Search

Bulk acoustic resonators support robust, long-lived mechanical modes, capable of coupling to various quantum systems. In separate works, such devices have achieved strong coupling to both superconducting qubits, via piezoelectricity, and optical cavities, via Brillouin interactions. In this work, we present a hybrid microwave–optical platform capable of coupling to bulk acoustic waves through cavity-enhanced piezoelectric and photoelastic interactions. The modular, tunable system achieves fully resonant and well-mode-matched interactions among a 3D microwave cavity, a high-frequency bulk acoustic resonator, and a Fabry–Perot cavity. We realize this piezo–Brillouin interaction in x-cut quartz, demonstrating the potential for strong optomechanical interactions and high cooperativity using optical cavity enhancement. We further show how this device functions as a bidirectional electro–opto–mechanical transducer, with transduction efficiency exceeding 10 − 8 , and a feasible path towards unity conversion efficiency. The high optical sensitivity and ability to apply a large resonant microwave field in this system also offers a tool for probing anomalous electromechanical couplings, which we demonstrate by investigating (nominally centrosymmetric) C a F 2 and revealing a parasitic piezoelectricity of 83 am/V. Such studies are an important topic for emerging quantum technologies, and highlight the versatility of this hybrid platform.

Dielectric loss is known to limit state-of-the-art superconducting qubit lifetimes. Recent experiments imply upper bounds on bulk dielectric loss tangents on the order of $100$ parts-per-billion, but because these inferences are drawn from fully fabricated devices with many loss channels, they do not definitively implicate or exonerate the dielectric. To resolve this ambiguity, we have devised a measurement method capable of separating and resolving bulk dielectric loss with a sensitivity at the level of $5$ parts per billion. The method, which we call the dielectric dipper, involves the in-situ insertion of a dielectric sample into a high-quality microwave cavity mode. Smoothly varying the sample's participation in the cavity mode enables a differential measurement of the sample's dielectric loss tangent. The dielectric dipper can probe the low-power behavior of dielectrics at cryogenic temperatures, and does so without the need for any lithographic process, enabling controlled comparisons of substrate materials and processing techniques. We demonstrate the method with measurements of EFG sapphire, from which we infer a bulk loss tangent of $62(7) \times 10^{-9}$ and a substrate-air interface loss tangent of $12(2) \times 10^{-4}$. For a typical transmon, this bulk loss tangent would limit device quality factors to less than $20$ million, suggesting that bulk loss is likely the dominant loss mechanism in the longest-lived transmons on sapphire. We also demonstrate this method on HEMEX sapphire and bound its bulk loss tangent to be less than $15(5) \times 10^{-9}$. As this bound is about 3 times smaller than the bulk loss tangent of EFG sapphire, use of HEMEX sapphire as a substrate would lift the bulk dielectric coherence limit of a typical transmon qubit to several milliseconds., Comment: 8 pages, 5 figures, and 13 page appendix. Submitted revision synchronizes content with associated journal article, including the addition of figure 7 (methods of cavity measurement) and Appendix H (bounding magnetic bulk loss)

The realization of robust universal quantum computation with any platform ultimately requires both the coherent storage of quantum information and (at least) one entangling operation between individual elements. The use of continuous-variable bosonic modes as the quantum element is a promising route to preserve the coherence of quantum information against naturally-occurring errors. However, operations between bosonic modes can be challenging. In analogy to the exchange interaction between discrete-variable spin systems, the exponential-SWAP unitary [$\mathbf{U}_{\mathrm{E}}\left(\theta_c\right)$] can coherently transfer the states between two bosonic modes, regardless of the chosen encoding, realizing a deterministic entangling operation for certain $\theta_c$. Here, we develop an efficient circuit to implement $\mathbf{U}_{\mathrm{E}}\left(\theta_c\right)$ and realize the operation in a three-dimensional circuit QED architecture. We demonstrate high-quality deterministic entanglement between two cavity modes with several different encodings. Our results provide a crucial primitive necessary for universal quantum computation using bosonic modes.

