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System noise identification is crucial to the engineering of robust quantum systems. Although existing quantum noise spectroscopy (QNS) protocols measure an aggregate amount of noise affecting a quantum system, they generally cannot distinguish between the underlying processes that contribute to it. Here, we propose and experimentally validate a spin-locking-based QNS protocol that exploits the multi-level energy structure of a superconducting qubit to achieve two notable advances. First, our protocol extends the spectral range of weakly anharmonic qubit spectrometers beyond the present limitations set by their lack of strong anharmonicity. Second, the additional information gained from probing the higher-excited levels enables us to identify and distinguish contributions from different underlying noise mechanisms., Comment: 23 pages, 9 figures

Models of light–matter interactions in quantum electrodynamics typically invoke the dipole approximation1,2, in which atoms are treated as point-like objects when compared to the wavelength of the electromagnetic modes with which they interact. However, when the ratio between the size of the atom and the mode wavelength is increased, the dipole approximation no longer holds and the atom is referred to as a ‘giant atom’2,3. So far, experimental studies with solid-state devices in the giant-atom regime have been limited to superconducting qubits that couple to short-wavelength surface acoustic waves4–10, probing the properties of the atom at only a single frequency. Here we use an alternative architecture that realizes a giant atom by coupling small atoms to a waveguide at multiple, but well separated, discrete locations. This system enables tunable atom–waveguide couplings with large on–off ratios3 and a coupling spectrum that can be engineered by the design of the device. We also demonstrate decoherence-free interactions between multiple giant atoms that are mediated by the quasi-continuous spectrum of modes in the waveguide—an effect that is not achievable using small atoms11. These features allow qubits in this architecture to switch between protected and emissive configurations in situ while retaining qubit–qubit interactions, opening up possibilities for high-fidelity quantum simulations and non-classical itinerant photon generation12,13. Superconducting giant atoms are realized in a waveguide by coupling small atoms to the waveguide at multiple discrete locations, producing tunable atom–waveguide coupling and enabling decoherence-free interactions.

Squeezing of the electromagnetic vacuum is an essential metrological technique used to reduce quantum noise in applications spanning gravitational wave detection, biological microscopy, and quantum information science. In superconducting circuits, the resonator-based Josephson-junction parametric amplifiers conventionally used to generate squeezed microwaves are constrained by a narrow bandwidth and low dynamic range. In this work, we develop a dual-pump, broadband Josephson traveling-wave parametric amplifier that combines a phase-sensitive extinction ratio of 56 dB with single-mode squeezing on par with the best resonator-based squeezers. We also demonstrate two-mode squeezing at microwave frequencies with bandwidth in the gigahertz range that is almost two orders of magnitude wider than that of contemporary resonator-based squeezers. Our amplifier is capable of simultaneously creating entangled microwave photon pairs with large frequency separation, with potential applications including high-fidelity qubit readout, quantum illumination and teleportation.

We introduce a simplified fabrication technique for Josephson junctions and demonstrate superconducting Xmon qubits with $T_1$ relaxation times averaging above 50$~��$s ($Q>$1.5$\times$ 10$^6$). Current shadow-evaporation techniques for aluminum-based Josephson junctions require a separate lithography step to deposit a patch that makes a galvanic, superconducting connection between the junction electrodes and the circuit wiring layer. The patch connection eliminates parasitic junctions, which otherwise contribute significantly to dielectric loss. In our patch-integrated cross-type (PICT) junction technique, we use one lithography step and one vacuum cycle to evaporate both the junction electrodes and the patch. In a study of more than 3600 junctions, we show an average resistance variation of 3.7$\%$ on a wafer that contains forty 0.5$\times$0.5-cm$^2$ chips, with junction areas ranging between 0.01 and 0.16 $��$m$^2$. The average on-chip spread in resistance is 2.7$\%$, with 20 chips varying between 1.4 and 2$\%$. For the junction sizes used for transmon qubits, we deduce a wafer-level transition-frequency variation of 1.7-2.5$\%$. We show that 60-70$\%$ of this variation is attributed to junction-area fluctuations, while the rest is caused by tunnel-junction inhomogeneity. Such high frequency predictability is a requirement for scaling-up the number of qubits in a quantum computer., 6 pages, 4 figures

We experimentally demonstrate a new method of generating entangled itinerant photons using waveguide quantum electrodynamics., Realizing a fully connected network of quantum processors requires the ability to distribute quantum entanglement. For distant processing nodes, this can be achieved by generating, routing, and capturing spatially entangled itinerant photons. In this work, we demonstrate the deterministic generation of such photons using superconducting transmon qubits that are directly coupled to a waveguide. In particular, we generate two-photon N00N states and show that the state and spatial entanglement of the emitted photons are tunable via the qubit frequencies. Using quadrature amplitude detection, we reconstruct the moments and correlations of the photonic modes and demonstrate state preparation fidelities of 84%. Our results provide a path toward realizing quantum communication and teleportation protocols using itinerant photons generated by quantum interference within a waveguide quantum electrodynamics architecture.

