Microwave photonic graph states provide a promising approach for robust quantum communication between remote superconducting chips using microwave photons. Recently, Besse et al. [Nat. Commun. 11, 4887 (2020)] demonstrated that 1D graph states can be generated using two transmon qubits. In this paper, we propose to use transmon qubits combined with other microwave devices to construct more complex graph states. Specifically, we consider 2D lattice and tree-like graph states. We compare the performance using fixed- versus tunable-frequency transmon qubits and also for different photonic qubit encodings. In each case, we estimate the fidelity of the resulting microwave graph state assuming current experimental parameters and identify the main factors that limit performance.
Coherent pulse control for quantum memory is viable in the optical domain but nascent in microwave quantum circuits. We show how to realize coherent storage and on-demand pulse retrieval entirely within a superconducting circuit by exploiting and extending existing electromagnetically induced transparency technology in superconducting quantum circuits. Our scheme employs a linear array of superconducting artificial atoms coupled to a microwave transmission line.
Because of their low energy content, microwave signals at the single-photon level are extremely challenging to measure. Guided by recent progress in single-photon optomechanics and hybrid optomechanical systems, we propose a multimode optomechanical transducer that can detect intensities significantly below the single-photon level via adiabatic transfer of the microwave signal to the optical frequency domain where the measurement is then performed. The influence of intrinsic quantum and thermal fluctuations is also discussed.
It has been shown that there are not only transverse but also longitudinal couplings between microwave fields and a superconducting qubit with broken inversion symmetry of the potential energy. Using multiphoton processes induced by longitudinal coupling fields and frequency matching conditions, we design a universal algorithm to produce arbitrary superpositions of two-mode photon states of microwave fields in two separated transmission line resonators, which are coupled to a superconducting qubit. Based on our algorithm, we analyze the generation of evenly-populated states and NOON states. Co…
Efficient transduction devices that reversibly convert optical and microwave quantum signals into each other are essential for integrating different technologies. Rare-earth ions in solids, and in particular Erbium ions, with both optical and microwave addressable transitions are promising candidates for designing transducers. We propose a microwave-to-optical quantum transducer scheme based on the dark state protocol in $\mathrm{^{167}Er}$ doped into yttrium orthosilicate (YSO) at zero external magnetic fields. Zero-field operation is beneficial for superconducting resonators that can incur e…
Over the past two decades, the performance of superconducting quantum circuits has tremendously improved. The progress of superconducting qubits enabled a new industry branch to emerge from global technology enterprises to quantum computing startups. Here, an overview of superconducting quantum circuit microwave control is presented. Furthermore, we discuss one of the persistent engineering challenges in the field, how to control the electromagnetic environment of increasingly complex superconducting circuits such that they are simultaneously protected and efficiently controllable.
The conversion between microwave photons and optical photons with quantum coherence is important for quantum communication and computation. In this paper, we report a proposal using an ensemble of atoms coupled to microwave and optical resonators. Input photons to one resonator are converted into output photons in the other resonator without active operation. Usually the conversion is only optimized at certain frequency. In our proposal, we find that the efficiency is almost a constant and can be close to 100% in a large interval of frequency, i.e. a high-bandwidth conversion can be realized w…
We present protocols to generate quantum entanglement on nonlocal magnons in hybrid systems composed of yttrium iron garnet (YIG) spheres, microwave cavities and a superconducting (SC) qubit. In the schemes, the YIGs are coupled to respective microwave cavities in resonant way, and the SC qubit is placed at the center of the cavities, which interacts with the cavities simultaneously. By exchanging the virtual photon, the cavities can indirectly interact in the far-detuning regime. Detailed protocols are presented to establish entanglement for two, three and arbitrary $N$ magnons with reasonabl…