Single-photon detectors are ubiquitous and integral components of photonic quantum cryptography, communication, and computation. Many applications, however, require not only detecting the presence of any photons, but distinguishing the number present with a single shot. Here, we implement a single-shot, high-fidelity photon number-resolving detector of up to 15 microwave photons in a cavity-qubit circuit QED platform. This detector functions by measuring a series of generalized parity operators which make up the bits in the binary decomposition of the photon number. Our protocol consists of successive, independent measurements of each bit by entangling the ancilla with the cavity, then reading out and resetting the ancilla. Photon loss and ancilla readout errors can flip one or more bits, causing nontrivial errors in the outcome, but these errors have a traceable form which can be captured in a simple hidden Markov model. Relying on the independence of each bit measurement, we mitigate biases in ensembles of measurements, showing good agreement with the predictions of the model. The mitigation improves the average total variation distance error of Fock states from $13.5\%$ to $1.1\%$. We also show that the mitigation is efficiently scalable to an $M$-mode system provided that the errors are independent and sufficiently small. Our work motivates the development of new algorithms that utilize single-shot, high-fidelity PNR detectors., Comment: 15 pages, 7 figures

Quantum bits are more robust to noise when they are encoded non-locally. In such an encoding, errors affecting the underlying physical system can then be detected and corrected before they corrupt the encoded information. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a qubit, which is delocalised in the phase-space of a single oscillator. However, implementing measurements that reveal error syndromes of the oscillator while preserving the encoded information has proved experimentally challenging: the only realisation so far relied on post-selection, which is incompatible with quantum error correction (QEC). The novelty of our experiment is precisely that it implements these non-destructive error-syndrome measurements for a superconducting microwave cavity. We design and implement an original feedback protocol that incorporates such measurements to prepare square and hexagonal GKP code states. We then demonstrate QEC of an encoded qubit with unprecedented suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous variable systems and, in contrast with previous implementations of QEC, can mitigate all logical errors generated by a wide variety of noise processes, and open a way towards fault-tolerant quantum computation., Text and figures edited for clarity. The claims of the paper remain the same. Author list fixed

Microwave photons are used to wire up modular quantum processors, but mitigating the effects of loss between modules remains a crucial challenge. We use a low-loss bus resonator to couple bosonic qubits across a superconducting network with protocols made robust to photon loss in the bus. We transfer a multiphoton qubit and track loss events, improving the fidelity to the break-even point with respect to the best uncorrectable encoding. We also demonstrate a entanglement protocol using Hong-Ou-Mandel interference and error detection to prepare a two-photon Bell state with fidelity 94% and success probability 0.79, halving the error obtained with a single photon. This network link also presents new opportunities for resource-efficient direct gates between modules., PRX Quantum, 2 (3), ISSN:2691-3399

A quantum computer has the potential to effciently solve problems that are intractable for classical computers. Constructing a large-scale quantum processor, however, is challenging due to errors and noise inherent in real-world quantum systems. One approach to this challenge is to utilize modularity--a pervasive strategy found throughout nature and engineering--to build complex systems robustly. Such an approach manages complexity and uncertainty by assembling small, specialized components into a larger architecture. These considerations motivate the development of a quantum modular architecture, where separate quantum systems are combined via communication channels into a quantum network. In this architecture, an essential tool for universal quantum computation is the teleportation of an entangling quantum gate, a technique originally proposed in 1999 which, until now, has not been realized deterministically. Here, we experimentally demonstrate a teleported controlled-NOT (CNOT) operation made deterministic by utilizing real-time adaptive control. Additionally, we take a crucial step towards implementing robust, error-correctable modules by enacting the gate between logical qubits, encoding quantum information redundantly in the states of superconducting cavities. Such teleported operations have significant implications for fault-tolerant quantum computation, and when realized within a network can have broad applications in quantum communication, metrology, and simulations. Our results illustrate a compelling approach for implementing multi-qubit operations on logical qubits within an error-protected quantum modular architecture., Comment: Main text: 7 pages, 4 figures; Supplementary Information: 26 pages, 13 figures