Systematic errors in qubit state preparation arise due to non-idealities in the qubit control lines such as impedance mismatch. Using a data-based methodology of short-open-load calibration at a temperature of 30 mK, we report calibrated 1-port scattering parameter data of individual qubit drive line components. At 5~GHz, cryogenic return losses of a 20-dB-attenuator, 10-dB-attenuator, a 230-mm-long 0.86-mm silver-plated cupronickel coaxial cable, and a 230-mm-long 0.86-mm NbTi coaxial cable were found to be 35$^{+3}_{-2}$ dB, 33$^{+3}_{-2}$ dB, 34$^{+3}_{-2}$ dB, and 29$^{+2}_{-1}$ dB respectively. For the same frequency, we also extract cryogenic insertion losses of 0.99$^{+0.04}_{-0.04}$ dB and 0.02$^{+0.04}_{-0.04}$ dB for the coaxial cables. We interpret the results using a master equation simulation of all XY gates performed on a single qubit. For example, we simulate a sequence of two 5 ns gate pulses (X & Y) through a 2-element Fabry-P��rot cavity with 276-mm path length directly preceding the qubit, and establish that the return loss of its reflective elements must be >9.7 dB (> 14.7 dB) to obtain 99.9 % (99.99 %) gate fidelity., 6 pages, 3 figures plus supplementary material (3 figures). The following article has been accepted by Applied Physics Letters. After it is published, it will be found at https://doi.org/10.1063/5.0081861

Models of light-matter interactions in quantum electrodynamics typically invoke the dipole approximation

Present-day, noisy, small or intermediate-scale quantum processors---although far from fault-tolerant---support the execution of heuristic quantum algorithms, which might enable a quantum advantage, for example, when applied to combinatorial optimization problems. On small-scale quantum processors, validations of such algorithms serve as important technology demonstrators. We implement the quantum approximate optimization algorithm (QAOA) on our hardware platform, consisting of two superconducting transmon qubits and one parametrically modulated coupler. We solve small instances of the NP-complete exact-cover problem, with 96.6% success probability, by iterating the algorithm up to level two., 9 pages, 7 figures

Superconducting qubits are leading candidates in the race to build a quantum computer capable of realizing computations beyond the reach of modern supercomputers. The superconducting qubit modality has been used to demonstrate prototype algorithms in the 'noisy intermediate scale quantum' (NISQ) technology era, in which non-error-corrected qubits are used to implement quantum simulations and quantum algorithms. With the recent demonstrations of multiple high fidelity two-qubit gates as well as operations on logical qubits in extensible superconducting qubit systems, this modality also holds promise for the longer-term goal of building larger-scale error-corrected quantum computers. In this brief review, we discuss several of the recent experimental advances in qubit hardware, gate implementations, readout capabilities, early NISQ algorithm implementations, and quantum error correction using superconducting qubits. While continued work on many aspects of this technology is certainly necessary, the pace of both conceptual and technical progress in the last years has been impressive, and here we hope to convey the excitement stemming from this progress., 28 pages, 4 figures

We investigate nondegenerate parametric oscillations in a multimode superconducting microwave resonator that is terminated by a SQUID. The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonance tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input., 7 pages, 8 figures

Quantum coherence and control is foundational to the science and engineering of quantum systems. In van der Waals (vdW) materials, the collective coherent behavior of carriers has been probed successfully by transport measurements. However, temporal coherence and control, as exemplified by manipulating a single quantum degree of freedom, remains to be verified. Here we demonstrate such coherence and control of a superconducting circuit incorporating graphene-based Josephson junctions. Furthermore, we show that this device can be operated as a voltage-tunable transmon qubit, whose spectrum reflects the electronic properties of massless Dirac fermions traveling ballistically. In addition to the potential for advancing extensible quantum computing technology, our results represent a new approach to studying vdW materials using microwave photons in coherent quantum circuits.

