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Loading quantum information deterministically onto a quantum node is an important step toward a quantum network. Here, we demonstrate that coherent-state microwave photons with an optimal temporal waveform can be efficiently loaded onto a single superconducting artificial atom in a semi-infinite one-dimensional (1D) transmission-line waveguide. Using a weak coherent state (the number of photons (

We report the implementation of a near-quantum-limited, traveling-wave parametric amplifier that uses three-wave mixing (3WM). To favor amplification by 3WM, we use the superconducting nonlinear asymmetric inductive element (SNAIL) loops, biased with a dc magnetic flux. In addition, we equip the device with dispersion engineering features to create a stop-band at the second harmonic of the pump and suppress the propagation of the higher harmonics that otherwise degrade the amplification. With a chain of 440 SNAILs, the amplifier provides up to 20 dB gain and a 3-dB bandwidth of 1 GHz. The added noise by the amplifier is found to be less than one photon., 6 pages, 6 figures

Hosting non-classical states of light in three-dimensional microwave cavities has emerged as a promising paradigm for continuous-variable quantum information processing. Here we experimentally demonstrate high-fidelity generation of a range of Wigner-negative states useful for quantum computation, such as Schr\"{o}dinger-cat states, binomial states, Gottesman-Kitaev-Preskill (GKP) states, as well as cubic phase states. The latter states have been long sought after in quantum optics and were never achieved experimentally before. To do so, we use a sequence of interleaved selective number-dependent arbitrary phase (SNAP) gates and displacements. We optimize the state preparation in two steps. First we use a gradient-descent algorithm to optimize the parameters of the SNAP and displacement gates. Then we optimize the envelope of the pulses implementing the SNAP gates. Our results show that this way of creating highly non-classical states in a harmonic oscillator is robust to fluctuations of the system parameters such as the qubit frequency and the dispersive shift.

In quantum optics, light–matter interaction has conventionally been studied using small atoms interacting with electromagnetic fields with wavelength several orders of magnitude larger than the atomic dimensions1,2. In contrast, here we experimentally demonstrate the vastly different ‘giant atom’ regime, where an artificial atom interacts with acoustic fields with wavelength several orders of magnitude smaller than the atomic dimensions. This is achieved by coupling a superconducting qubit3 to surface acoustic waves at two points with separation on the order of 100 wavelengths. This approach is comparable to controlling the radiation of an atom by attaching it to an antenna. The slow velocity of sound leads to a significant internal time-delay for the field to propagate across the giant atom, giving rise to non-Markovian dynamics4. We demonstrate the non-Markovian character of the giant atom in the frequency spectrum as well as non-exponential relaxation in the time domain. By coupling a superconducting qubit to surface acoustic waves the ‘giant atom’ regime is realized, where an atom is coupled to a field with wavelength orders of magnitude smaller than the atomic size. This leads to non-Markovian qubit dynamics.

We benchmark the decoherence of superconducting qubits to examine the temporal stability of energy-relaxation and dephasing. By collecting statistics during measurements spanning multiple days, we find the mean parameters $\overline{T_{1}}$ = 49 $\mu$s and $\overline{T_{2}^{*}}$ = 95 $\mu$s, however, both of these quantities fluctuate explaining the need for frequent re-calibration in qubit setups. Our main finding is that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems (TLS). Through statistical analysis, we determine switching rates of these TLS and observe the coherent coupling between an individual TLS and a transmon qubit. Finally, we find evidence that the qubit's frequency stability is limited by capacitance noise. Importantly, this produces a 0.8 ms limit on the pure dephasing which we also observe. Collectively, these findings raise the need for performing qubit metrology to examine the reproducibility of qubit parameters, where these fluctuations could affect qubit gate fidelity., Comment: 15 pages ArXiv version rev2

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 investigate three types of amplification processes for light fields coupling to an atom near the end of a one-dimensional (1D) semi-infinite waveguide. We consider two setups where a drive creates population inversion in the bare or dressed basis of a three-level atom and one setup where the amplification is due to higher-order processes in a driven two-level atom. In all cases, the end of the waveguide acts as a mirror for the light. We find that this enhances the amplification in two ways compared to the same setups in an open waveguide. Firstly, the mirror forces all output from the atom to travel in one direction instead of being split up into two output channels. Secondly, interference due to the mirror enables tuning of the ratio of relaxation rates for different transitions in the atom to increase population inversion. We quantify the enhancement in amplification due to these factors and show that it can be demonstrated for standard parameters in experiments with superconducting quantum circuits.