The ability to engineer and manipulate different types of quantum mechanical objects allows us to take advantage of their unique properties and create useful hybrid technologies. Thus far, complex quantum states and exquisite quantum control have been demonstrated in systems ranging from trapped ions to superconducting resonators. Recently, there have been many efforts to extend these demonstrations to the motion of complex, macroscopic objects. These mechanical objects have important applications as quantum memories or transducers for measuring and connecting different types of quantum systems. In particular, there have been a few experiments that couple motion to nonlinear quantum objects such as superconducting qubits. This opens up the possibility of creating, storing, and manipulating non-Gaussian quantum states in mechanical degrees of freedom. However, before sophisticated quantum control of mechanical motion can be achieved, we must realize systems with long coherence times while maintaining a sufficient interaction strength. These systems should be implemented in a simple and robust manner that allows for increasing complexity and scalability in the future. Here we experimentally demonstrate a high frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction. In contrast to previous experiments with qubit-mechanical systems, our device requires only simple fabrication methods, extends coherence times to many microseconds, and provides controllable access to a multitude of phonon modes. We use this system to demonstrate basic quantum operations on the coupled qubit-phonon system. Straightforward improvements to the current device will allow for advanced protocols analogous to what has been shown in optical and microwave resonators, resulting in a novel resource for implementing hybrid quantum technologies., 21 pages, 12 figures, including supplementary information

The ability to transfer quantum information from a memory to a flying qubit is important for building quantum networks. The very fast release of a multiphoton state in a microwave cavity memory into propagating modes is demonstrated.

To solve classically hard problems, quantum computers need to be resilient to the influence of noise and decoherence. In such a fault-tolerant quantum computer, noise-induced errors must be detected and corrected in real-time to prevent them from propagating between components. This requirement is especially pertinent while applying quantum gates, when the interaction between components can cause errors to quickly spread throughout the system. However, the large overhead involved in most fault-tolerant architectures makes implementing these systems a daunting task, which motivates the search for hardware-efficient alternatives. Here, we present a gate enacted by a multilevel ancilla transmon on a cavity-encoded logical qubit that is fault-tolerant with respect to decoherence in both the ancilla and the encoded qubit. We maintain the purity of the encoded qubit in the presence of ancilla errors by detecting those errors in real-time, and applying the appropriate corrections. We show a reduction of the logical gate error by a factor of two in the presence of naturally occurring decoherence, and demonstrate resilience against ancilla bit-flips and phase-flips by observing a sixfold suppression of the gate error with increased energy relaxation, and a fourfold suppression with increased dephasing noise. The results demonstrate that bosonic logical qubits can be controlled by error-prone ancilla qubits without inheriting the ancilla's inferior performance. As such, error-corrected ancilla-enabled gates are an important step towards fully fault-tolerant processing of bosonic qubits., 15 pages, 8 figures

A striking characteristic of superconducting circuits is that their eigenspectra and intermode coupling strengths are well predicted by simple Hamiltonians representing combinations of quantum circuit elements. Of particular interest is the Cooper-pair-box Hamiltonian used to describe the eigenspectra of transmon qubits, which can depend strongly on the offset-charge difference across the Josephson element. Notably, this offset-charge dependence can also be observed in the dispersive coupling between an ancillary readout mode and a transmon fabricated in the offset-charge-sensitive (OCS) regime. We utilize this effect to achieve direct, high-fidelity dispersive readout of the joint plasmon and charge-parity state of an OCS transmon, which enables efficient detection of charge fluctuations and nonequilibrium-quasiparticle dynamics. Specifically, we show that additional high-frequency filtering can extend the charge-parity lifetime of our device by two orders of magnitude, resulting in a significantly improved energy relaxation time $T_1\sim200~\mu\mathrm{s}$., Comment: 11 pages, 9 figures

The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. For addressing systems with underlying bosonic structure, it is advantageous to utilize a naturally bosonic platform. Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging. Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra [J. Huh et al., Nat. Photonics 9, 615 (2015)NPAHBY1749-488510.1038/nphoton.2015.153] in a two-mode superconducting device. In addition to enacting the requisite set of Gaussian operations across both modes, we fulfill the scalability requirement by demonstrating, for the first time in any platform, a high-fidelity single-shot photon number resolving detection scheme capable of resolving up to 15 photons per mode. Furthermore, we exercise the capability of synthesizing non-Gaussian input states to simulate spectra of molecular ensembles in vibrational excited states. We show the reprogrammability of our implementation by extracting the spectra of photoelectron processes in H_{2}O, O_{3}, NO_{2}, and SO_{2}. The capabilities highlighted in this work establish the superconducting architecture as a promising platform for bosonic simulations, and by combining them with tools such as Kerr interactions and engineered dissipation, enable the simulation of a wider class of bosonic systems.