We describe a multi-mode quantum memory for propagating microwave photons that combines a solid-state spin ensemble resonantly coupled to a frequency tunable single-mode microwave cavity. We first show that high efficiency mapping of the quantum state transported by a free photon to the spin ensemble is possible both for strong and weak coupling between the cavity mode and the spin ensemble. We also show that even in the weak coupling limit unit efficiency and faithful retrieval can be obtained through time reversal inhomogeneous dephasing based on spin echo techniques. This is possible provid…
Frequency conversion between microwave and optical photons is a key enabling technology to create links between superconducting quantum processors and to realize distributed quantum networks. We propose a microwave-optical transduction platform based on long-coherence-time superconducting radio-frequency (SRF) cavities coupled to electro-optic optical cavities to mitigate the loss mechanisms that limit the attainment of high conversion efficiency. In the design, we optimize the microwave-optical field overlap and optical coupling losses, while achieving long microwave and optical photon lifeti…
The interaction of photons and coherent quantum systems can be employed to detect electromagnetic radiation with remarkable sensitivity. We introduce a quantum radiometer based on the photon-induced-dephasing process of a superconducting qubit for sensing microwave radiation at the sub-unit-photon level. Using this radiometer, we demonstrated the radiative cooling of a 1-K microwave resonator and measured its mode temperature with an uncertainty ~0.01 K. We have thus developed a precise tool for studying the thermodynamics of quantum microwave circuits, which provides new solutions for calibra…
Solid-state qubits with transition frequencies in the microwave regime, such as superconducting qubits, are at the forefront of quantum information processing. However, high-fidelity, simultaneous control of superconducting qubits at even a moderate scale remains a challenge, partly due to the complexities of packaging these devices. Here, we present an approach to microwave package design focusing on material choices, signal line engineering, and spurious mode suppression. We describe design guidelines validated using simulations and measurements used to develop a 24-port microwave package. A…
We describe a scheme to coherently convert a microwave photon of a superconducting co-planar waveguide resonator to an optical photon emitted into a well-defined temporal and spatial mode. The conversion is realized by a cold atomic ensemble trapped above the surface of the superconducting atom chip, near the antinode of the microwave cavity. The microwave photon couples to a strong Rydberg transition of the atoms that are also driven by a pair of laser fields with appropriate frequencies and wavevectors for an efficient wave-mixing process. With only few thousand atoms in an ensemble of moder…
In recent years, superconducting qubits show great potential in quantum computation. Hence, microwave photons become very interesting qubits for quantum information processing assisted by superconducting quantum computation. Here, we present the first protocol for the entanglement concentration on microwave photons, resorting to the cross-Kerr effect in circuit quantum electrodynamics (QED). Two superconducting transmission line resonators (TLRs) coupled to superconducting molecule with the N-type level structure induce the effective cross-Kerr effect for realizing the quantum nondemolition (Q…
We theoretically study the transmission of a weak probe field under the influence of a strong pump field in a coupled nanomechanical resonator-superconducting microwave cavity system. Using the standard input-output theory, we find that both pulse delay (slow light effect) and advancement (fast light effect) of the probe field can appear in this coupled system provided that we choose the suitable detuning of the pump field from cavity resonance. The magnitude of the delay (advancement) can be tuned continuously by adjusting the power of the pump field. This technique demonstrates great potenti…
We explore the role played by the intrinsic decoherence in superconducting charge qubits in the presence of a microwave field applied as a magnetic flux. We study how the delayed creation of entanglement, which is opposite to the sudden death of entanglement, can be induced. We compute the time evolution of the population inversion, total correlation and entanglement, taking into account the junction mixed state and dissipation of the cavity field. We show that although decoherence destroys the correlation of the junction and field, information of the initial state may be obtained via quasi-pr…
We propose a detector of microwave photons which can distinguish the vacuum state, one-photon state, and the states with two or more photons. Its operation is based on the two-photon transition in a biased Josephson junction and detection occurs when it switches from a superconducting to a normal state. We model the detector theoretically. The detector performs with more than 90% success probability in several microseconds. It is sensitive for the 8.2GHz photons. The working frequency could be set at the design stage in the range from about 1GHz to 20GHz.