Exploiting multiple modes in a quantum acoustic device could enable applications in quantum information in a hardware-efficient setup, including quantum simulation in a synthetic dimension and continuous-variable quantum computing with cluster states.We develop a multimode surface acoustic wave (SAW) resonator with a superconducting quantum interference device (SQUID) integrated in one of the Bragg reflectors. The interaction with the SQUID-shunted mirror gives rise to coupling between the more than 20 accessible resonator modes. We exploit this coupling to demonstrate two-mode squeezing of SAW phonons, as well as four-mode multipartite entanglement. Our results open avenues for continuous-variable quantum computing in a compact hybrid quantum system.

We report the observation of Electromagnetically Induced Transparency (EIT) of a mechanical field, where a superconducting artificial atom is coupled to a 1D-transmission line for surface acoustic waves. An electromagnetic microwave drive is used as the control field, rendering the superconducting transmon qubit transparent to the acoustic probe beam. The strong frequency dependence of the acoustic coupling enables EIT in a ladder configuration due to the suppressed relaxation of the upper level. Our results show that superconducting circuits can be engineered to interact with acoustic fields in parameter regimes not readily accessible to purely electromagnetic systems.

Microscopic two-level system (TLS) defects at dielectric surfaces and interfaces are among the dominant sources of loss in superconducting quantum circuits, and their properties have been extensively probed using superconducting resonators and qubits. We report on spectroscopy of TLSs coupling to the strain field in a surface acoustic wave (SAW) resonator. The narrow free spectral range of the resonator allows for two-tone spectroscopy where a strong pump is applied at one resonance, while a weak signal is used to probe a different mode. We map the spectral hole burnt by the pump tone as a function of frequency and extract parameters of the TLS ensemble. Our results suggest that detuned acoustic pumping can be used to enhance the coherence of superconducting devices by saturating TLSs.

The ability to control and measure the temperature of propagating microwave modes down to very low temperatures is indispensable for quantum information processing, and may open opportunities for studies of heat transport at the nanoscale, also in the quantum regime. Here we propose and experimentally demonstrate primary thermometry of propagating microwaves using a transmon-type superconducting circuit. Our device operates continuously, with a sensitivity down to $4\times 10^{-4}$ photons/$\sqrt{\mbox{Hz}}$ and a bandwidth of 40 MHz. We measure the thermal occupation of the modes of a highly attenuated coaxial cable in a range of 0.001 to 0.4 thermal photons, corresponding to a temperature range from 35 mK to 210 mK at a frequency around 5 GHz. To increase the radiation temperature in a controlled fashion, we either inject calibrated, wideband digital noise, or heat the device and its environment. This thermometry scheme can find applications in benchmarking and characterization of cryogenic microwave setups, temperature measurements in hybrid quantum systems, and quantum thermodynamics.

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

We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor Q i. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure Q i as function of frequency, power and temperature. We observe a linear increase of Q i with frequency, as predicted by the simulations for a constant electromechanical coupling. Additionally, Q i shows a weak power dependence and a negligible temperature dependence around 10 mK, excluding two level systems and non-equilibrium quasiparticles as the main source of losses at that temperature.

We explore routing of propagating phonons in analogy with previous experiments on photons. Surface acoustic waves (SAWs) in the microwave regime are scattered by a superconducting transmon qubit. The transmon can be tuned on or off resonance with the incident SAW field using an external magnetic field or the Autler-Townes effect, and thus the reflection and transmission of the SAW field can be controlled in time. We observe 80% extinction in the transmission of the low power continuous signal and a 40 ns rise time of the router. The slow propagation speed of SAWs on solid surfaces allows for in-flight manipulations of the propagating phonons. The ability to route short, 100 ns, pulses enables new functionality, for instance to catch an acoustic phonon between two qubits and then release it in a controlled direction., 10 pages, 11 figures put into 4 figures, 1 table

Today, surface acoustic waves (SAWs) and bulk acoustic waves are already two of the very few phononic technologies of industrial relevance and can been found in a myriad of devices employing these nanoscale earthquakes on a chip. Acoustic radio frequency filters, for instance, are integral parts of wireless devices. SAWs in particular find applications in life sciences and microfluidics for sensing and mixing of tiny amounts of liquids. In addition to this continuously growing number of applications, SAWs are ideally suited to probe and control elementary excitations in condensed matter at the limit of single quantum excitations. Even collective excitations, classical or quantum are nowadays coherently interfaced by SAWs. This wide, highly diverse, interdisciplinary and continuously expanding spectrum literally unites advanced sensing and manipulation applications. Remarkably, SAW technology is inherently multiscale and spans from single atomic or nanoscopic units up even to the millimeter scale. The aim of this Roadmap is to present a snapshot of the present state of surface acoustic wave science and technology in 2019 and provide an opinion on the challenges and opportunities that the future holds from a group of renown experts, covering the interdisciplinary key areas, ranging from fundamental quantum effects to practical applications of acoustic devices in life science.

Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and exceeding the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it., Comment: 7+5 pages, 4+2 figures

Artificial atoms coupled to surface acoustic waves (SAWs) have played a crucial role in the recent development of circuit quantum acoustodynamics (cQAD). In this paper, we have investigated the interaction of an artificial atom and SAWs beyond the weak coupling regime, focusing on the role of the interdigital transducer (IDT) that enables the coupling. We find a parameter regime in which the IDT acts as a cavity for the atom, rather than an antenna. In other words, the atom forms its own cavity. Similar to an atom coupled to an explicit cavity, this regime is characterized by vacuum-Rabi splitting, as the atom hybridizes with the phononic vacuum inside the IDT. This hybridization is possible because of the interdigitated coupling, which has a large spatial extension, and the slow propagation speed of SAWs. We work out a criterion for entering this regime from a model based on standard circuit-quantization techniques, taking only material parameters as inputs. Most notably, we find this regime hard to avoid for an atom on top of a strong piezoelectric material, such as LiNbO$_3$. The SAW-coupled atom on top of LiNbO$_3$ can thus be regarded as an atom-cavity-bath system. On weaker piezoelectric materials, the number of IDT electrodes need to be large in order to reach this regime., 11 pages, 5 figures

We present a comprehensive study of internal quality factors in superconducting stub-geometry three-dimensional cavities made of aluminum. We use wet etching, annealing, and electrochemical polishing to improve the as machined quality factor. We find that the dominant loss channel is split between the two-level system loss and an unknown source with a 40:60 proportion. A total of 17 cavities of different purity, resonance frequency, and size were studied. Our treatment results in reproducible cavities, with 10 of them showing internal quality factors above 80 x 10(6) at a power corresponding to an average of a single photon in the cavity. The best cavity has an internal quality factor of 115 x 10(6) at a single photon level. (C) 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:// creativecommons.org/licenses/by/4.0/).

We present an experimental demonstration as well as a theoretical model of an integrated circuit designed for the manipulation of a microwave field down to the single-photon level. The device is made of a superconducting resonator coupled to a transmission line via a second frequency-tunable resonator. The tunable resonator can be used as a tunable coupler between the fixed resonator and the transmission line. Moreover, the manipulation of the microwave field between the two resonators is possible. In particular, we demonstrate the swapping of the field from one resonator to the other by pulsing the frequency detuning between the two resonators. The behavior of the system, which determines how the device can be operated, is analyzed as a function of one key parameter of the system, the damping ratio of the coupled resonators. We show a good agreement between experiments and simulations, realized by solving a set of coupled differential equations., 10 pages, 6 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

We report on the experimental observation of period multiplication in parametrically driven tunable superconducting resonators. We modulate the magnetic flux through a superconducting quantum interference device, attached to a quarter-wavelength resonator, with frequencies $n\omega$ close to multiples, $n=2,\,3,\,4,\,5$, of the resonator fundamental mode and observe intense output radiation at $\omega$. The output field manifests $n$-fold degeneracy with respect to the phase, the $n$ states are phase shifted by $2\pi/n$ with respect to each other. Our demonstration verifies the theoretical prediction by Guo et al. in PRL 111, 205303 (2013), and paves the way for engineering complex macroscopic quantum cat states with microwave photons.

Entangled pairs of microwave photons are commonly produced in the narrow frequency band of a resonator, which represents a modified vacuum density of states. We generate and investigate the entanglement of a stream of photon pairs, generated in a semi-infinite broadband transmission line, terminated by a superconducting quantum interference device (SQUID). A weak pump signal modulates the SQUID inductance, resulting in a single time-varying boundary condition, and we detect all four quadratures of the microwave radiation emitted at two different frequencies separated by 0.7 GHz. Power calibration is done in situ, and we find positive logarithmic negativity and two-mode squeezing below the vacuum in the observed radiation, indicating entanglement.

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.