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High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel however degrade entanglement fidelity, thereby increasing the error rates of entangled state protocols. Entanglement purification provides a method to alleviate these non-idealities, by distilling impure states into higher-fidelity entangled states. Here we demonstrate the entanglement purification of Bell pairs shared between two remote superconducting quantum nodes connected by a moderately lossy, 1-meter long superconducting communication cable. We use a purification process to correct the dominant amplitude damping errors caused by transmission through the cable, with fractional increases in fidelity as large as $25\%$, achieved for higher damping errors. The best final fidelity the purification achieves is $94.09\pm 0.98\%$. In addition, we use both dynamical decoupling and Rabi driving to protect the entangled states from local noise, increasing the effective qubit dephasing time by a factor of 4, from $3~\rm \mu s$ to $12~\rm\mu s$. These methods demonstrate the potential for the generation and preservation of very high-fidelity entanglement in a superconducting quantum communication network.

Phonon modes at microwave frequencies can be cooled to their quantum ground state using conventional cryogenic refrigeration, providing a convenient way to study and manipulate quantum states at the single phonon level. Phonons are of particular interest because mechanical deformations can mediate interactions with a wide range of different quantum systems, including solid-state defects, superconducting qubits, as well as optical photons when using optomechanically-active constructs. Phonons thus hold promise for quantum-focused applications as diverse as sensing, information processing, and communication. Here, we describe a piezoelectric quantum bulk acoustic resonator (QBAR) with a 4.88 GHz resonant frequency that at cryogenic temperatures displays large electromechanical coupling strength combined with a high intrinsic mechanical quality factor $Q_i \approx 4.3 \times 10^4$. Using a recently-developed flip-chip technique, we couple this QBAR resonator to a superconducting qubit on a separate die and demonstrate quantum control of the mechanics in the coupled system. This approach promises a facile and flexible experimental approach to quantum acoustics and hybrid quantum systems.

Variable microwave-frequency couplers are highly useful components in classical communication systems, and likely will play an important role in quantum communication applications. Conventional semiconductor-based microwave couplers have been used with superconducting quantum circuits, enabling for example the in situ measurements of multiple devices via a common readout chain. However, the semiconducting elements are lossy, and furthermore dissipate energy when switched, making them unsuitable for cryogenic applications requiring rapid, repeated switching. Superconducting Josephson junction-based couplers can be designed for dissipation-free operation with fast switching and are easily integrated with superconducting quantum circuits. These enable on-chip, quantum-coherent routing of microwave photons, providing an appealing alternative to semiconductor switches. Here, we present and characterize a chip-based broadband microwave variable coupler, tunable over 4-8 GHz with over 1.5 GHz instantaneous bandwidth, based on the superconducting quantum interference device (SQUID) with two parallel Josephson junctions. The coupler is dissipation-free, features large on-off ratios in excess of 40 dB, and the coupling can be changed in about 10 ns. The simple design presented here can be readily integrated with superconducting qubit circuits, and can be easily generalized to realize a four- or more port device., Comment: 11 pages, 8 figures

Converting seamlessly between optical and microwave frequencies would enable ultralow-loss long-distance communication of both classical and quantum signals, and could enable a quantum telecommunication repeater. High conversion rates with low loss are needed for any practical technology. The authors present a significant step toward both of those goals: an integrated electromechanical and optomechanical design that yields significantly lower loss with megahertz conversion rates, which is promising for future bidirectional quantum communication. Their design includes a number of innovations for generating and transmitting the rf acoustic signals that are key to device operation.

Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surface-acoustic-wave communication channel into which one superconducting qubit can emit itinerant phonons that the same or a second qubit can later re-capture. If the first qubit releases only half of a phonon, the system follows a superposition of paths during the phonon propagation: either an itinerant phonon is in the channel, or the first qubit remains in its excited state. These two paths are made to constructively or destructively interfere by changing the relative phase of the two intermediate states, resulting in a phase-dependent modulation of the first qubit's final state, following interaction with the half-phonon. A heralding mechanism is added to this construct, entangling a heralding phonon with the signalling phonon. The first qubit emits a phonon herald conditioned on the qubit being in its excited state, with no signaling phonon, and the second qubit catches this heralding phonon, storing which-path information which can either be read out, destroying the signaling phonon's self-interference, or erased., 16 pages, 8 figures

