Circuit Quantum Electrodynamics System Research Articles

Effects of linear modulation of qubits–resonator coupling on quantum entanglement in circuit QED

We investigate to efficiently maintain the quantum entanglement between qubits through linearly modulating the coupling coefficient between qubits and field in circuit quantum electrodynamics system. We find that the maintenance time of entanglement between coupling qubits is closely related with the modulation type. Compared to the case of constant coupling coefficients, the first disappearance of entanglement between qubits is largely delayed when the coupling coefficients are linearly modulated with a small ramp. However, it is unfavorable for the maintenance of entanglement even leads to fast disappearance if the coupling coefficients are modulated with a large slope. The disappearance time of entanglement not only relies on the quantum state of coupling qubits, but also depends on the average photon number. The more the average photon number is, the more disadvantageous quantum entanglement maintains.

Characterizing errors on qubit operations via iterative randomized benchmarking

With improved gate calibrations reducing unitary errors, we achieve a benchmarked single-qubit gate fidelity of $0.9995\ifmmode\pm\else\textpm\fi{}0.0002$ with superconducting qubits in a circuit quantum electrodynamics system. We present a method for distinguishing between unitary and nonunitary errors in quantum gates by interleaving repetitions of a target gate within a randomized benchmarking sequence. The benchmarking fidelity decays quadratically with the number of interleaved gates for unitary errors but linearly for nonunitary errors, allowing us to separate systematic coherent errors from decoherent effects. With this protocol, we show that the fidelity of the gates is not limited by unitary errors.

Exploring Interacting Quantum Many-Body Systems by Experimentally Creating Continuous Matrix Product States in Superconducting Circuits

Improving the understanding of strongly correlated quantum many body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research and chemistry. Enormous progress has been made in the past decades in developing both classical and quantum approaches to calculate, simulate and experimentally probe the properties of such systems. In this work we use a combination of classical and quantum methods to experimentally explore the properties of an interacting quantum gas by creating experimental realizations of continuous matrix product states - a class of states which has proven extremely powerful as a variational ansatz for numerical simulations. By systematically preparing and probing these states using a circuit quantum electrodynamics (cQED) system we experimentally determine a good approximation to the ground-state wave function of the Lieb-Liniger Hamiltonian, which describes an interacting Bose gas in one dimension. Since the simulated Hamiltonian is encoded in the measurement observable rather than the controlled quantum system, this approach has the potential to apply to exotic models involving multicomponent interacting fields. Our findings also hint at the possibility of experimentally exploring general properties of matrix product states and entanglement theory. The scheme presented here is applicable to a broad range of systems exploiting strong and tunable light-matter interactions.

Quantum-enabled temporal and spectral mode conversion of microwave signals.

Electromagnetic waves are ideal candidates for transmitting information in a quantum network as they can be routed rapidly and efficiently between locations using optical fibres or microwave cables. Yet linking quantum-enabled devices with cables has proved difficult because most cavity or circuit quantum electrodynamics systems used in quantum information processing can only absorb and emit signals with a specific frequency and temporal envelope. Here we show that the temporal and spectral content of microwave-frequency electromagnetic signals can be arbitrarily manipulated with a flexible aluminium drumhead embedded in a microwave circuit. The aluminium drumhead simultaneously forms a mechanical oscillator and a tunable capacitor. This device offers a way to build quantum microwave networks using separate and otherwise mismatched components. Furthermore, it will enable the preparation of non-classical states of motion by capturing non-classical microwave signals prepared by the most coherent circuit quantum electrodynamics systems.

V-shaped superconducting artificial atom based on two inductively coupled transmons

Circuit quantum electrodynamics systems are typically built from resonators and two-level artificial atoms, but the use of multilevel artificial atoms instead can enable promising applications in quantum technology. Here we present an implementation of a Josephson junction circuit dedicated to operate as a V-shape artificial atom. Based on a concept of two internal degrees of freedom, the device consists of two transmon qubits coupled by an inductance. The Josephson nonlinearity introduces a strong diagonal coupling between the two degrees of freedom that finds applications in quantum nondemolition readout schemes, and in the realization of microwave cross-Kerr media based on superconducting circuits.

