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Funding Information: The authors thank S Pirandola, and S Gasparinetti for useful discussions, and thank the support from Project QMiCS (820505) of the EU Flagship on Quantum Technologies. M C, E Z C, R A, G F, S G, and Y O thank the support from FCT—Fundação para a Ciência e a Tecnologia (Portugal), namely through Projects UIDB/50008/2020 and UIDB/04540/2020, as well as from Project TheBlinQC supported by the EU H2020 QuantERA ERA-NET Cofund in Quantum Technologies and by FCT (QuantERA/0001/2017). M C acknowledges support from the DP-PMI and FCT through scholarship PD/BD/135186/2017. G F acknowledges support from FCT through scholarship SFRH/BD/145572/2019. T G-R, M R and M S acknowledge financial support from Basque Government QUANTEK Project from ELKARTEK program (KK-2021/00070), Spanish Ramón y Cajal Grant RYC-2020-030503-I, as well as from OpenSuperQ (820363) of the EU Flagship on Quantum Technologies, and the EU FET-Open Projects Quromorphic (828826) and EPIQUS (899368), and IQM Quantum Computers under the Project ‘Generating quantum algorithms and quantum processor optimization’. M R acknowledges support from UPV/EHU PhD Grant PIF21/289. M M and G C acknowledge funding from the European Research Council under Consolidator Grant No. 681311 (QUESS), and from the Academy of Finland through its Centers of Excellence Program (Project Nos. 312300 and 336810) and QEMP Project (319579). M R, K G F, and F D acknowledge support by the German Research Foundation via Germany’s Excellence Strategy (EXC-2111-390814868), the Elite Network of Bavaria through the program ExQM, the EU Flagship Project QMiCS (Grant No. 820505), the German Federal Ministry of Education and Research via the Projects QUARATE (Grant No. 13N15380) and QuaMToMe (Grant No. 16KISQ036), and the State of Bavaria via the Munich Quantum Valley and the Hightech Agenda Bayern Plus. | openaire: EC/H2020/820505/EU//QMiCS | openaire: EC/H2020/820363/EU//OpenSuperQ | openaire: EC/H2020/681311/EU//QUESS The field of propagating quantum microwaves is a relatively new area of research that is receiving increased attention due to its promising technological applications, both in communication and sensing. While formally similar to quantum optics, some key elements required by the aim of having a controllable quantum microwave interface are still on an early stage of development. Here, we argue where and why a fully operative toolbox for propagating quantum microwaves will be needed, pointing to novel directions of research along the way: from microwave quantum key distribution to quantum radar, bath-system learning, or direct dark matter detection. The article therefore functions both as a review of the state-of-the-art, and as an illustration of the wide reach of applications the future of quantum microwaves will open.

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 pave the way for applying superconducting microwave resonators in complex circuits.

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 electrical properties of a microwave resonator in a single step. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.