International audience; Quantum entanglement is a key resource for quantum computation and quantum communication \cite{Nielsen2010}. Scaling to large quantum communication or computation networks further requires the deterministic generation of multi-qubit entanglement \cite{Gottesman1999,Duan2001,Jiang2007}. The deterministic entanglement of two remote qubits has recently been demonstrated with microwave photons \cite{Kurpiers2018,Axline2018,Campagne2018,Leung2019,Zhong2019}, optical photons \cite{Humphreys2018} and surface acoustic wave phonons \cite{Bienfait2019}. However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily due to limited state transfer fidelities. Here, we report a quantum network comprising two separate superconducting quantum nodes connected by a 1 meter-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the coaxial cable to one qubit in each node, we can transfer quantum states between the nodes with a process fidelity of $0.911\pm0.008$. Using the high-fidelity communication link, we can prepare a three-qubit Greenberger-Horne-Zeilinger (GHZ) state \cite{Greenberger1990,Neeley2010,Dicarlo2010} in one node and deterministically transfer this state to the other node, with a transferred state fidelity of $0.656\pm 0.014$. We further use this system to deterministically generate a two-node, six-qubit GHZ state, globally distributed within the network, with a state fidelity of $0.722\pm0.021$. The GHZ state fidelities are clearly above the threshold of $1/2$ for genuine multipartite entanglement \cite{Guhne2010}, and show that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers \cite{Monroe2014,Chou2018}.

Effective quantum communication between remote quantum nodes requires high fidelity quantum state transfer and remote entanglement generation. Recent experiments have demonstrated that microwave photons, as well as phonons, can be used to couple superconducting qubits, with a fidelity limited primarily by loss in the communication channel. Adiabatic protocols can overcome channel loss by transferring quantum states without populating the lossy communication channel. Here we present a unique superconducting quantum communication system, comprising two superconducting qubits connected by a 0.73 m-long communication channel. Significantly, we can introduce large tunable loss to the channel, allowing exploration of different entanglement protocols in the presence of dissipation. When set for minimum loss in the channel, we demonstrate an adiabatic quantum state transfer protocol that achieves 99% transfer efficiency as well as the deterministic generation of entangled Bell states with a fidelity of 96%, all without populating the intervening communication channel, and competitive with a qubit-resonant mode-qubit relay method. We also explore the performance of the adiabatic protocol in the presence of significant channel loss, and show that the adiabatic protocol protects against loss in the channel, achieving higher state transfer and entanglement fidelities than the relay method., Comment: 27 pages, 14 figures

Flip-chip architectures have recently enabled significant scaling-up of multi-qubit circuits and have been used to assemble hybrid quantum systems that combine different substrates, for example, for quantum acoustics experiments. The standard flip-chip method uses superconducting galvanic connections between two substrates, typically implemented using sophisticated indium wafer-bonding systems, which give highly reliable and temperature-cyclable assemblies, but are expensive, somewhat inflexible in design, and require robust substrates that can sustain the large compressive forces required to cold-weld the indium bonds. A much simpler method is to assemble dies using very low-force contacts and air-dried adhesives, although this does not provide a galvanic contact between the dies. Here, we demonstrate that the latter technique can be used to reliably couple superconducting qubit circuits, in which the qubits are on separate dies, without the need for a galvanic connection. We demonstrate full vector qubit control of each qubit on each of the two dies, with high-fidelity single-shot readout, and further demonstrate entanglement-generating excitation swaps as well as benchmark a controlled-Z entangling gate between the two qubits on the two dies. This exemplifies a simple and inexpensive assembly method for two-plus-one-dimensional quantum circuit integration that supports the use of delicate or unusually shaped substrates.

Broadband quantum-limited amplifiers play a critical role in the single-shot readout of superconducting qubits, but a popular implementation, the traveling wave parametric amplifier, involves a complex design and fabrication process. Here, we present a simple design for a Josephson parametric amplifier, using a lumped element resonator comprising a superconducting quantum interference device whose useful bandwidth is enhanced with an on-chip impedance-matching circuit. We demonstrate a flux-coupling geometry that maximizes the coupling to the Josephson loop and minimizes spurious excitation of the amplifier resonant circuit. The amplifier, which operates in a flux-pumped mode, is demonstrated with a power gain of more than 20 dB over a bandwidth of about 300 MHz, where approximate noise measurements indicate quantum-limited performance. A procedure is given for optimizing the bandwidth for this kind of amplifier, using a linearized circuit simulation while minimizing non-linearities.

Recent significant advances in coupling superconducting qubits to acoustic wave resonators has led to demonstrations of quantum control of surface and bulk acoustic resonant modes as well Wigner tomography of quantum states in these modes. These advances were achieved through the efficient coupling afforded by piezoelectric materials combined with GHz-frequency acoustic Fabry-Perot cavities. Quantum control of itinerant surface acoustic waves appears in reach, but is challenging due to the limitations of conventional transducers in the appropriate GHz-frequency band. In particular, GHz-frequency unidirectional transducers would provide an important addition to the desired quantum toolbox, promising unit efficiency with directional control over the surface acoustic wave emission pattern. Here we report the design, fabrication and experimental characterization of unidirectional distributed acoustic reflection transducers (DARTs) demonstrating a high transduction frequency of 4.8 GHz with a peak directivity larger than 25 dB and a directivity greater than 15 dB over a bandwidth of 17 MHz. A numerical model reproduces the main features of the transducer response quite well, with ten adjustable parameters (most of which are constrained by geometric and physical considerations). This represents a significant step towards quantum control of itinerant quantum acoustic waves., Comment: Main paper: 5 pages, 3 figures. Supplementary: 6 pages, 2 figures