Preparation of multi-qubit W states in multiple resonators coupled by a superconducting qubit via adiabatic passage

We propose an efficient scheme to prepare W state of $$N$$N superconducting (SC) qubits in $$N$$N spatially separated coplanar waveguide (CPW) resonators via adiabatic passage. The $$N$$N CPW resonators, each trapping a SC qubit, are coupled only by a superconducting coupler (SCC) qubit. Based on a circuit quantum electrodynamics system, our scheme can be controlled and implemented easily in experiment. As a model of a plurality of separated cavities coupled to a SCC qubit, our protocol can be useful in scalable distributed quantum networks. By introducing adiabatic passage into our model, there is no need to control the Rabi frequency of classical field and the interaction time precisely during the whole operation. Also, the dissipation from the resonators and the energy relaxation can be omitted approximately.

Rabi model as a quantum coherent heat engine: From quantum biology to superconducting circuits

We propose a multilevel quantum heat engine with a working medium described by a generalized Rabi model which consists of a two-level system coupled to a single-mode bosonic field. The model is constructed to be a continuum limit of a quantum biological description of light-harvesting complexes so that it can amplify quantum coherence by a mechanism which is a quantum analog of classical Huygens clocks. The engine operates in a quantum Otto cycle where the working medium is coupled to classical heat baths in the isochoric processes of the four-stroke cycle, while either the coupling strength or the resonance frequency is changed in the adiabatic stages. We found that such an engine can produce work with an efficiency close to the Carnot bound when it operates at low temperatures and in the ultrastrong-coupling regime. The interplay of the effects of quantum coherence and quantum correlations on the engine performance is discussed in terms of second-order coherence, quantum mutual information, and the logarithmic negativity of entanglement. We point out that the proposed quantum Otto engine can be implemented experimentally with modern circuit quantum electrodynamic systems where flux qubits can be coupled ultrastrongly to superconducting transmission-line resonators.

The -type four-particle entangled state generated by using superconducting artificial atoms with broken symmetry

We propose a scheme for generating a genuine -type four-particle entangled state of superconducting artificial atoms with broken symmetry by using one-dimensional transmission line resonator as a data bus. With the help of the Circuit quantum electrodynamics system composed of -type three-level artificial atoms and transmission line resonator, our scheme also has long coherence time and storage time. Meanwhile, the -type three-level artificial atom used in the scheme is different from natural atom and has cyclic transitions. Furthermore, our scheme is easy to control and flexible. Through a suitable choice of the Rabi frequencies and detunings of the classical fields, we can use this system to implement the selective coupling between two arbitrary qubits. After suitable interaction time and simple operations, the desired entangled state can be obtained. Since artificial atomic excited states and photonic states are adiabatically eliminated, our scheme is robust against the spontaneous emissions of artificial atoms and the decays of transmission line resonator. We also analyze the performance and the experimental feasibility of the scheme, and show that our scheme is feasible under existing experimental conditions.

基于电路量子电动力学系统实现一维cluster态的制备

基于电路量子电动力学系统实现一维cluster态的制备

Generation and stabilization of a three-qubit entangledWstate in circuit QED via quantum feedback control

Circuit cavity quantum electrodynamics (QED) is proving to be a powerful platform to implement quantum feedback control schemes due to the ability to control superconducting qubits and microwaves in a circuit. Here, we present a simple and promising quantum feedback control scheme for deterministic generation and stabilization of a three-qubit $W$ state in the superconducting circuit QED system. The control scheme is based on continuous joint Zeno measurements of multiple qubits in a dispersive regime, which enables us not only to infer the state of the qubits for further information processing but also to create and stabilize the target $W$ state through adaptive quantum feedback control. We simulate the dynamics of the proposed quantum feedback control scheme using the quantum trajectory approach with an effective stochastic maser equation obtained by a polaron-type transformation method and demonstrate that in the presence of moderate environmental decoherence, the average state fidelity higher than $0.9$ can be achieved and maintained for a considerable long time (much longer than the single-qubit decoherence time). This control scheme is also shown to be robust against measurement inefficiency and individual qubit decay rate differences. Finally, the comparison of the polaron-type transformation method to the commonly used adiabatic elimination method to eliminate the cavity mode is presented.