Funding Information: The authors thank R. Assouly, R. Dassonneville, and B. Huard for useful discussions. All authors acknowledge support from QMiCS (Grant No. 820505) of the EU Flagship on Quantum Technologies. T.G.-R. and M.S. acknowledge financial support from the Basque Government QUANTEK project under the ELKARTEK program (KK-2021/00070), the Spanish Ramón y Cajal Grant No. RYC-2020-030503-I, project Grant No. PID2021-125823NA-I00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” and “ERDF Invest in your Future”, OpenSuperQ (820363) of the EU Flagship on Quantum Technologies, the EU FET-Open projects Quromorphic (828826) and EPIQUS (899368), and IQM Quantum Computers under the project “Generating quantum algorithms and quantum processor optimization”. M.C. and Y.O. thank the support from FCT – Fundação para a Ciência e a Tecnologia (Portugal), namely through project UIDB/04540/2020, as well as from project TheBlinQC supported by the EU H2020 QuantERA ERA-NET Cofund in QuantumTechnologies and by FCT (QuantERA/0001/2017). M.C. acknowledges support from the DP-PMI and FCT through scholarship PD/BD/135186/2017. M.R., F.F., F.D., and K.F. acknowledge support from the German Research Foundation via Germany’s Excellence Strategy (EXC-2111-390814868), Elite Network of Bavaria through program ExQM, and the German Federal Ministry of Education and Research via project QUARATE (Grant No. 13N15380) and project QuaMToMe (Grant No. 16KISQ036). This research is part of the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus. The research of V.S. is supported by the Basque Government through the BERC 2022–2025 program and by the Ministry of Science, Innovation, and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718. M.M. acknowledges funding from the European Research Council under Consolidator Grant No. 681311 (QUESS), from the Jane and Aatos Erkko Foundation and the Technology Industries of Finland Centennial Foundation through their Future Makers program, and from the Academy of Finland through its Centers of Excellence Program (Projects No. 312300 and No. 336810). | openaire: EC/H2020/820505/EU//QMiCS | openaire: EC/H2020/681311/EU//QUESS Microwave technology plays a central role in current wireless communications, including mobile communication and local area networks. The microwave range shows relevant advantages with respect to other frequencies in open-air transmission, such as low absorption losses and low-energy consumption, and in addition, it is the natural working frequency in superconducting quantum technologies. Entanglement distribution between separate parties is at the core of secure quantum communications. Therefore, understanding its limitations in realistic open-air settings, especially in the rather unexplored microwave regime, is crucial for transforming microwave quantum communications into a mainstream technology. Here, we investigate the feasibility of an open-air entanglement distribution scheme with microwave two-mode squeezed states. First, we study the reach of direct entanglement transmission in open air, obtaining a maximum distance of approximately 500 m with parameters feasible for state-of-the-art experiments. Subsequently, we adapt entanglement distillation and entanglement swapping protocols to microwave technology in order to reduce the environment-induced entanglement degradation. The employed entanglement distillation helps to increase quantum correlations in the short-distance low-squeezing regime by up to 46%, and the reach of entanglement increases by 14% with entanglement swapping. Importantly, we compute the fidelity of a continuous-variable quantum teleportation protocol using open-air-distributed entanglement as a resource. Finally, we adapt this machinery to explore the limitations of quantum communication between satellites, where the impact of thermal noise is substantially reduced and diffraction losses are dominant.

Description, Experimental microwave teleportation brings quantum local area networks within reach by exceeding the no-cloning limit., The field of quantum communication promises to provide efficient and unconditionally secure ways to exchange information, particularly, in the form of quantum states. Meanwhile, recent breakthroughs in quantum computation with superconducting circuits trigger a demand for quantum communication channels between spatially separated superconducting processors operating at microwave frequencies. In pursuit of this goal, we demonstrate the unconditional quantum teleportation of propagating coherent microwave states by exploiting two-mode squeezing and analog feedforward over a macroscopic distance of d = 0.42 m. We achieve a teleportation fidelity of F = 0.689 ± 0.004, exceeding the asymptotic no-cloning threshold. Thus, the quantum nature of the teleported states is preserved, opening the avenue toward unconditional security in microwave quantum communication.

We have fabricated and studied a system of two tunable and coupled nonlinear superconducting resonators. The nonlinearity is introduced by galvanically coupled dc superconducting quantum interference devices. We simulate the system response by means of a circuit model, which includes an additional signal path introduced by the electromagnetic environment. Furthermore, we present two methods allowing us to experimentally determine the nonlinearity. First, we fit the measured frequency and flux dependence of the transmission data to simulations based on the equivalent circuit model. Second, we fit the power dependence of the transmission data to a model that is predicted by the nonlinear equation of motion describing the system. Our results show that we are able to tune the nonlinearity of the resonators by almost two orders of magnitude via an external coil and two on-chip antennas. The studied system represents a basic building block for larger systems, allowing for quantum simulations of bosonic many-body systems with a larger number of lattice sites.

Quantum communication protocols based on nonclassical correlations can be more efficient than known classical methods and offer intrinsic security over direct state transfer. In particular, remote state preparation aims at the creation of a desired and known quantum state at a remote location using classical communication and quantum entanglement. We present an experimental realization of deterministic continuous-variable remote state preparation in the microwave regime over a distance of 35 cm. By employing propagating two-mode squeezed microwave states and feedforward, we achieve the remote preparation of squeezed states with up to 1.6 dB of squeezing below the vacuum level. Finally, security of remote state preparation is investigated by using the concept of the one-time pad and measuring the von Neumann entropies. We find nearly identical values for the entropy of the remotely prepared state and the respective conditional entropy given the classically communicated information and, thus, demonstrate close-to-perfect security., Continuous-variable remote state preparation in the microwave domain would allow to leverage the superconducting technology for quantum networks applications. Here, the authors show how to deterministically prepare squeezed Gaussian states across 35 cm using previously shared entanglement.