Nanofabrication techniques for superconducting qubits rely on resist-based masks patterned by electron-beam or optical lithography. We have developed an alternative nanofabrication technique based on free-standing silicon shadow masks fabricated from silicon-on-insulator wafers. These silicon shadow masks not only eliminate organic residues associated with resist-based lithography, but also provide a pathway to better understand and control surface-dielectric losses in superconducting qubits by decoupling mask fabrication from substrate preparation. We have successfully fabricated aluminum 3D transmon superconducting qubits with these shadow masks and found coherence quality factors comparable to those fabricated with standard techniques., Comment: 6 pages, 6 figures, additional experimental data - new figure, typos corrected, supplementary material (2 pages, 1 figure, 1 table)

Low-loss cavities are important in building high-coherence superconducting quantum computers. Generating high quality joints between parts is crucial to the realization of a scalable quantum computer using the circuit quantum electrodynamics (cQED) framework. In this paper, we adapt the technique of indium bump bonding to the cQED architecture to realize high quality superconducting microwave joints between chips. We use this technique to fabricate compact superconducting cavities in the multilayer microwave integrated quantum circuits (MMIQC) architecture and achieve single photon quality factor over 300 million or single-photon lifetimes approaching 5 ms. To quantify the performance of the resulting seam, we fabricate microwave stripline resonators in multiple sections connected by different numbers of bonds, resulting in a wide range of seam admittances. The measured quality factors combined with the designed seam admittances allow us to bound the conductance of the seam at $g_\text{seam} \ge 2\times 10^{10} /(\Omega \text{m})$. Such a conductance should enable construction of micromachined superconducting cavities with quality factor of at least a billion. These results demonstrate the capability to construct very high quality microwave structures within the MMIQC architecture.

We have realized a new interaction between superconducting qubits and a readout cavity that results in the displacement of a coherent state in the cavity, conditioned on the state of the qubit. This conditional state, when it reaches the cavity-following, phase-sensitive amplifier, matches its measured observable, namely, the in phase quadrature. In a setup where several qubits are coupled to the same readout resonator, we show it is possible to measure the state of a target qubit with minimal dephasing of the other qubits. Our results suggest novel directions for faster readout of superconducting qubits and implementations of bosonic quantum error-correcting codes.

Quantum computation presents a powerful new paradigm for information processing. A robust universal quantum computer can be realized with any well controlled quantum system, but a successful platform will ultimately require the combination of highly coherent, error-correctable quantum elements with at least one entangling operation between them

Quantum states of mechanical motion can be important resources for quantum information, metrology, and studies of fundamental physics. Recent demonstrations of superconducting qubits coupled to acoustic resonators have opened up the possibility of performing quantum operations on macroscopic motional modes, which can act as long-lived quantum memories or transducers. In addition, they can potentially be used to test for novel decoherence mechanisms in macroscopic objects and other modifications to standard quantum theory. Many of these applications call for the ability to create and characterize complex quantum states, putting demanding requirements on the speed of quantum operations and the coherence of the mechanical mode. In this work, we demonstrate the controlled generation of multi-phonon Fock states in a macroscopic bulk-acoustic wave resonator. We also perform Wigner tomography and state reconstruction to highlight the quantum nature of the prepared states. These demonstrations are made possible by the long coherence times of our acoustic resonator and our ability to selectively couple to individual phonon modes. Our work shows that circuit quantum acousto-dynamics (circuit QAD) enables sophisticated quantum control of macroscopic mechanical objects and opens the door to using acoustic modes as novel quantum resources., Includes main text and supplementary information

Entangling gates between qubits are a crucial component for performing algorithms in quantum computers. However, any quantum algorithm must ultimately operate on error-protected logical qubits encoded in high-dimensional systems. Typically, logical qubits are encoded in multiple two-level systems, but entangling gates operating on such qubits are highly complex and have not yet been demonstrated. Here, we realize a controlled NOT (CNOT) gate between two multiphoton qubits in two microwave cavities. In this approach, we encode a qubit in the high-dimensional space of a single cavity mode, rather than in multiple two-level systems. We couple two such encoded qubits together through a transmon, which is driven by an RF pump to apply the gate within 190 ns. This is two orders of magnitude shorter than the decoherence time of the transmon, enabling a high-fidelity gate operation. These results are an important step towards universal algorithms on error-corrected logical qubits., Comment: 10 pages, 11 figures (incl. Supplementary Information)