Theory of deterministic down-conversion of single photons occurring at an impedance-matched Λ system

We theoretically investigate the optical response of a Λ system interacting with a semi-infinite waveguide field. In particular, we focus on the case of an impedance-matched Λ system, in which the two decay rates from the top level are identical. We derive the analytical formulae to evaluate the amplitude and the power spectrum of the output field, and present numerical results assuming an implementation by a circuit quantum electrodynamics system. For a low input power (single-photon regime), input photons are down-converted deterministically by inducing the Raman transition in the Λ system. In contrast, for a high input power (multi-photon regime), the conversion efficiency decreases because of the saturation of the Λ system.

Non-equilibrium correlations and entanglement in a semiconductor hybrid circuit-QED system

We present a theoretical study of a hybrid circuit-quantum electrodynamics system composed of two semiconducting charge-qubits confined in a microwave resonator. The qubits are defined in terms of the charge states of two spatially separated double quantum dots (DQDs) which are coupled to the same photon mode in the microwave resonator. We analyse a transport setup where each DQD is attached to electronic reservoirs and biased out-of-equilibrium by a large voltage, and study how electron transport across each DQD is modified by the coupling to the common resonator. In particular, we show that the inelastic current through each DQD reflects an indirect qubit–qubit interaction mediated by off-resonant photons in the microwave resonator. As a result of this interaction, both charge qubits stay entangled in the steady (dissipative) state. Finite shot noise cross-correlations between currents across distant DQDs are another manifestation of this nontrivial steady-state entanglement.

Mesoscopic entangled coherent states implemented with a circuit quantum electrodynamics system

We show a scheme to generate entangled coherent states in a circuit quantum electrodynamics system, which consists of a nanomechanical resonator, a superconducting Cooper-pair box (CPB), and a superconducting transmission line resonator. In the system, the CPB plays the role of a nonlinear medium and can be conveniently controlled by a gate voltage including direct-current and alternating-current components. The scheme provides a powerful tool for preparing the multipartite mesoscopic entangled coherent states.

Optimality of qubit purification protocols in the presence of imperfections

Quantum control is an essential tool for the operation of quantum technologies such as quantum computers, simulators, and sensors. Although there are sophisticated theoretical tools for developing quantum control protocols, formulating optimal protocols while incorporating experimental conditions remains a challenge. In this paper, motivated by recent advances in realization of real-time feedback control in circuit quantum electrodynamics systems, we study the effect of experimental imperfections on the optimality of qubit purification protocols. Specifically, we find that the optimal control solutions in the presence of detector inefficiency and non-negligible decoherence can be significantly different from the known solutions to idealized dynamical models. In addition, we present a simplified form of the verification theorem to examine the global optimality of a control protocol.

Large-scale maximal entanglement and Majorana bound states in coupled circuit quantum electrodynamic systems

We study the effect of ultrastrong cavity-qubit coupling on the low-lying excitations of a chain of coupled circuit quantum electrodynamic (QED) systems. We show that, in the presence of the onsite ultrastrong coupling, the photon hopping between cavities can be mapped to the Ising interaction between the lowest two levels of individual circuit QED of the chain. Based on our mapping, we predict two nearly degenerate ground states whose wave functions involve maximal entanglement between the macroscopic quantum states of the cavities and the states of qubits and identify that they are mathematically equivalent to Majorana bound states. Further, we devise a scheme for the dispersive measurement of the ground states using an additional resonator attached to one end of the circuit QED chain. Finally, we discuss the effects of disorders and local noises on the coherence of the ground states.