Quantum communication is a holy grail to achieve secure communication among a set of partners, since it is provably unbreakable by physical laws. Quantum sensing employs quantum entanglement as an extra resource to determine parameters by either using less resources or attaining a precision unachievable in classical protocols. A paradigmatic example is the quantum radar, which allows one to detect an object without being detected oneself, by making use of the additional asset provided by quantum entanglement to reduce the intensity of the signal. In the optical regime, impressive technological advances have been reached in the last years, such as the first quantum communication between ground and satellites, as well as the first proof-of-principle experiments in quantum sensing. The development of microwave quantum technologies turned out, nonetheless, to be more challenging. Here, we will discuss the challenges regarding the use of microwaves for quantum communication and sensing. Based on this analysis, we propose a roadmap to achieve real-life applications in these fields., Long version of the article published in the Proceedings

The concept of parity describes the inversion symmetry of a system and is of fundamental relevance in the standard model, quantum information processing, and field theory. In quantum electrodynamics, parity is conserved and large field gradients are required to engineer the parity of the light-matter interaction operator. In this work, we engineer a potassium-like artificial atom represented by a specifically designed superconducting flux qubit. We control the wave function parity of the artificial atom with an effective orbital momentum provided by a resonator. By irradiating the artificial atom with spatially shaped microwave fields, we select the interaction parity in situ. In this way, we observe dipole and quadrupole selection rules for single state transitions and induce transparency via longitudinal coupling. Our work advances the design of tunable artificial multilevel atoms to a new level, which is particularly promising with respect to quantum chemistry simulations with near-term superconducting circuits., Comment: Published manuscript (6 pages, 3 figures) plus supplemental materials (8 pages, 2 figures)

Two-mode squeezing is a fascinating example of quantum entanglement manifested in cross-correlations of non-commuting observables between two subsystems. At the same time, these subsystems themselves may contain no quantum signatures in their self-correlations. These properties make two-mode squeezed (TMS) states an ideal resource for applications in quantum communication. Here, we generate propagating microwave TMS states by a beam splitter distributing single mode squeezing emitted from distinct Josephson parametric amplifiers along two output paths. We experimentally study the fundamental dephasing process of quantum cross-correlations in continuous-variable propagating TMS microwave states and accurately describe it with a theory model. In this way, we gain the insight into finite-time entanglement limits and predict high fidelities for benchmark quantum communication protocols such as remote state preparation and quantum teleportation. We acknowledge support by the German Research Foundation through FE 1564/1-1, Spanish MINECO/FEDER FIS2015-69983-P, UPV/EHU PhD grant, Basque Government Grant IT986-16, European Project AQuS (Project No. 640800), Elite Network of Bavaria through the program ExQM, the projects JST ERATO (Grant No. JPMJER1601) and JSPS KAKENHI (Grant No. 26220601 and Grant No. 15K17731). E.S. acknowledges support from a TUM August-Wilhelm Scheer Visiting Professorship and hospitality of Walther-Meissner-Institut and TUM Institute for Advanced Study. We would like to thank K. Kusuyama for assistance with part of the JPA fabrication.