Quantum communication relies on the efficient generation of entanglement between remote quantum nodes, as entanglement is required to achieve and verify secure communications1. Remote entanglement has been realized using a number of different probabilistic schemes2,3, but deterministic remote entanglement has only been demonstrated recently, using a variety of superconducting circuit approaches4–6. However, the deterministic violation of a Bell inequality7, a strong measure of quantum correlation, has not been demonstrated so far in a superconducting quantum communication architecture, in part because achieving sufficiently strong correlation requires fast and accurate control of the emission and capture of the entangling photons. Here, we present a simple and robust architecture for achieving this benchmark result in a superconducting system. A deterministic violation of the Bell inequality is reported between two superconducting circuits, providing a necessary test for establishing strong enough quantum entanglement to achieve secure quantum communications.

The superposition of quantum states is one of the hallmarks of quantum physics, and clear demonstrations of superposition have been achieved in a number of quantum systems. However, mechanical systems have remained a challenge, with only indirect demonstrations of mechanical state superpositions, in spite of the intellectual appeal and technical utility such a capability would bring. This is due in part to the highly linear response of most mechanical systems, making quantum operation difficult, as well as their characteristically low frequencies, making it difficult to reach the quantum ground state. In this work, we demonstrate full quantum control of the mechanical state of a macroscopic mechanical resonator. We strongly couple a surface acoustic wave resonator to a superconducting qubit, using the qubit to control and measure quantum states in the mechanical resonator. Most notably, we generate a quantum superposition of the zero and one phonon states and map this and other states using Wigner tomography. This precise, programmable quantum control is essential to a range of applications of surface acoustic waves in the quantum limit, including using surface acoustic waves to couple disparate quantum systems.

A challenge faced by experimenters exploring hybrid quantum systems is how to integrate and interconnect different materials and different substrates in a quantum-coherent fashion. Here, we present a simple and inexpensive flip-chip bonding process, suitable for integrating hybrid quantum devices on chips from different substrates. The process only requires equipment and materials used routinely for contact photolithography, and it is possible to undo the bonding and reuse the chips. The technique requires minimal compressive force, so it is compatible with a wide range of different substrates. Unlike indium-based bonding, this process does not establish a galvanic connection between the two chips, but as we show, in some situations this is not necessary. We demonstrate the technique using lithographically patterned quarter-wave coplanar waveguide resonators, fabricated on one chip, and couple these inductively to a transmission line patterned lithographically on a separate chip. The two chips have a vertical interchip gap of about 7 μm, and we can repeatedly achieve lateral alignments of better than 2 μm. We measure electromagnetic resonances with low-power (∼1 photon) internal quality factors Qi around 5 × 105, comparable to single-chip performances, with as-designed coupling quality factors Qc ranging from 2 × 102 to 5 × 105.

Qi-Wa refers to the up curl on the lengths of hand scrolls and hanging scrolls, which has troubled Chinese artisans and emperors for as long as the art of painting and calligraphy has existed. This warp is unwelcome not only for aesthetic reasons, but its potential damage to the fiber and ink. Although it is generally treated as a part of the cockling and curling due to moisture, consistency of paste, and defects from the mounting procedures, we demonstrate that the spontaneous extrinsic curvature incurred from the storage is in fact more essential to understanding and curing Qi-Wa. In contrast to the former factors whose effects are less predictable, the plastic deformation and strain distribution on a membrane are a well-defined mechanical problem. We study this phenomenon by experiments, theoretical models, and molecular dynamics simulation, and obtain consistent scaling relations for the Qi-Wa height. This knowledge enables us to propose modifications on the traditional mounting techniques that are tested on real mounted paper to be effective at mitigating Qi-Wa. By experimenting on polymer-based films, we demonstrate the possible relevance of our study to the modern development of flexible electronic paper.

We study whether and how the energy scalings based on the single-ridge approximation are revised in an actual crumpled sheet; namely, in the presence of ridge-ridge interactions. Molecular Dynamics Simulation is employed for this purpose. In order to improve the data quality, modifications are introduced to the common protocol. As crumpling proceeds, we find that the average storing energy changes from being proportional to one-third of the ridge length to a linear relation, while the ratio of bending and stretching energies decreases from 5 to 2. The discrepancy between previous simulations and experiments on the material-dependence for the power-law exponent is resolved. We further determine the averaged ridge length to scale linearly with the crumpled ball size $R$, the ridge number as $1/R^2$, and the average storing energy per unit ridge length as $1/R^{2.364\sim 2.487}$. These results are consistent with the mean-field predictions. Finally, we extend the existent simulations to the high-pressure region for completeness, and verify the existence of a new scaling relation that is more general than the familiar power law at covering the whole density range., Comment: 4 pages, 6 figures