Single photon detectors are fundamental tools of investigation in quantum optics and play a central role in measurement theory and quantum informatics. Photodetectors based on different technologies exist at optical frequencies and much effort is currently being spent on pushing their efficiencies to meet the demands coming from the quantum computing and quantum communication proposals. In the microwave regime however, a single photon detector has remained elusive although several theoretical proposals have been put forth. In this article, we review these recent proposals, especially focusing …
We present a design for a superconducting, on-chip circulator composed of dynamically modulated transfer switches and delays. Design goals are set for the multiplexed readout of superconducting qubits. Simulations of the device show that it allows for low-loss circulation (insertion loss < 0.35 dB and isolation >20 dB) over an instantaneous bandwidth of 2.3 GHz. As the device is estimated to be linear for input powers up to -65 dBm, this design improves on the bandwidth and power-handling of previous superconducting circulators by over a factor of 50, making it ideal for integration with broad…
In this Letter, we demonstrate the generation of multimode entangled states of propagating microwaves. The entangled states are generated by parametrically pumping a multimode superconducting cavity. By combining different pump frequencies, applied simultaneously to the device, we can produce different entanglement structures in a programable fashion. The Gaussian output states are fully characterized by measuring the full covariance matrices of the modes. The covariance matrices are absolutely calibrated using an in situ microwave calibration source, a shot noise tunnel junction. Applying a v…
A quantum memory that can store quantum states faithfully and retrieve them on demand has wide applications in quantum information science. An efficient quantum memory in the microwave regime working alongside quantum processors based on superconducting quantum circuits may serve as an important architecture for quantum computers. Here we realize on-demand storage and retrieval of weak coherent microwave photon pulses at the single-photon level. We implement a superconducting multi-resonator quantum memory which is composed of a set of frequency-tunable coplanar transmission line (CPW) resonat…
Using different configurations of applied strong driving and weak probe fields, we find that only a single three-level superconducting quantum circuit (SQC) is enough to realize amplification, attenuation and frequency conversion of microwave fields. Such a three-level SQC has to possess $Δ$-type cyclic transitions. Different from the parametric amplification (attenuation) and frequency conversion in nonlinear optical media, the real energy levels of the three-level SQC are involved in the energy exchange when these processes are completed. We quantitatively discuss the effects of amplificatio…
We present a scalable quantum-bus-based device for generating the entanglement on microwave photons (MPs) in distant superconducting resonators (SRs). Different from the processors in previous works with some resonators coupled to a superconducting qubit (SQ), our device is composed of some 1D SRs $r_j$ which are coupled to the quantum bus (another common resonator $R$) in its different positions simply, assisted by superconducting quantum interferometer devices. By using the technique for catching and releasing a MP state in a 1D SR, it can work as an entanglement generator or a node in quant…
Crosstalk is a major concern in the implementation of large-scale quantum computation since it can degrade the performance of qubit addressing and cause gate errors. Finding the origin of crosstalk and separating contributions from different channels are essential prerequisites for figuring out crosstalk mitigation schemes. Here, by performing circuit analysis of two coupled floating transmon qubits, we demonstrate that, even if the stray coupling, e.g., between a qubit and the drive line of its nearby qubit, is absent, microwave crosstalk between qubits can still exist due to the presence of …
We propose a way for implementing quantum information transfer with two superconducting flux qubits, by coupling them to a resonator. This proposal does not require adjustment of the level spacings or uniformity in the device parameters. Moreover, neither adiabatic passage nor a second-order detuning is needed by this proposal, thus the operation can be performed much faster when compared with the previous proposals.