In the cavity-QED architecture, photon number fluctuations from residual cavity photons cause qubit dephasing due to the ac Stark effect. These unwanted photons originate from a variety of sources, such as thermal radiation, leftover measurement photons, and cross talk. Using a capacitively shunted flux qubit coupled to a transmission line cavity, we demonstrate a method that identifies and distinguishes coherent and thermal photons based on noise-spectral reconstruction from time-domain spin-locking relaxometry. Using these measurements, we attribute the limiting dephasing source in our system to thermal photons rather than coherent photons. By improving the cryogenic attenuation on lines leading to the cavity, we successfully suppress residual thermal photons and achieve T_{1}-limited spin-echo decay time. The spin-locking noise-spectroscopy technique allows broad frequency access and readily applies to other qubit modalities for identifying general asymmetric nonclassical noise spectra.

As the field of quantum computing advances from the few-qubit stage to larger-scale processors, qubit addressability and extensibility will necessitate the use of 3D integration and packaging. While 3D integration is well-developed for commercial electronics, relatively little work has been performed to determine its compatibility with high-coherence solid-state qubits. Of particular concern, qubit coherence times can be suppressed by the requisite processing steps and close proximity of another chip. In this work, we use a flip-chip process to bond a chip with superconducting flux qubits to another chip containing structures for qubit readout and control. We demonstrate that high qubit coherence (T 1, T 2,echo > 20 μs) is maintained in a flip-chip geometry in the presence of galvanic, capacitive, and inductive coupling between the chips. Superconducting qubits are a leading technology for realizing a quantum computer. To date, experiments have demonstrated control of up to ten qubits using interconnects that laterally address the qubits from the edge of a chip. Extending to larger numbers, however, will require utilizing the third dimension to avoid interconnect crowding and enable control and readout of all qubits in a two-dimensional array. Danna Rosenberg and a team led by William D. Oliver at MIT Lincoln Laboratory and MIT campus have developed a 3D design for efficiently addressing large numbers of qubits, comprising a stack of three bonded chips, each of which performs a different function. The team performed a proof-of-principle experiment using two bonded chips, demonstrating off-chip control and read out of a qubit without significantly impacting the quality of the qubit performance. This demonstration is an important step towards the 3D integration required to build larger-scale devices for quantum information processing.

We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, $k_B T \ll \hbar\omega$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, $\omega/2\pi \sim 5\,$GHz, when the resonator was driven by a current at $3\omega$ with an amplitude exceeding an instability threshold. The output radiation was red-detuned from the fundamental mode. We observed three stable radiative states with equal amplitudes and phase-shifted by $120^\circ$. The downconversion from $3\omega$ to $\omega$ is strongly enhanced by resonant excitation of the second mode of the resonator, and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.

We have developed and tested a doubly tunable resonator, with the intention to simulate fast motion of the resonator boundaries in real space. Our device is a superconducting coplanar-waveguide half-wavelength microwave resonator, with fundamental resonant frequency ~5 GHz. Both of its ends are terminated by dc-SQUIDs, which serve as magnetic-flux-controlled inductances. Applying a flux to either SQUID allows tuning of the resonant frequency by approximately 700 MHz. By using two separate on-chip magnetic-flux lines, we modulate the SQUIDs with two tones of equal frequency, close to twice that of the resonator's fundamental mode. We observe photon generation, at the fundamental frequency, above a certain pump amplitude threshold. By varying the relative phase of the two pumps we are able to control the photon generation threshold, in good agreement with a theoretical model for the modulation of the boundary conditions. At the same time, some of our observations deviate from the theoretical predictions, which we attribute to parasitic couplings, resulting in current driving of the SQUIDs., Comment: 7 pages, 4 figures

The aim of this review is to provide quantum engineers with an introductory guide to the central concepts and challenges in the rapidly accelerating field of superconducting quantum circuits. Over the past twenty years, the field has matured from a predominantly basic research endeavor to one that increasingly explores the engineering of larger-scale superconducting quantum systems. Here, we review several foundational elements -- qubit design, noise properties, qubit control, and readout techniques -- developed during this period, bridging fundamental concepts in circuit quantum electrodynamics (cQED) and contemporary, state-of-the-art applications in gate-model quantum computation., Comment: 67 pages, 28 figures

