Circuit Quantum Electrodynamics System Research Articles

Efficient multimode Wigner tomography.

Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales exponentially with the number of modes in both computational and experimental measurement requirement, which becomes prohibitive as the system size increases. Here, we implement a state reconstruction method whose sampling requirement instead scales polynomially with system size, and thus mode number, for states that can be represented within such a polynomial subspace. We demonstrate this improved scaling with Wigner tomography of multimode entangled W states of up to 4 modes on a 3D circuit quantum electrodynamics (cQED) system. This approach performs similarly in efficiency to existing matrix inversion methods for 2 modes, and demonstrates a noticeable improvement for 3 and 4 modes, with even greater theoretical gains at higher mode numbers.

Realization of fractional quantum Hall state with interacting photons.

Fractional quantum Hall (FQH) states are known for their robust topological order and possess properties that are appealing for applications in fault-tolerant quantum computing. An engineered quantum platform would provide opportunities to operate FQH states without an external magnetic field and enhance local and coherent manipulation of these exotic states. We demonstrate a lattice version of photon FQH states using a programmable on-chip platform based on photon blockade and engineering gauge fields on a two-dimensional circuit quantum electrodynamics system. We observe the effective photon Lorentz force and butterfly spectrum in the artificial gauge field, a prerequisite for FQH states. After adiabatic assembly of Laughlin FQH wave function of 1/2 filling factor from localized photons, we observe strong density correlation and chiral topological flow among the FQH photons. We then verify the unique features of FQH states in response to external fields, including the incompressibility of generating quasiparticles and the smoking-gun signature of fractional quantum Hall conductivity. Our work illustrates a route to the creation and manipulation of novel strongly correlated topological quantum matter composed of photons and opens up possibilities for fault-tolerant quantum information devices.

Shaping photons: Quantum information processing with bosonic cQED

With its rich dynamics, the quantum harmonic oscillator is an innate platform for understanding real-world quantum systems and could even excel as the heart of a quantum computer. A particularly promising and rapidly advancing platform that harnesses quantum harmonic oscillators for information processing is the bosonic circuit quantum electrodynamics (cQED) system. In this article, we provide perspectives on the progress, challenges, and future directions in building a bosonic cQED quantum computer. We describe the main hardware building blocks and how they facilitate quantum error correction, metrology, and simulation. We conclude with our views of the key challenges that lie on the horizon, as well as scientific and cultural strategies for overcoming them and building a practical quantum computer with bosonic cQED hardware.

Nonequilibrium dynamics of the Jaynes-Cummings dimer.

We investigate the nonequilibrium dynamics of a Josephson-coupled Jaynes-Cummings dimer in the presence of Kerr nonlinearity, which can be realized in the cavity and circuit quantum electrodynamics systems. The semiclassical dynamics is analyzed systematically to chart out a variety of photonic Josephson oscillations and their regime of stability. Different types of transitions between the dynamical states lead to the self-trapping phenomenon, which results in photon population imbalance between the two cavities. We also study the dynamics quantum mechanically to identify characteristic features of different steady states and to explore fascinating quantum effects, such as spin dephasing, phase fluctuation, and revival phenomena of the photon field, as well as the entanglement of spin qubits. For a particular "self-trapped" state, the mutual information between the atomic qubits exhibits a direct correlation with the photon population imbalance, which is promising for generating photon mediated entanglement between two non interacting qubits in a controlled manner. Under a sudden quench from stable to unstable regime, the photon distribution exhibits phase space mixing with a rapid loss of coherence, resembling a thermal state. Finally, we discuss the relevance of the new results in experiments, which can have applications in quantum information processing and quantum technologies.

Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator

We report experimental and theoretical results on the extremely large Lamb shift in a multimode circuit quantum electrodynamics (QED) system in the deep-strong coupling (DSC) regime, where the qubit-resonator coupling strength is comparable to or larger than the qubit and resonator frequencies. The system comprises a superconducting flux qubit (FQ) and a quarter-wavelength coplanar waveguide resonator (lambda /4 CPWR) that are coupled inductively through a shared edge that contains a Josephson junction to achieve the DSC regime. Spectroscopy is performed around the frequency of the fundamental mode of the CPWR, and the spectrum is fitted by the single-mode quantum Rabi Hamiltonian to obtain the system parameters. Since the qubit is also coupled to a large number of higher modes in the resonator, the single-mode fitting does not provide the bare qubit energy but a value that incorporates the renormalization from all the other modes. We derive theoretical formulas for the Lamb shift in the multimode resonator system. As shown in previous studies, there is a cut-off frequency omega _{textrm{cutoff}} for the coupling between the FQ and the modes in the CPWR, where the coupling grows as sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}ll 1 and decreases as 1/sqrt{omega _n} for omega _n/omega _{textrm{cutoff}}gg 1. Here omega _n is the frequency of the nth mode. The cut-off effect occurs because the qubit acts as an obstacle for the current in the resonator, which suppresses the current of the modes above omega _{textrm{cutoff}} at the location of the qubit and results in a reduced coupling strength. Using our observed spectrum and theoretical formulas, we estimate that the Lamb shift from the fundamental mode is 82.3% and the total Lamb shift from all the modes is 96.5%. This result illustrates that the coupling to the large number of modes in a CPWR yields an extremely large Lamb shift but does not suppress the qubit energy to zero, which would happen in the absence of a high-frequency cut-off.

Probing Two Driven Double Quantum Dots Strongly Coupled to a Cavity.

We experimentally and theoretically study a driven hybrid circuit quantum electrodynamics (cQED) system beyond the dispersive coupling regime. Treating the cavity as part of the driven system, we develop a theory applicable to such strongly coupled and to multiqubit systems. The fringes measured for a single driven double quantum dot (DQD)-cavity setting and the enlarged splittings of the hybrid Floquet states in the presence of a second DQD are well reproduced with our model. This opens a path to study Floquet states of multiqubit systems with arbitrarily strong coupling and reveals a new perspective for understanding strongly driven hybrid systems.

Quantum heat diode versus light emission in circuit quantum electrodynamical system.

Precisely controlling heat transfer in a quantum mechanical system is particularly significant for designing quantum thermodynamical devices. With the technology of experiment advances, circuit quantum electrodynamics (circuit QED) has become a promising system due to controllable light-matter interactions as well as flexible coupling strengths. In this paper, we design a thermal diode in terms of the two-photon Rabi model of the circuit QED system. We find that the thermal diode can not only be realized in the resonant coupling but also achieve better performance, especially for the detuned qubit-photon ultrastrong coupling. We also study the photonic detection rates and their nonreciprocity, which indicate similar behaviors with the nonreciprocal heat transport. This provides the potential to understand thermal diode behavior from the quantum optical perspective and could shed new insight into the relevant research on thermodynamical devices.

Dynamical N-photon bundle emission

Engineering multiphoton resources is of importance in quantum metrology, quantum lithography, and biological sensing. Here we propose a concept of dynamical emission of N strongly-correlated photons. This is realized in a circuit quantum electrodynamical system driven by two Gaussian-pulse sequences. The underlying physical mechanism relies on the stimulated Raman adiabatic passage that allows efficient and selective preparation of target multiphoton states. Assisted by the photon decay, a highly pure N-photon bundle emission takes place in this system. In particular, the dynamical N-photon bundle emission can be tuned by controlling the time interval between consecutive pulses so that the device behaves as an N-photon gun, which can be triggered on demand. Our work opens up a route to achieve multiphoton source devices, which have wide potential applications in quantum information processing and quantum metrology.

Multi-Mode Bus Coupling Architecture of Superconducting Quantum Processor

Resonators in circuit quantum electrodynamics systems naturally carry multiple modes, which may have non-negligible influence on qubit parameters and device performance. While new theories and techniques are under investigation to deal with the multi-mode effects in circuit quantum electrodynamics systems, researchers have proposed novel engineering designs featuring multi-mode resonators to achieve enhanced functionalities of superconducting quantum processors. Here, we propose multi-mode bus coupling architecture, in which superconducting qubits are coupled to multiple bus resonators to gain larger coupling strength. Applications of multi-mode bus couplers can be helpful for improving iSWAP gate fidelity and gate speed beyond the limit of single-mode scenario. The proposed multi-mode bus coupling architecture is compatible with a scalable variation of the traditional bus coupling architecture. It opens up new possibilities for realization of scalable superconducting quantum computation with circuit quantum electrodynamics systems.