Superconducting 3D microwave cavities offer state-of-the-art coherence times and a well controlled environment for superconducting qubits. In order to realize at the same time fast readout and long-lived quantum information storage, one can couple the qubit both to a low-quality readout and a high-quality storage cavity. However, such systems are bulky compared to their less coherent 2D counterparts. A more compact and scalable approach is achieved by making use of the multimode structure of a 3D cavity. In our work, we investigate such a device where a transmon qubit is capacitively coupled to two modes of a single 3D cavity. The external coupling is engineered so that the memory mode has an about 100 times larger quality factor than the readout mode. Using an all-microwave second-order protocol, we realize a lifetime enhancement of the stored state over the qubit lifetime by a factor of $6$ with a fidelity of approximately $80\%$ determined via quantum process tomography. We also find that this enhancement is not limited by fundamental constraints., 5 pages, 4 figures

For quantum information processing with superconducting circuits, efficient amplification of weak microwave signals is often required. For this purpose, Josephson parametric amplifiers (JPAs) are commonly used, due to their quantum-limited noise performance. The authors show that flux-driven JPAs exhibit hysteresis, even for negligible screening parameters, and that their amplification properties depend strongly on the resonator characteristics. These phenomena are important for a full understanding of the magnetic field response and parametric amplification in JPAs, and thus their application.

In quantum illumination entangled light is employed to enhance the detection accuracy of an object when compared with the best classical protocol. On the other hand, cloaking is a stealth technology based on covering a target with a material deflecting the light around the object to avoid its detection. Here, we propose a quantum illumination protocol especially adapted to quantum microwave technology. This protocol seizes the phase-shift induced by some cloaking techniques, such as scattering reduction, allowing for a 3 dB improvement in the detection of a cloaked target. The method can also be employed for the detection of a phase-shift in bright environments in different frequency regimes. Finally, we study the minimal efficiency required by the photocounter for which the quantum illumination protocol still shows a gain with respect to the classical protocol. The authors thank Ryan Sweke, A. Marx and S. Pogorzalek for the useful discussions. We acknowledge support from Spanish MINECO/FEDER FIS2015-69983-P, Basque Government IT472-10, UPV/EHU PhD grant, AQuS project, the German Research Foundation through FE 1564/1-1, Elite Network of Bavaria through the program ExQM, and the IMPRS Quantum Science and Technology.

In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the $n^{2}\,{+}\,n$ photon number variance of thermal microwave photons emitted from a black-body radiator for mean photon numbers $0.05\,{\lesssim}\,n\,{\lesssim}\,1.5$. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier., Comment: containing supplemental material

Displacement of propagating quantum states of light is a fundamental operation for quantum communication. It enables fundamental studies on macroscopic quantum coherence and plays an important role in quantum teleportation protocols with continuous variables. In our experiments, we have successfully implemented this operation for propagating squeezed microwave states. We demonstrate that, even for strong displacement amplitudes, there is no degradation of the squeezing level in the reconstructed quantum states. Furthermore, we confirm that path entanglement generated by using displaced squeezed states remains constant over a wide range of the displacement power.

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY).-- et al., We realize a device allowing for tunable and switchable coupling between two frequency-degenerate superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current flux qubit. We characterize the tunable and switchable coupling in the frequency and time domains and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by controlling the qubit population via a microwave drive. Our measurements allow us to find parameter regimes for optimal coupler performance and quantify the tunability range., This work is supported by the German Research Foundation through SFB 631, Spanish MINECO FIS2012-36673-C03-02; UPV/EHU UFI 11/55; Basque Government IT472-10; CCQED, PROMISCE, and SCALEQIT EU projects. B.P. acknowledges support from the STC Center for Integrated Quantum Materials, NSF Grant No. DMR-1231319.

Under the terms of the Creative Commons Attribution license.-- et al., We report on ultrastrong coupling between a superconducting flux qubit and a resonant mode of a system comprised of two superconducting coplanar stripline resonators coupled galvanically to the qubit. With a coupling strength as high as 17.5% of the mode frequency, exceeding that of previous circuit quantum electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The spectroscopic response of our multimode system reveals a clear breakdown of the Jaynes-Cummings approximation. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction. ©2016 American Physical Society, Thiswork is supported by the German Research Foundation through SFB 631 and FE 1564/1-1; Spanish MINECO FIS2012-36673-03-02, MAT2014-53432-C5-1-R, FIS2014- 55867-P and FIS2012-33022; CAM Research Network QUITEMAD+; UPV/EHU UFI 11/55, UPV/EHU PhD Grant, and Basque Government IT472-10; the Fondo Nacional de Desarrollo Cientifico y Tecnológico (FONDECYT, Chile) under Grant 1150653; the EU projects CCQED, PROMISCE, and SCALEQIT. We further acknowledge GEFENOL.