Le whistleblowing est un élément fondamental de la liberté d'expression et de la liberté de conscience. Il joue également un rôle important dans la lutte contre la corruption. Depuis plusieurs années, la Cour européenne des droits de l'homme (CEDH) développe une jurisprudence en matière de whistleblowing fondée en particulier sur le droit à la liberté d'expression consacré par l'article 10 de la CEDH. Elle a dégagé sur ce fondement juridique six points clefs qui constituent les critères de la protection juridique des lanceurs d’alerte. Suite au rapport de M. Peter Omzigt en 2009, l'Assemblée parlementaire du Conseil de l'Europe (APCE) a adopté la résolution (1729) 2010 puis la recommandation (1916) 2010. La Recommandation CM / rec (2014) 7 définit l'intérêt général en matière de whistleblowing ainsi que le rôle de l’alerte éthique dans la détection et la prevention des malversations. Elle décrit également les éléments constitutifs d’un cadre juridique solide permettant le lancement d’alerte et la protection des lanceurs d’alerte. S’agissant de la transposition de la recommandation dans le système normatif des Etats membres, le Conseil de l'Europe ne s’attache pas au caractère simple ou pluriel de la législation applicable mais à son effectivité. Le CDCJ œuvre en faveur de la promotion et de la mise en œuvre de la recommandation dans les Etats membres par plusieurs actions. L'une des premières actions menées a consisté en la publication de brèves lignes directrices qui peuvent être consultées sur le site Web du CDCJ. Le CDCJ a également adopté un plan d'action en 2014 pour promouvoir la mise en œuvre de la recommandation. D'autres actions pourraient être mises en œuvre à la demande des autorités nationales et le CDCJ se félicite du lancement en France de ce nouveau projet de recherche sur l’alerte éthique. Whistleblowing is a fundamental aspect of freedom of expression and freedom of conscience and it is important also in the fight against corruption. For several years, the European Court of Human rights has made some significant ruling with regards to whistleblowing, setting out six key principles when considering whistleblowing, in particular, on the right to freedom of expression enshrined in Article 10 ECHR. Those six key points are the reasoning of the Court to see if the whistleblowers can benefit from a legal protection. Further to the report of M. Peter Omzigt in 2009, the Parliamentary Assembly of the Council of Europe (PACE) adopted resolution (1729)2010 and Recommendation (1916)2010. Recommendation CM/rec (2014)7 explains what public interest whistleblowing is and its value in deterring and preventing wrongdoing and malpractice. It also describes what a robust framework for facilitating whistleblowing and protecting whistleblowers should look like. Regarding to the normative framework of the recommendation into the member states, the recommendation is very flexible. The recommendation should be seen as a practical tool for member states and it does not take into account whether or not it should be single law or plural laws as long as again it is effective. The CDCJ is willing to promote and support the implementation of the recommendation into member states by several and different activities. One of the first activities which have already been done was the publication of brief guidelines which can be found on the CDCJ website. The CDCJ has also adopted a plan of action in 2014 to promote recommendations on whistleblowers. Other activities could be upon request by national authorities and the CDCJ welcomes this new research project in France.

We report on the fabrication of Josephson junction and superconducting bridges using a damascene CMP process applied for a first time to superconductors. The demonstrated industrial reliability of damascene CMP processes on large scale semiconductor circuits is a major incentive for our research that should allow large numbers of nanometric Josephson junctions to be fabricated in both Nb and Al, the two main material employed in superconducting quantum computing (qubit) and RSFQ electronics fabrication.We carried out a Chemical-Mechanical Polishing (CMP) process on Nb and Al films deposited on a SiO2 layer patterned with trenches of 100 to 300nm of nominal depth. The process formed long bridges, 1 to 4μm wide. The susceptibility and resistive transitions showed that CMP has no observable influence on superconductivity.We have also developed a hybrid technique that uses Al/Al2O3/Al shadow evaporation in the trenches before the damascene CMP process. This allows for high quality “in-situ” junction oxidation with the size reduction benefit provided by the damascene CMP process. We easily reach junctions sizes near 0.5μm2 which are difficult to fabricate by other methods.We describe these techniques and report on measurements on large bridges and junctions and on the fabrication and measurements of Al and Nb nanobridges.

The design, simulation and measurements of an on-chip Mach-Zehnder interferometer operating in the microwave regime are described. Using microwave signals in microfabricated superconducting Al waveguides, the concept of an interferometer is transferred from optics to on-chip. Tuning of the path length of one of the interferometer arms is executed through the tunable inductance of a SQUID. By placing one or more SQUIDs in the waveguide structure and by varying the magnetic flux through the SQUID loop, the total SQUID inductance can be tuned. In this way, a phase difference leading to destructive or constructive interference at the interferometer output can be achieved. Thorough software simulations were performed to determine the different design parameters, assign a desired working frequency and provide a reference for comparison with experimental results. Measurements at 300 mK show an effective working frequency close to the simulations, with a deviation smaller than 0.05 GHz. The behavior of the interferometer is very similar to the simulations as well. The on-off ratio exceeds 40 dB.