Numerical gate synthesis for quantum heuristics on bosonic quantum processors

There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results of numerical pulse engineering on the closed system for parametrized gates useful to implement Quantum Approximate Optimization Algorithm (QAOA) for qudits. The results show that high fidelity (>0.99) is achievable with sufficient computational effort for most cases under study, and extensions to multiple modes and open, noisy systems are possible. The tailored pulses can be stored and used as calibrated primitives for a future compiler in circuit quantum electrodynamics (cQED) systems.

Superconducting-qubit readout via low-backaction electro-optic transduction.

Entangling microwave-frequency superconducting quantum processors through optical light at ambient temperature would enable means of secure communication and distributed quantum information processing1. However, transducing quantum signals between these disparate regimes of the electro-magnetic spectrum remains an outstanding goal2-9, and interfacing superconducting qubits, which are constrained to operate at millikelvin temperatures, with electro-optic transducers presents considerable challenges owing to the deleterious effects of optical photons on superconductors9,10. Moreover, many remote entanglement protocols11-14 require multiple qubit gates both preceding and following the upconversion of the quantum state, and thus an ideal transducer should impart minimal backaction15 on the qubit. Here we demonstrate readout of a superconducting transmon qubit through a low-backaction electro-optomechanical transducer. The modular nature of the transducer and circuit quantum electrodynamics system used in this work enable complete isolation of the qubit from optical photons, and the backaction on the qubit from the transducer is less than that imparted by thermal radiation from the environment. Moderate improvements in the transducer bandwidth and the added noise will enable us to leverage the full suite of tools available in circuit quantum electrodynamics to demonstrate transduction of non-classical signals from a superconducting qubit to the optical domain.

Tuning nonequilibrium heat current and two-photon statistics via composite qubit-resonator interaction

Quantum thermal transport and two-photon statistics serve as two representative nonequilibrium features in circuit quantum electrodynamics (cQED) systems. Here we investigate quantum heat flow and two-photon correlation function at steady state in a composite qubit-resonator model, where one qubit shows both transverse and longitudinal couplings to a single-mode optical resonator. With weak qubit-resonator interaction, we unravel two microscopic transport pictures, i.e., cotunneling and cyclic heat exchange processes corresponding to transverse and longitudinal couplings, respectively. The nonmonotonic behavior of the heat current is exhibited by tuning the temperature bias with the weak longitudinal coupling. At strong qubit-resonator coupling, the heat current also exhibits a nonmonotonic feature by increasing qubit-resonator coupling strength, which tightly relies on the scattering processes between the qubit and the corresponding thermal bath. Furthermore, the longitudinal coupling is preferred to enhance heat current in the strong qubit-resonator coupling regime. For two-photon correlation function, it exhibits an antibunching-to-bunching transition by tuning the composite angle, which is mainly dominated by the modulation of the energy gap between the first and the second excited eigenstates. Our results are expected to deepen the understanding of nonequilibrium thermal transport and nonclassical photon radiation based on the cQED platform.

Quantum Correlations in Jahn-Teller Molecular Systems Simulated with Superconducting Circuits

We explore quantum correlations, in particular, quantum entanglement, among vibrational phonon modes as well as between electronic and vibrational degrees of freedom in molecular systems, described by Jahn-Teller mechanism. Specifically, to isolate and simplify the phonon- electron interactions in a complex molecular system, the basis of our discussions is taken to be the proposal of simulating two-frequency Jahn- Teller systems using superconducting circuit quantum electrodynamics systems (circuit QED) by Tekin Dereli and co-workers in 2012. We evaluate the quantum correlations, in particular entanglement between the vibrational phonon modes, and present analytical explanations using a single privileged Jahn-Teller mode picture. Furthermore, spin-orbit entanglement or quantum correlations between electronic and vibrational degrees of freedom are examined. We conclude by discussing experimental feasibility to detect such quantum correlations, considering the dephasing and decoherence in state-of-the-art superconducting two-level systems (qubits).