Superconducting circuits are a strong contender for realizing quantum computing systems, and are also successfully used to study quantum optics and hybrid quantum systems. However, their cryogenic operation temperatures and the current lack of coherence-preserving microwave-to-optical conversion solutions have hindered the realization of superconducting quantum networks either spanning different cryogenics systems or larger distances. Here, we report the successful operation of a cryogenic waveguide coherently linking transmon qubits located in two dilution refrigerators separated by a physica…
A switch capable of routing microwave signals at cryogenic temperatures is a desirable component for state-of-the-art experiments in many fields of applied physics, including but not limited to quantum information processing, communication and basic research in engineered quantum systems. Conventional mechanical switches provide low insertion loss but disturb operation of dilution cryostats and the associated experiments by heat dissipation. Switches based on semiconductors or microelectromechanical systems have a lower thermal budget but are not readily integrated with current superconducting…
Superconducting circuits and microwave signals are good candidates to realize quantum networks, which are the backbone of quantum computers. We have realized a quantum node based on a 3D microwave superconducting cavity parametrically coupled to a transmission line by a Josephson ring modulator. We first demonstrate the time-controlled capture, storage and retrieval of an optimally shaped propagating microwave field, with an efficiency as high as 80%. We then demonstrate a second essential ability, which is the timed-controlled generation of an entangled state distributed between the node and …
We describe a unified quantum approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. We also generalize the method to a chain of resonators with time delays, and reveal several transport properties similar to a photonic crystal. It is shown that both the quantum and classical analyses provide consistent results, and they together reveal different decay and decoherence mechanisms in a general microwave resonator. These results form a solid basis for understanding the scattering spectrums of networks of microwave resonators, and p…
We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.
Microwave photonics is a remarkably powerful system for quantum simulation and technologies, but its integration in superconducting circuits, superior in many aspects, is constrained by the long wavelengths and impedance mismatches in this platform. We introduce a solution to these difficulties via compact networks of high-kinetic inductance microstrip waveguides and coupling wires with strongly reduced phase velocities. We demonstrate broadband capabilities for superconducting microwave photonics in terms of routing, emulation and generalized linear and nonlinear networks.
We study the propagation and amplification of a microwave field in a four-level cascade quantum system which is realized in a superconducting phase quantum circuit. It is shown that by increasing the microwave pump tones feeding the system, the normal dispersion switches to the anomalous and the gain-assisted superluminal microwave propagation is obtained in this system. Moreover, it is demonstrated that the stimulated microwave field is generated via four-wave mixing without any inversion population in the energy levels of the system (amplification without inversion) and the group velocity of…
We propose a novel hybrid quantum gate between an atom and a microwave photon in a superconducting coplanar waveguide cavity by exploiting the strong resonant microwave coupling between adjacent Rydberg states. Using experimentally achievable parameters gate fidelities $> 0.99$ are possible on sub-$μ$s timescales for waveguide temperatures below 40 mK. This provides a mechanism for generating entanglement between two disparate quantum systems and represents an important step in the creation of a hybrid quantum interface applicable for both quantum simulation and quantum information processing.
We analyze the design of a potential replacement technology for the commercial ferrite circulators that are ubiquitous in contemporary quantum superconducting microwave experiments. The lossless, lumped element design is capable of being integrated on chip with other superconducting microwave devices, thus circumventing the many performance-limiting aspects of ferrite circulators. The design is based on the dynamic modulation of DC superconducting microwave quantum interference devices (SQUIDs) that function as nearly linear, tunable inductors. The connection to familiar ferrite-based circulat…
We propose a method for detecting the presence of a single spin in a crystal by coupling it to a high-quality factor superconducting planar resonator. By confining the microwave field in a constriction of nanometric dimensions, the coupling constant can be as high as $5-10$\,kHz. This coupling affects the amplitude of the field emitted by the resonator, and the integrated homodyne signal allows detection of a single spin with unit signal-to-noise ratio within few milliseconds. We further show that a stochastic master equation approach and a Bayesian analysis of the full time dependent homodyne…
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%.
We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multi-photon processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.