The transient dynamics of long overlap Josephson junctions in the frame of the sine-Gordon model with a white noise source is investigated. The effect of noise delayed decay is observed for the case of overdamped sine-Gordon equation. It is shown that this noise induced effect, in the range of small noise intensities, vanishes for junctions lengths greater than several Josephson penetration length., Comment: 7 pages, 9 figures, to appear in Journ. of Bifurcation and Chaos, 2008

10 pags., 5 figs., We realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance between the resonators. We present a spectroscopic characterization of the device. In particular, we observe couplings g/2π ranging between –320 MHz and 37 MHz. In the case of g 0, the microwave power cross transmission between the two resonators is reduced by almost four orders of magnitude as compared to the case where the coupling is switched on., The authors acknowledge support from the German Research Foundation through SFB 631 and FE 1564/1-1; the EU projects CCQED, PROMISCE and SCALEQIT; the doctorate program ExQM of the Elite Network of Bavaria; the Spanish MINECO projects FIS2012-33022, FIS2012-36673-C03-02, and FIS2015-69983-P; the CAM Research Network QUITEMAD+; the Basque Government IT472-10 and UPV/EHU UFI 11/55.

Nonreciprocal microwave transmission through a long Josephson junction in the flux-flow regime is studied analytically and numerically within the framework of the perturbed sine-Gordon model. We demonstrate that the maximum attenuation of the transmitted power occurs when the direction of the flux flow is opposite to the direction of the microwave propagation. This attenuation is nonreciprocal with respect to the flux-flow direction and can be enhanced by increasing the system length and proper impedance matching of the junction ends to external transmission line., 5 pages, 5 figures

In a coupled system of one classical and one quantum mechanical degree of freedom, the quantum degree of freedom can facilitate the escape of the whole system. Such unusual escape characteristics have been theoretically predicted as "M\"unchhausen effect". We implement such a system by shunting one of the two junctions of a dc-SQUID with an additional capacitance. In our experiments, we detect a crossover between quantum and classical escape processes related to the direction of escape. We find that, under varying external magnetic flux, macroscopic quantum tunneling periodically alternates with thermally activated escape, a hallmark of the "M\"unchhausen effect".

Thermal microwave states are omnipresent noise sources in superconducting quantum circuits covering all relevant frequency regimes. We use them as a probe to identify three second-order decoherence mechanisms of a superconducting transmon. First, we quantify the efficiency of a resonator filter in the dispersive Jaynes-Cummings regime and find evidence for parasitic loss channels. Second, we probe second-order noise in the low-frequency regime and demonstrate the expected $T^{3}$ temperature dependence of the qubit dephasing rate. Finally, we show that qubit parameter fluctuations due to two-level states are enhanced under the influence of thermal microwave states. In particular, we experimentally confirm the $T^{2}$-dependence of the fluctuation spectrum expected for noninteracting two-level states., Comment: 13 pages, 10 figures

We describe fabrication and testing of composite flux qubits combining Nb- and Al-based superconducting circuit technology. This hybrid approach to making qubits allows for employing pi-phase shifters fabricated using well-established Nb-based technology of superconductor-ferromagnet-superconductor Josephson junctions. The important feature here is to obtain high interface transparency between Nb and Al layers without degrading sub-micron shadow mask. We achieve this by in-situ Ar etching using e-beam gun. Shadow-evaporated Al/AlOx/Al Josephson junctions with Nb bias pads show the expected current-voltage characteristics with reproducible critical currents. Using this technique, we fabricated composite Nb/Al flux qubits with Nb/CuNi/Nb pi-shifters and measured their magnetic field response. The observed offset between the field responses of the qubits with and without pi-junction is attributed to the pi phase shift. The reported approach can be used for implementing a variety of hybrid Nb/Al superconducting quantum circuits., 9 pages, 5 figures

Quantum computing using superconducting circuits underwent rapid development in the last decade. This field has propelled from quantum manipulation of single two-level systems to complex designs employing multiple coupled qubits allowing one to execute simple quantum algorithms. On the way to a practical quantum computer, a need for scalable interfaces between classical circuits and the quantum counterparts has arisen. Low-temperature superconducting single-flux quantum (SFQ) logic employs magnetic fluxons in Josephson transmission lines (JTLs) as basic bits for classical computation. Here, we report on an experiment implementing a direct link between SFQ electronics and a superconducting qubit. We demonstrate a readout of the state of a flux qubit through a frequency shift of a single fluxon oscillating in a JTL. The energy spectrum of the flux qubit is measured using this technique. The demonstrated approach may open ways to future full-scale integration of solid-state quantum computers with digital SFQ electronics.