Shortcuts to adiabaticity for open systems in circuit quantum electrodynamics

Shortcuts to adiabaticity are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various shortcuts to adiabaticity protocols have been demonstrated in closed systems. However, realizing shortcuts to adiabaticity for open quantum systems has presented a challenge due to the complex controls in existing proposals. Here, we present the experimental demonstration of shortcuts to adiabaticity for open quantum systems, using a superconducting circuit quantum electrodynamics system. By applying a counterdiabatic driving pulse, we reduce the adiabatic evolution time of a single lossy mode from 800 ns to 100 ns. In addition, we propose and implement an optimal control protocol to achieve fast and qubit-unconditional equilibrium of multiple lossy modes. Our results pave the way for precise time-domain control of open quantum systems and have potential applications in designing fast open-system protocols of physical and interdisciplinary interest, such as accelerating bioengineering and chemical reaction dynamics.

Implementation of controlled phase gate based on superadiabatic shortcut in circuit quantum electrodynamics

With high speed and big storage power, quantum computer has received increasing attention. The operation on the quantum computer can be composed of several single-bit and multi-bit quantum logic gates, among which the controlled phase gate is one of the essential two-qubit logic gates. Usually, the quantum gate is realized in a real physical system, and the circuit quantum electrodynamics system (QED) has become a promising candidate due to its long coherent time, easily coupled with other physical system and scaled up to large scale. In this work, we propose a scheme to fast implement a two-qubit controlled phase gate based on the circuit QED by using the superadiabatic-based shortcut, in order to solve the problem that the adiabatic algorithm needs a long time in the process of system evolution. Here, a coding strategy is first designed for the circuit QED system and the two transmon qubits, and the effective Hamiltonian of the system is then presented by dividing different initial states in the rotating-wave approximation. By using the superadiabatic-based shortcut algorithm for two iterations, a correction term in the same form as the system effective Hamiltonian is obtained through anti-diabatic driving, so that the effective Hamiltonian can suppress unwanted transitions between different instantaneous eigenstates. According to the evolution path, the appropriate boundary conditions are also obtained to complete the preparation of the controlled phase gate. The numerical simulation results show the availability of the proposed scheme, that is, the <inline-formula><tex-math id="M1">\begin{document}$ - \left| {11} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20220248_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20220248_M1.png"/></alternatives></inline-formula> state can be obtained by system evolution when the initial state is <inline-formula><tex-math id="M2">\begin{document}$ \left| {11} \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20220248_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20220248_M2.png"/></alternatives></inline-formula>, while the system does not change at all when the other initial states are prepared. Furthermore, the controlled phase gate with high-fidelity can be obtained . It is shown that the fidelity of the controlled phase gate is stable and greater than 0.991 when the evolution time is greater than <inline-formula><tex-math id="M3">\begin{document}$0.7{t \mathord{\left/ {\vphantom {t {{t_f}}}} \right. } {{t_{\rm f}}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20220248_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20220248_M3.png"/></alternatives></inline-formula>. In addition, the proposed scheme can accelerate the evolution and is robust to decoherence. By the resonator decay and the spontaneous emission and dephasing of qubit, the final fidelity of the controlled phase gate is greater than 0.984. Since the controlled phase gate does not need additional parameters, the propsoed scheme is feasible in experiment.

