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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.

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.

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 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

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

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.

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

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

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.