We present a systematic analysis of the internal losses of superconducting coplanar waveguide microwave resonators based on niobium thin films on silicon substrates. In particular, we investigate losses introduced by Nb/Al interfaces in the center conductor, which is important for experiments where Al based Josephson junctions are integrated into Nb based circuits. We find that these interfaces can be a strong source for two-level state (TLS) losses, when the interfaces are not positioned at current nodes of the resonator. In addition to TLS losses, for resonators including Al, quasiparticle losses become relevant above 200 mK. Finally, we investigate how losses generated by eddy currents in conductive material on the backside of the substrate can be minimized by using thick enough substrates or metals with high conductivity on the substrate backside.

We have measured the bidirectional propagation of microwaves through a long Josephson junction in a flux-flow regime. We demonstrate that the transmitted microwave power depends on the direction of microwave propagation with respect to the direction of the flux flow. This nonreciprocal behavior is explained by the interaction of the microwave signal with the moving fluxon chain inside the junction. Thus a long junction may act as an on-chip isolator for external microwave signals, with its transmission properties being fully controlled by the bias current and in-plane magnetic field.

The computer simulations of fluctuational dynamics of an annular system governed by the sine-Gordon model with a white noise source are performed. It is demonstrated that the mean escape time (MET) of a phase string for an annular structure can be much larger than for a linear one and has a strongly pronounced maximum as a function of system's length. The location of the MET maximum roughly equals the size of the kink-antikink pair, which leads to evidence of a spatial crossover between two dynamical regimes: when the phase string escapes over the potential barrier as a whole and when the creation of kink-antikink pairs is the main mechanism of the escape process. For large lengths and in the limit of small noise intensity gamma, for both MET and inverse concentration of kinks, we observe the same dependence versus the kink energy E(k): approximately exp(2E(k)/gamma) for the annular structure and approximately exp(E(k)/gamma) for the linear one.

Computer simulations of the fluctuational dynamics of a long-overlap Josephson junction in the frame of the sine-Gordon model with a white noise source have been performed. It has been demonstrated that for the case of constant critical current density the mean escape time (MET) increases with increasing junction length; and for homogeneous bias current distribution the MET tends to a constant, while for inhomogeneous current distribution the MET quickly decreases after approaching a few Josephson lengths. The mean voltage (measured in the noise-induced regime where the phase consequently jumps between neighboring potential minima) versus junction length behaves inversely in comparison with the MET.

Experiments towards realizing a readout of superconducting qubits by using ballistic Josephson vortices are reported. We measured the microwave radiation induced by a fluxon moving in an annular Josephson junction. By coupling a flux qubit as a current dipole to the annular junction, we detect periodic variations of the fluxon's oscillation frequency versus magnetic flux through the qubit. We found that the scattering of a fluxon on a current dipole can lead to the acceleration of a fluxon regardless of a dipole polarity. We use the perturbation theory and numerical simulations of the perturbed sine-Gordon equation to analyze our results.

The low-noise amplification of weak microwave signals is crucial for countless protocols in quantum information processing. Quantum mechanics sets an ultimate lower limit of half a photon to the added input noise for phase-preserving amplification of narrowband signals, also known as the standard quantum limit (SQL). This limit, which is equivalent to a maximum quantum efficiency of 0.5, can be overcome by employing nondegenerate parametric amplification of broadband signals. We show that, in principle, a maximum quantum efficiency of unity can be reached. Experimentally, we find a quantum efficiency of 0.69 ± 0.02, well beyond the SQL, by employing a flux-driven Josephson parametric amplifier and broadband thermal signals. We expect that our results allow for fundamental improvements in the detection of ultraweak microwave signals.