to generate two-mode entangled coherent state in two separated cavities and realize the entanglement reciprocation between the superconducting charge qubits and continuous-variable system. By measuring the state of charge qubits, we find that the entanglement of two charge qubits, which are initially prepared in the maximally entangled state, can be transferred to the two-cavity field, and at this time the two-cavity field is in the entangled coherent state. We also find that the entanglement can be retrieved back to the two charge qubits after measuring the state of the two-cavity field.     

Entanglement reciprocation between two charge qubits and two-cavity field

We propose a simple scheme to generate two-mode entangled coherent state in two separated cavities and realize the entanglement reciprocation between the superconducting charge qubits and continuous-variable system. By measuring the state of charge qubits, we find that the entanglement of two charge qubits, which are initially prepared in the maximally entangled state, can be transferred to the two-cavity field, and at this time the two-cavity field is in the entangled coherent state. We also find that the entanglement can be retrieved back to the two charge qubits after measuring the state of the two-cavity field.      

Generating mixtures of spatial qubits

In a recent letter [L. Neves, G. Lima, J.G. Aguirre Gómez, C.H. Monken, C. Saavedra, S. Pádua, Phys. Rev. Lett. 94 (2005) 100501], we presented a scheme for generating pure entangled states of spatial qudits (D-dimensional quantum systems) by using the momentum transverse correlation of the parametric down-converted photons. In this work, we discuss a generalization of this process to enable the creation of mixed states. With the technique proposed we experimentally generated a mixture of two spatial qubits.     

Quantum deficits and correlations of two superconducting charge qubits

Motivated by recent experiments [Y.A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura, D.V. Averin, J.S. Tsai, Nature 421 (2003) 823] that show coherent oscillations of two superconducting qubits system, we consider a system of two charge qubits coupled to a common stripline microwave resonator. We discuss the separable and entangled behavior as well as the quantum and classical information deficits. Numerical computation of these quantities is performed for several regimes. We find that for less entangled states the partner can extract much more information by means of classical communication and local operations.     

基于SQUIDs和腔场相互作用传送量子信息的方案

本文提出了一个基于SQUIDs和腔场的大失谐相互作用传送量子信息的方案,此方案可以直接地、百分之百地实现量子信息的传送.该方案中腔场和SQUIDs系统之间没有量子信息的传递,腔场只是虚激发,这样对腔的品质因子的要求大大的降低了.同时也可以在SQUIDs之间建立传送量子信息的量子网络.     

Entanglement Dynamics of Three Superconducting Charge Qubits Coupled to a Cavity

We investigate the entanglement dynamics of a quantum system consisting of three superconducting charge qubits (SCQs) interacting with a microwave field. For separable and entangled states of the SCQs, the evolutions are studied under various photon numbers of cavity field. The results show that the amplitude and period of the bipartite entanglement square concurrences can be controlled by the choice of initial states of SCQs and photon numberof cavity field, respectively. This simple model of a quantum register allows us to understand the dynamic process of the quantum storage of information carried by charge qubit.     

Producing cluster states in charge qubits and flux qubits

We propose a method to efficiently generate cluster states in charge qubits, both semiconducting and superconducting, as well as flux qubits. We show that highly entangled cluster states can be realized by a "one-touch" entanglement operation by tuning gate bias voltages for charge qubits. We also investigate the robustness of these cluster states for nonuniform qubits, which are unavoidable in solid-state systems. We find that quantum computation based on cluster states is a promising approach for solid-state qubits.     

Synthesis of maximally entangled mixed states and disentanglement in coupled Josephson charge qubits

We analyze a controllable generation of maximally entangled mixed states of a circuit containing two-coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Illustrative variational calculations were performed to demonstrate the effect on the two-qubits entanglement. At sufficiently deviation between the Josephson energies of the qubits and/or strong coupling regime, maximally entangled mixed states at certain instances of time is synthesized. We show that entanglement has an interesting subsequent time evolution, including the sudden death effect. This enables us to completely characterize the phenomenon of entanglement sharing in the coupling of two superconducting charge qubits, a system of both theoretical and experimental interest.     

Simple all-microwave entangling gate for fixed-frequency superconducting qubits

We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88, and quantum process tomography reveals a gate fidelity of 81%.     

Control of purity and entanglement for two spatially two-separated qubits via phase damping

Control of purity and entanglement of two two-qubits dispersively coupled to a field with a reservoir are investigated.Initially the qubits are entangled,while the field is either in a coherent state or a statistical mixture of two coherent states.For an alternative entanglement measure we calculate the negativity of the eigenvalues of the partially transposed density matrix.A measure related to the mutual entropy,namely the index of entropy,is employed to measure the entanglement.Its results agree well with the negativity.It is found that the entanglement and purity have strong sensitivity to phase damping.The asymptotic behaviour of the states of the field,the two two-qubits,and the total system fall into mixed states.     

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.     

Deterministic entanglement of photons in two superconducting microwave resonators

Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spinlike systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states (entangled states |N0> + |0N>) as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two resonators, and we completely characterize the entangled states with bipartite Wigner tomography. These results demonstrate a significant advance in the quantum control of linear resonators in superconducting circuits.