We propose and demonstrate a new read-out technique for a superconducting qubit by dispersively coupling it to a Josephson parametric oscillator. We employ a tunable quarter-wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with $185\pm15$ photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot readout performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing., Comment: 11 pages, 5 figures

We characterize a novel Josephson parametric amplifier based on a flux-tunable quarter-wavelength resonator. The fundamental resonance frequency is ~1GHz, but we use higher modes of the resonator for our measurements. An on-chip tuning line allows for magnetic flux pumping of the amplifier. We investigate and compare degenerate parametric amplification, involving a single mode, and nondegenerate parametric amplification, using a pair of modes. We show that we reach quantum-limited noise performance in both cases, and we show that the added noise can be less than 0.5 added photons in the case of low gain.

We experimentally study the behavior of a parametrically pumped nonlinear oscillator, which is based on a superconducting quarter wavelength resonator, and is terminated by a flux-tunable superconducting quantum interference device. We extract parameters for two devices. In particular, we study the effect of the nonlinearities in the system and compare to theory. The Duffing nonlinearity is determined from the probe-power dependent frequency shift of the oscillator, and the nonlinearity related to the parametric flux pumping, is determined from the pump amplitude for the onset of parametric oscillations. Both nonlinearities depend on the parameters of the device and can be tuned in situ by the applied dc flux. We also suggest how to cancel the effect of by adding a small dc flux and a pump tone at twice the pump frequency.

A quantum coherent interface between optical and microwave photons can be used as a basic building block within a future quantum information network. The interface is envisioned as an ensemble of rare-earth ions coupled to a superconducting resonator, allowing for coherent transfer between optical and microwave photons. Towards this end, we have realized a hybrid device coupling a Er$^{3+}$ doped Y$_2$SiO$_5$ crystal in a superconducting coplanar waveguide cavity. We observe a collective spin coupling of 4 MHz and a spin linewdith of down to 75 MHz., Comment: 5 pages, 4 figures

We have directly measured the thickness distribution of the tunnel barriers in state-of-the-art Al/AlOx/Al tunnel junctions. From the distribution we can conclude that less than 10% of the junction area dominates the electron tunnelling. The barriers have been studied by transmission electron microscopy, specifically using atomic resolution annular dark field (ADF) scanning transmission electron microscopy (STEM) imaging. The direct observation of the local barrier thickness shows a Gaussian distribution of the barrier thickness variation along the junction, from ~1 to ~2nm. We have investigated how the thickness distribution varies with oxygen pressure (Po) and oxidation time (to) and we find, in agreement with resistance measurements, that an increased to has a larger impact on barrier thickness and its uniformity compared to an increased Po.

The interface between the Al bottom contact layer and Si substrates in Al based Josephson junctions is believed to have a significant effect on the noise observed in Al based superconducting devices. We have studied the atomic structure of it by transmission electron microscopy. An amorphous layer with a thickness of ∼5 nm was found between the bottom Al electrode and HF-treated Si substrate. It results from intermixing between Al, Si, and O. We also studied the chemical bonding states among the different species using energy loss near edge structure. The observations are of importance for the understanding of the origin of decoherence mechanisms in qubits based on these junctions.

We describe a circuit model for a flux-driven Superconducting QUantum Interference Device (SQUID). This is useful for developing insight into how these devices perform as active elements in parametric amplifiers. The key concept is that frequency mixing in a flux-pumped SQUID allows for the appearance of an effective negative resistance. In the three-wave, degenerate case treated here, a negative resistance appears only over a certain range of allowed input signal phase. This model readily lends itself to testable predictions of more complicated circuits.

Proper grounding between different ground planes in coplanar superconducting qubit circuits is important to avoid spurious resonances which increase decoherence. Here, the authors present a possible solution to suppress such undesired modes using superconducting aluminum air-bridges which have been fabricated on top of aluminum coplanar waveguide transmission lines. 3D electromagnetic simulations were done to guide the design of the air-bridges such that the input reflection (S11) of the bridges was kept at a minimum level. A fabrication method based on optical lithography techniques was developed and it resulted in air-bridges with a height of approximately 10 μm and lengths of up to 500 μm. The method can be generalized to arbitrary length air-bridge with heights even exceeding 15 μm.

A thickness variation of only one Angstrom makes a significant difference in the current through a tunnel junction due to the exponential thickness dependence of the current. It is thus important to achieve a uniform thickness along the barrier to enhance, for example, the sensitivity and speed of single electron transistors based on the tunnel junctions. Here, we have observed that grooves at Al grain boundaries are associated with a local increase of tunnel barrier thickness. The uniformity of the barrier thickness along the tunnel junction thus increases with increasing Al grain size. We have studied the effect of oxidation time, partial oxygen pressure and also temperature during film growth on the grain size. The implications are that the uniformity improves with higher temperature during film growth.