Interference experiments provide a simple yet powerful tool to unravel fundamental features of quantum physics. Here we engineer an RF-driven, time-dependent bilinear coupling that can be tuned to implement a robust 50:50 beamsplitter between stationary states stored in two superconducting cavities in a three-dimensional architecture. With this, we realize high contrast Hong-Ou- Mandel (HOM) interference between two spectrally-detuned stationary modes. We demonstrate that this coupling provides an efficient method for measuring the quantum state overlap between arbitrary states of the two cavities. Finally, we showcase concatenated beamsplitters and differential phase shifters to implement cascaded Mach-Zehnder interferometers, which can control the signature of the two-photon interference on-demand. Our results pave the way toward implementation of scalable boson sampling, the application of linear optical quantum computing (LOQC) protocols in the microwave domain, and quantum algorithms between long-lived bosonic memories., Comment: 6 pages, 5 figures

Non-equilibrium quasiparticle excitations degrade the performance of a variety of superconducting circuits. Understanding the energy distribution of these quasiparticles will yield insight into their generation mechanisms, the limitations they impose on superconducting devices, and how to efficiently mitigate quasiparticle-induced qubit decoherence. To probe this energy distribution, we systematically correlate qubit relaxation and excitation with charge-parity switches in an offset-charge-sensitive transmon qubit, and find that quasiparticle-induced excitation events are the dominant mechanism behind the residual excited-state population in our samples. By itself, the observed quasiparticle distribution would limit $T_1$ to $\approx200~\mu\mathrm{s}$, which indicates that quasiparticle loss in our devices is on equal footing with all other loss mechanisms. Furthermore, the measured rate of quasiparticle-induced excitation events is greater than that of relaxation events, which signifies that the quasiparticles are more energetic than would be predicted from a thermal distribution describing their apparent density., Comment: 6+6 pages, 5+3 figures

International audience; Quantum error correction can allow quantum computers to operate despite the presence of noise and imperfections. A critical component of any error correcting scheme is the mapping of error syndromes onto an ancillary measurement system. However, errors occurring in the ancilla can propagate onto the logical qubit, and irreversibly corrupt the encoded information. Here, we demonstrate a fault-tolerant syndrome measurement scheme that dramatically suppresses forward propagation of ancilla errors. We achieve a fivefold reduction of the logical error probability per measurement, while maintaining the syndrome assignment fidelity. We use the same method to prevent the propagation of thermal ancilla excitations, increasing the logical qubit dephasing time by more than an order of magnitude. Our approach is hardware-efficient, as it uses a single multilevel transmon ancilla and a cavity-encoded logical qubit, whose interaction is engineered in situ using an off-resonant sideband drive. These results demonstrate that hardware-efficient approaches which exploit system-specific error models can yield practical advances towards fault-tolerant quantum computation.

Modular quantum computing architectures require fast and efficient distribution of quantum information through propagating signals. Here we report rapid, on-demand quantum state transfer between two remote superconducting cavity quantum memories through traveling microwave photons. We demonstrate a quantum communication channel by deterministic transfer of quantum bits with 76% fidelity. Heralding on errors induced by experimental imperfection can improve this to 87% with a success probability of 0.87. By partial transfer of a microwave photon, we generate remote entanglement at a rate that exceeds photon loss in either memory by more than a factor of three. We further show the transfer of quantum error correction code words that will allow deterministic mitigation of photon loss. These results pave the way for scaling superconducting quantum devices through modular quantum networks., main text 7 pages, 4 figures; supplement 16 pages, 16 figures

Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally. The LEGO-like nature of superconducting circuits makes them particularly suited for building and coupling artificial atoms. Here, we introduce an artificial molecule, composed of two strongly coupled fluxonium atoms, which possesses a tunable magnetic moment. Using an applied external flux, one can tune the molecule between two regimes: one in which the ground-excited state manifold has a magnetic dipole moment and one in which the ground-excited state manifold has only a magnetic quadrupole moment. By varying the applied external flux, we find the coherence of the molecule to be limited by local flux noise. The ability to engineer and control artificial molecules paves the way for building more complex circuits for protected qubits and quantum simulation., Comment: 10 pages, 8 figures

A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and precise control over the entire system. Whether based on multiple physical qubits or larger dimensional modes such as oscillators, the individual elements in realistic devices will always have residual interactions, which must be accounted for when designing logical operations. Here we demonstrate a holistic control strategy which exploits accurate knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system. We use this approach to realize high-fidelity (98.5%, inferred), decoherence-limited operations on a logical qubit encoded in a superconducting cavity resonator using four-component cat states. Our results show the power of applying numerical techniques to control linear oscillators and pave the way for utilizing their large Hilbert space as a resource in quantum information processing., A logical qubit is a two-dimensional subspace of a higher dimensional system, whose manipulation requires precise control over the whole system. Here the authors demonstrate a control strategy which exploits precise knowledge of the Hamiltonian to manipulate a coupled oscillator-transmon system.