Generating mesoscopic entanglement of coherence and squeezed states in circuit QED system

We propose a scheme for generating the superposition and entanglement among superconducting charge qubit, coherent state and squeezed state and the entanglement between coherent state and squeezed state in the circuit quantum electrodynamics system, which consists of a nanomechanical resonator (NAMR), a superconducting Cooper-pair box (CPB), and a superconducting transmission line resonator (STLR). In the system, the CPB plays the role of “nonlinear media” and can be conveniently controlled by a gate voltage with direct current (DC) and alternating current (AC) components. The scheme will provide a powerful tool for preparing the mesoscopic entanglement of coherence and squeezed states.

Quantum simulation of an artificial Abelian gauge field using nitrogen-vacancy-center ensembles coupled to superconducting resonators

We propose a potentially practical scheme to simulate artificial Abelian gauge field for polaritons using a hybrid quantum system consisting of nitrogen-vacancy center ensembles (NVEs) and superconducting transmission line resonators (TLR). In our case, the collective excitations of NVEs play the role of bosonic particles, and our multiport device tends to circulate polaritons in a behavior like a charged particle in an external magnetic field. We discuss the possibility of identifying signatures of the Hofstadter "butterfly" in the optical spectra of the resonators, and analyze the ground state crossover for different gauge fields. Our work opens new perspectives in quantum simulation of condensed matter and many-body physics using hybrid spin-ensemble circuit quantum electrodynamics system. The experimental feasibility and challenge are justified using currently available technology.

On the schemes of cavity photon elimination in circuit-quantum electrodynamics systems

The solid-state superconducting circuit-QED (quantum electrodynamics) system is a promising candidate for quantum computing and quantum information processing, which serves also as an ideal platform for quantum measurement and quantum control studies. In this context, a large number of cavity photons may be involved in the quantum dynamics and will degrade the simulation efficiency. To avoid this difficulty, it is helpful to eliminate the degrees of freedom of the cavity photons, and obtain an effective master-equation description which contains only the qubit states. In this work, we examine two such schemes, the adiabatic elimination (AE) and the more recently proposed polaron transformation (PT) approaches, by comparing their results with exact numerical simulations. We find that in the absence of qubit-flip, which is a specific quantum nondemolition (QND) measurement, the PT scheme is superior to the AE method. Actually, in this case the PT scheme catches the measurement dynamics exactly. However, in the presence of qubit-flip such as for qubit oscillation measurement, the PT scheme is no longer better than the AE approach. We conclude that both schemes, in the weak measurement regime, can work almost equally well. This corresponds to strong cavity damping or weak coupling between the qubit and cavity photons. Out of this regime, unfortunately, one has to include the cavity photons into numerical simulations and more advanced methods/techniques are waiting for their exploration in this field.

On the scheme of cavity photon elimination in multi-qubit circuit-quantum electrodynamics system

Solid-state superconducting circuit-quantum electrodynamics (QED) system is a promising candidate for quantum information processing and an ideal platform for quantum measurement and quantum control studies. As an extension to our previous simulation for single qubit circuit-QED, in this work we simulate the quantum measurement and control of multi-qubit system. Particularly, we consider the deterministic generation of a two-qubit Bell state. In this context we examine the validity conditions of two cavity-photon-elimination scheme. On the level of quantum trajectory simulation, we find that, owing to the qubit flip caused by feedback, the advanced polaron-transformation scheme is no longer applicable if the measurement is not weak, which also makes meaningless the elegant effective measurement operator.

One-Step Generation of Multiqubit Greenberger—Horne—Zeilinger States in a Driven Circuit QED System

We propose an efficient scheme to generate multiqubit Greenberger—Horne—Zeilinger (GHZ) states by one-step quantum operation in a driven circuit quantum electrodynamics (QED) system. Our proposal is based on a unitary evolution exp[−iλS2x], with Sx being the collective spin operator in x direction and λ a controllable parameter, induced by driving the resonator. The quantum operation avoids resonator-field decay and may achieve the GHZ states with ideal success probability. The feasibility with the experimentally-demonstrated circuit QED system is also discussed.