Rydberg helium atoms traveling in pulsed supersonic beams have been coupled to microwave fields in a superconducting coplanar waveguide (CPW) resonator. The atoms were initially prepared in the 1s55s $^3$S$_1$ Rydberg level by two-color two-photon laser excitation from the metastable 1s2s $^3$S$_1$ level. Two-photon microwave transitions between the 1s55s $^3$S$_1$ and 1s56s $^3$S$_1$ levels were then driven by the 19.556 GHz third-harmonic microwave field in a quarter-wave CPW resonator. This superconducting microwave resonator was fabricated from niobium nitride on a silicon substrate and op…
We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment and theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct them in typical measurement results. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or bridge-type resonator does also contain a reference point which can be used to characterize the elect…
We present a way to realize a 3-qubit quantum controlled-phase gate with superconducting qubit systems coupled to a cavity. This proposal does not require adjustment of the qubit level spacings or identical qubit-cavity coupling constants. Moreover, since only a resonant interaction is applied, the gate can be performed fast, within $\sim $ 10 nanosecond. This proposal is quite general, which can be applied to various types of superconducting qubits, atoms trapped in a cavity, or quantum dots coupled to a resonator.
Silicon-Germanium (SiGe) is a material that possesses a multitude of applications ranging from transistors to eletro-optical modulators and quantum dots. The diverse properties of SiGe also make it attractive to implementations involving superconducting quantum computing. Here we demonstrate the fabrication of transmon quantum bits on SiGe layers and investigate the microwave loss properties of SiGe at cryogenic temperatures and single photon microwave powers. We find relaxation times of up to 100 $μ$s, corresponding to a quality factor Q above 4 M for large pad transmons. The high Q values ob…
In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in…
We propose a two-qubit quantum logic gate between a superconducting atom and a propagating microwave photon. The atomic qubit is encoded on its lowest two levels and the photonic qubit is encoded on its carrier frequencies. The gate operation completes deterministically upon reflection of a photon, and various two-qubit gates (SWAP, $\sqrt{\rm SWAP}$, and Identity) are realized through {\it in situ} control of the drive field. The proposed gate is applicable to construction of a network of superconducting atoms, which enables gate operations between non-neighboring atoms.
We describe the high fidelity dispersive measurement of a superconducting qubit using a microwave amplifier based on the Superconducting Low-inductance Undulatory Galvanometer (SLUG). The SLUG preamplifier achieves gain of 19 dB and yields a signal-to-noise ratio improvement of 9 dB over a state-of-the-art HEMT amplifier. We demonstrate a separation fidelity of 99% at 700 ns compared to 59% with the HEMT alone. The SLUG displays a large dynamic range, with an input saturation power corresponding to 700 photons in the readout cavity.
The performance of superconducting circuits for quantum computing is limited by materials losses. In particular, coherence times are typically bounded by two-level system (TLS) losses at single photon powers and millikelvin temperatures. The identification of low loss fabrication techniques, materials, and thin film dielectrics is critical to achieving scalable architectures for superconducting quantum computing. Superconducting microwave resonators provide a convenient qubit proxy for assessing performance and studying TLS loss and other mechanisms relevant to superconducting circuits such as…
We introduce a new entangling gate between two fixed-frequency qubits statically coupled via a microwave resonator bus which combines the following desirable qualities: all-microwave control, appreciable qubit separation for reduction of crosstalk and leakage errors, and the ability to function as a two-qubit conditional-phase gate. A fixed, always-on interaction is explicitly designed between higher energy (non-computational) states of two transmon qubits, and then a conditional-phase gate is `activated' on the otherwise unperturbed qubit subspace via a microwave drive. We implement this micr…
We present an approach to achieve efficient single-photon frequency conversion in the microwave domain based on coherent control in superconducting quantum circuits, which consist of a driven artificial atom coupled to a semi-infinite transmission line. Using the full quantum-mechanical method, we analyze the single-photon scattering process in this system and find that single-photon frequency up- or down-conversion with efficiency close to unity can be achieved by adjusting the parameters of the control field applied to the artificial atom. We further show that our approach is experimentally …
We present a nonlinear multimode superconducting electroacoustic system, where the interplay between superconducting kinetic inductance and piezoelectric strong coupling establishes an effective Kerr nonlinearity among multiple acoustic modes at 10 GHz that could hardly be achieved via intrinsic mechanical nonlinearity. By exciting this multimode Kerr system with a single microwave tone, we further demonstrate a coherent electroacoustic frequency comb and provide theoretical understanding of multimode nonlinear interaction in the superstrong coupling limit. This nonlinear superconducting elect…