Large-scale quantum information processing networks will most probably require the entanglement of distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computational resources, and flying ones, acting as quantum buses. We report the deterministic entanglement of two remote transmon qubits by Raman stimulated emission and absorption of a traveling photon wavepacket. We achieve a Bell state fidelity of 73 %, well explained by losses in the transmission line and decoherence of each qubit.

Atomic systems display a rich variety of quantum dynamics due to the different possible symmetries obeyed by the atoms. These symmetries result in selection rules that have been essential for the quantum control of atomic systems. Superconducting artificial atoms are mainly governed by parity symmetry. Its corresponding selection rule limits the types of quantum systems that can be built using electromagnetic circuits at their optimal coherence operation points ("sweet spots"). Here, we use third-order nonlinear coupling between the artificial atom and its readout resonator to drive transitions forbidden by the parity selection rule for linear coupling to microwave radiation. A Lambda-type system emerges from these newly accessible transitions, implemented here in the fluxonium artificial atom coupled to its "antenna" resonator. We demonstrate coherent manipulation of the fluxonium artificial atom at its sweet spot by stimulated Raman transitions. This type of transition enables the creation of new quantum operations, such as the control and readout of physically protected artificial atoms., Comment: 10 pages, 7 figures

Most quantum-error correcting codes assume that the decoherence of each physical qubit is independent of the decoherence of any other physical qubit. We can test the validity of this assumption in an experimental setup where a microwave feedline couples to multiple qubits by examining correlations between the qubits. Here, we investigate the correlations between fluxonium qubits located in a single waveguide. Despite being in a wide-bandwidth electromagnetic environment, the qubits have measured relaxation times in excess of 100 us. We use cascaded Josephson parametric amplifiers to measure the quantum jumps of two fluxonium qubits simultaneously. No correlations are observed between the relaxation times of the two fluxonium qubits, which indicates that the sources of relaxation are local to each qubit. Our architecture can easily be scaled to monitor larger numbers of qubits.

Entangling two remote quantum systems which never interact directly is an essential primitive in quantum information science and forms the basis for the modular architecture of quantum computing. When protocols to generate these remote entangled pairs rely on using traveling single photon states as carriers of quantum information, they can be made robust to photon losses, unlike schemes that rely on continuous variable states. However, efficiently detecting single photons is challenging in the domain of superconducting quantum circuits because of the low energy of microwave quanta. Here, we report the realization of a robust form of concurrent remote entanglement based on a novel microwave photon detector implemented in the superconducting circuit quantum electrodynamics (cQED) platform of quantum information. Remote entangled pairs with a fidelity of $0.57\pm0.01$ are generated at $200$ Hz. Our experiment opens the way for the implementation of the modular architecture of quantum computation with superconducting qubits., Main paper: 7 pages, 4 figures; Appendices: 14 pages, 9 figures

There are two general requirements to harness the computational power of quantum mechanics: the ability to manipulate the evolution of an isolated system and the ability to faithfully extract information from it. Quantum error correction and simulation often make a more exacting demand: the ability to perform non-destructive measurements of specific correlations within that system. We realize such measurements by employing a protocol adapted from [S. Nigg and S. M. Girvin, Phys. Rev. Lett. 110, 243604 (2013)], enabling real-time selection of arbitrary register-wide Pauli operators. Our implementation consists of a simple circuit quantum electrodynamics (cQED) module of four highly-coherent 3D transmon qubits, collectively coupled to a high-Q superconducting microwave cavity. As a demonstration, we enact all seven nontrivial subset-parity measurements on our three-qubit register. For each we fully characterize the realized measurement by analyzing the detector (observable operators) via quantum detector tomography and by analyzing the quantum back-action via conditioned process tomography. No single quantity completely encapsulates the performance of a measurement, and standard figures of merit have not yet emerged. Accordingly, we consider several new fidelity measures for both the detector and the complete measurement process. We measure all of these quantities and report high fidelities, indicating that we are measuring the desired quantities precisely and that the measurements are highly non-demolition. We further show that both results are improved significantly by an additional error-heralding measurement. The analyses presented here form a useful basis for the future characterization and validation of quantum measurements, anticipating the demands of emerging quantum technologies., 10 pages, 5 figures, plus supplement