Quantum Monte Carlo study of superradiant supersolid of light in the extended Jaynes-Cummings-Hubbard model

Searching for and investigating supersolids is a long-term outstanding problem in physics. In addition to the solid element $^{4}\mathrm{He}$ and cold atoms as potential candidates for the supersolid, the quantum system of light realized by circuit quantum electrodynamics is also a promising platform. In this paper, we propose a supersolid phase, i.e., a superradiant supersolid of light, where superradiant, superfluid, and solid orders coexist. We theoretically simulate the extended Jaynes-Cummings-Hubbard model describing the circuit quantum electrodynamics systems, mainly by the large-scale worm quantum Monte Carlo method, and find that a superradiant supersolid phase exists on triangular lattices due to the antiferromagnetic correlation between photons via light-atom coupling. We also confirm that the previous supersolid of light given by Bujnowski et al. [Phys. Rev. A 90, 043801 (2014)] is not stable. The phase transition between our superradiant supersolid phase and the superradiant solid phase can be continuous (first order) and above (below) the ``symmetry point.'' This is not the same as the pure Bose-Hubbard model on triangular lattices. The results herein could help in the search for a new superradiant supersolid phase in circuit quantum electrodynamic experiments and other light-matter coupling systems.

Fast flux control of 3D transmon qubits using a magnetic hose

Fast magnetic flux control is a crucial ingredient for circuit quantum electrodynamics (cQED) systems. So far, it has been a challenge to implement this technology with the high coherence 3D cQED architecture. In this paper, we control the magnetic field inside a superconducting waveguide cavity using a magnetic hose, which allows flux control of 3D transmon qubits on time scales less than 100 ns while maintaining a cavity quality factor larger than 106. The magnetic hose is designed as an effective microwave filter to not compromise the energy relaxation time of the qubit. The magnetic hose is a promising tool for fast magnetic flux control in various platforms intended for quantum information processing and quantum optics.

Macroscopic Circuit Quantum Electrodynamics: A New Look Toward Developing Full-Wave Numerical Models

Devices built using superconducting circuits are a popular approach being pursued to develop quantum information processing hardware. These systems involve the quantized interactions of electromagnetic fields with large coherent collections of charges in superconductors, and so are typically referred to as macroscopic circuit quantum electrodynamics (QED) devices or simply circuit QED devices. Although significant progress has been made recently, substantial engineering efforts are required to improve performance and scale these devices so they can address problems of practical interest. Performing these engineering efforts is difficult due to the absence of rigorous numerical modeling approaches. This work begins to address this by providing a new mathematical description of a commonly used circuit QED system, a transmon qubit coupled to microwave transmission lines. Expressed in terms of three-dimensional vector fields, our new model is better suited to developing rigorous numerical solvers than approximate lumped element circuit descriptions used in the literature. We present details on the quantization of our model, and derive equations of motion for the coupled field-transmon system. These results can be used in developing full-wave solvers in the future. To make this work more accessible, we assume a limited amount of training in quantum physics and provide many background details.

Fast generation of W state via superadiabatic-based shortcut in circuit quantum electrodynamics* *Project supported by the National Natural Science Foundation of China (Grant No. 61871234) and sponsored by NUPTSF (Grant Nos. NY218097 and NY220178).

We propose a scheme to fast prepare the three-qubit W state via superadiabatic-based shortcuts in a circuit quantum electrodynamics (circuit QED) system. We derive the effective Hamiltonian to suppress the unwanted transitions between different eigenstates by counterdiabatic driving, and obtain the W state with high-fidelity based on the superadiabatic passage. The numerical simulation results demonstrate that the proposed scheme can accelerate the evolution, and is more efficient than that with the adiabatic passage. In addition, the proposed scheme is robust to the decoherence caused by the resonator decay and qubit relaxation, and does not need additional parameters, which could be feasible in experiment.

Multiphoton resonance and chiral transport in the generalized Rabi model

The generalized Rabi model (gRM) with both one- and two-photon coupling terms has been successfully implemented in circuit quantum electrodynamics systems. In this paper, we examine theoretically multiphoton resonances in the gRM and derive their effective Hamiltonians. With different detunings in the system, we show that all three- to six-photon resonances can be achieved by involving two intermediate states. Furthermore, we study the interplay between multiphoton resonance and chiral transport of photon Fock states in a resonator junction with broken time-reversal symmetry. Depending on the qubit-photon interaction and photon-hopping amplitude, we find that the system can demonstrate different short-time dynamics.