We demonstrate and contrast two approaches to the stabilization of qubit entanglement by feedback. Our demonstration is built on a feedback platform consisting of two superconducting qubits coupled to a cavity which are measured by a nearly-quantum-limited measurement chain and controlled by high-speed classical logic circuits. This platform is used to stabilize entanglement by two nominally distinct schemes: a "passive" reservoir engineering method and an "active" correction based on conditional parity measurements. In view of the instrumental roles that these two feedback paradigms play in quantum error-correction and quantum control, we directly compare them on the same experimental setup. Further, we show that a second layer of feedback can be added to each of these schemes, which heralds the presence of a high-fidelity entangled state in realtime. This "nested" feedback brings about a marked entanglement fidelity improvement without sacrificing success probability., Comment: 40 pages, 12 figures

As experimental quantum information processing (QIP) rapidly advances, an emerging challenge is to design a scalable architecture that combines various quantum elements into a complex device without compromising their performance. In particular, superconducting quantum circuits have successfully demonstrated many of the requirements for quantum computing, including coherence levels that approach the thresholds for scaling. However, it remains challenging to couple a large number of circuit components through controllable channels while suppressing any other interactions. We propose a hardware platform intended to address these challenges, which combines the advantages of integrated circuit fabrication and long coherence times achievable in three-dimensional circuit quantum electrodynamics (3D cQED). This multilayer microwave integrated quantum circuit (MMIQC) platform provides a path toward the realization of increasingly complex superconducting devices in pursuit of a scalable quantum computer., Comment: 5 pages, 2 figures

Quantum error correction (QEC) can overcome the errors experienced by qubits1 and is therefore an essential component of a future quantum computer. To implement QEC, a qubit is redundantly encoded in a higher-dimensional space using quantum states with carefully tailored symmetry properties. Projective measurements of these parity-type observables provide error syndrome information, with which errors can be corrected via simple operations2. The ‘break-even’ point of QEC—at which the lifetime of a qubit exceeds the lifetime of the constituents of the system—has so far remained out of reach3. Although previous works have demonstrated elements of QEC4–16, they primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to preserve a qubit over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of Schrodinger-cat states17 of a superconducting resonator18–21. We implement a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode and correct. As measured by full process tomography, without any post-selection, the corrected qubit lifetime is 320 microseconds, which is longer than the lifetime of any of the parts of the system: 20 times longer than the lifetime of the transmon, about 2.2 times longer than the lifetime of an uncorrected logical encoding and about 1.1 longer than the lifetime of the best physical qubit (the |0〉f and |1〉f Fock states of the resonator). Our results illustrate the benefit of using hardware-efficient qubit encodings rather than traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming basic concepts to exploring the metrics that drive system performance and the challenges in realizing a fault-tolerant system.

We present a method for calculating the energy levels of superconducting circuits that contain highly anharmonic, inductively-shunted modes with arbitrarily strong coupling. Our method starts by calculating the normal modes of the linearized circuit and proceeds with numerical diagonalization in this basis. As an example, we analyze the Hamiltonian of a fluxonium qubit inductively coupled to a readout resonator. While elementary, this simple example is nontrivial because it cannot be efficiently treated by the method known as "black-box quantization," numerical diagonalization in the bare harmonic oscillator basis, or perturbation theory. Calculated spectra are compared to measured spectroscopy data, demonstrating excellent quantitative agreement between theory and experiment., Comment: 10 pages, 7 figures

Quantum jumps of a qubit are usually observed between its energy eigenstates, also known as its longitudinal pseudo-spin component. Is it possible, instead, to observe quantum jumps between the transverse superpositions of these eigenstates? We answer positively by presenting the first continuous quantum nondemolition measurement of the transverse component of an individual qubit. In a circuit QED system irradiated by two pump tones, we engineer an effective Hamiltonian whose eigenstates are the transverse qubit states, and a dispersive measurement of the corresponding operator. Such transverse component measurements are a useful tool in the driven-dissipative operation engineering toolbox, which is central to quantum simulation and quantum error correction., Comment: 6 pages, 4 figures and an additional supplementary material

We present a device demonstrating a lithographically patterned transmon integrated with a micromachined cavity resonator. Our two-cavity, one-qubit device is a multilayer microwave integrated quantum circuit (MMIQC), comprising a basic unit capable of performing circuit-QED (cQED) operations. We describe the qubit-cavity coupling mechanism of a specialized geometry using an electric field picture and a circuit model, and finally obtain specific system parameters using simulations. Fabrication of the MMIQC includes lithography, etching, and metallic bonding of silicon wafers. Superconducting wafer bonding is a critical capability that is demonstrated by a micromachined storage cavity lifetime $34.3~\mathrm{\mu s}$, corresponding to a quality factor of 2 million at single-photon energies. The transmon coherence times are $T_1=6.4~\mathrm{\mu s}$, and $T_2^{Echo}= 11.7~\mathrm{\mu s}$. We measure qubit-cavity dispersive coupling with rate $\chi_{q\mu}/2\pi=-1.17~$MHz, constituting a Jaynes-Cummings system with an interaction strength $g/2\pi=49~$MHz. With these parameters we are able to demonstrate cQED operations in the strong dispersive regime with ease. Finally, we highlight several improvements and anticipated extensions of the technology to complex MMIQCs.

Thorough control of quantum measurement is key to the development of quantum information technologies. Many measurements are destructive, removing more information from the system than they obtain. Quantum non-demolition (QND) measurements allow repeated measurements that give the same eigenvalue. They could be used for several quantum information processing tasks such as error correction, preparation by measurement, and one-way quantum computing. Achieving QND measurements of photons is especially challenging because the detector must be completely transparent to the photons while still acquiring information about them. Recent progress in manipulating microwave photons in superconducting circuits has increased demand for a QND detector which operates in the gigahertz frequency range. Here we demonstrate a QND detection scheme which measures the number of photons inside a high quality-factor microwave cavity on a chip. This scheme maps a photon number onto a qubit state in a single-shot via qubit-photon logic gates. We verify the operation of the device by analyzing the average correlations of repeated measurements, and show that it is 90% QND. It differs from previously reported detectors because its sensitivity is strongly selective to chosen photon number states. This scheme could be used to monitor the state of a photon-based memory in a quantum computer., 5 pages, 4 figures, includes supplementary material

The processing of the single-quantum-level signals produced by current nanoscale solid-state devices such as qubits and nanomechanical resonators would require the development of very sensitive active circuits, such as amplifiers or frequency up- and down-converters that could attain the ultimate performances limited by the laws of quantum mechanics, while remaining of practical use. Bergeal et al. now demonstrate a phase-preserving, superconducting parametric amplifier with ultra-low noise properties, following theoretical principles recently presented in Nature Physics ( http://go.nature.com/F7lwR2 ). Based on a Josephson ring modulator, the new device can operate within a factor of three of the quantum limit. Possible applications include quantum analog signal processing such as the production of entangled microwave signal pairs. Recent progress in solid-state quantum information processing has stimulated the search for amplifiers and frequency converters with quantum-limited performance in the microwave range. Here, a phase-preserving, superconducting parametric amplifier with ultra-low-noise properties has been experimentally realized. Recent progress in solid-state quantum information processing1 has stimulated the search for amplifiers and frequency converters with quantum-limited performance in the microwave range. Depending on the gain applied to the quadratures of a single spatial and temporal mode of the electromagnetic field, linear amplifiers can be classified into two categories (phase sensitive and phase preserving) with fundamentally different noise properties2. Phase-sensitive amplifiers use squeezing to reduce the quantum noise, but are useful only in cases in which a reference phase is attached to the signal, such as in homodyne detection. A phase-preserving amplifier would be preferable in many applications, but such devices have not been available until now. Here we experimentally realize a proposal3 for an intrinsically phase-preserving, superconducting parametric amplifier of non-degenerate type. It is based on a Josephson ring modulator, which consists of four Josephson junctions in a Wheatstone bridge configuration. The device symmetry greatly enhances the purity of the amplification process and simplifies both its operation and its analysis. The measured characteristics of the amplifier in terms of gain and bandwidth are in good agreement with analytical predictions. Using a newly developed noise source, we show that the upper bound on the total system noise of our device under real operating conditions is three times the quantum limit. We foresee applications in the area of quantum analog signal processing, such as quantum non-demolition single-shot readout of qubits4, quantum feedback5 and the production of entangled microwave signal pairs6.