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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

The practical viability of any qubit technology stands on long coherence times and high-fidelity operations, with the superconducting qubit modality being a leading example. However, superconducting qubit coherence is impacted by broken Cooper pairs, referred to as quasiparticles, with a density that is empirically observed to be orders of magnitude greater than the value predicted for thermal equilibrium by the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. Previous work has shown that infrared photons significantly increase the quasiparticle density, yet even in the best isolated systems, it still remains higher than expected, suggesting that another generation mechanism exists. In this Letter, we provide evidence that ionizing radiation from environmental radioactive materials and cosmic rays contributes to this observed difference, leading to an elevated quasiparticle density that would ultimately limit superconducting qubits of the type measured here to coherence times in the millisecond regime. We further demonstrate that introducing radiation shielding reduces the flux of ionizing radiation and positively correlates with increased coherence time. Albeit a small effect for today's qubits, reducing or otherwise mitigating the impact of ionizing radiation will be critical for realizing fault-tolerant superconducting quantum computers., Comment: 16 pages, 12 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.

The pursuit of superconducting-based quantum computers has advanced the fabrication of and experimentation with custom lattices of qubits and resonators. Here, we describe a roadmap to use present experimental capabilities to simulate an interacting many-body system of bosons and measure quantities that are exponentially difficult to calculate numerically. We focus on the two-dimensional hard-core Bose–Hubbard model implemented as an array of floating transmon qubits. We describe a control scheme for such a lattice that can perform individual qubit readout and show how the scheme enables the preparation of a highly excited many-body state, in contrast with atomic implementations restricted to the ground state or thermal equilibrium. We discuss what observables could be accessed and how they could be used to better understand the properties of many-body systems, including the observation of the transition of eigenstate entanglement entropy scaling from area-law behavior to volume-law behavior.

Since the first observation of coherent quantum behaviour in a superconducting qubit, now more than 20 years ago, there have been substantial developments in the field of superconducting quantum circuits. One such advance is the introduction of the concepts of cavity quantum electrodynamics (QED) to superconducting circuits, to yield what is now known as circuit QED. This approach realizes in a single architecture the essential requirements for quantum computation, and has already been used to run simple quantum algorithms and to operate tens of superconducting qubits simultaneously. For these reasons, circuit QED is one of the leading architectures for quantum computation. In parallel to these advances towards quantum information processing, circuit QED offers new opportunities for the exploration of the rich physics of quantum optics in novel parameter regimes in which strongly nonlinear effects are readily visible at the level of individual microwave photons. We review circuit QED in the context of quantum information processing and quantum optics, and discuss some of the challenges on the road towards scalable quantum computation. The introduction of concepts from cavity quantum electrodynamics to superconducting circuits yielded circuit quantum electrodynamics, a platform eminently suitable to quantum information processing and for the exploration of novel regimes in quantum optics.

One major challenge to scaling quantum dot qubits is the dense wiring requirements, making it difficult to envision fabricating large 2D arrays of nearest-neighbor-coupled qubits necessary for error correction. We describe a method to ameliorate this issue by spacing out the qubits using superconducting resonators facilitated by 3D integration. To prove the viability of this approach, we use integration to couple an off-chip high-impedance TiN resonator to a double quantum dot in a Si/SiGe heterostructure. Using the resonator as a dispersive gate sensor, we tune the device down to the single electron regime with an SNR = 5.36. Characterizing the individual systems shows 3D integration can be done while maintaining low-charge noise for the quantum dots and high-quality factors for the superconducting resonator (single photon QL = 2.14 × 104 with Qi ≈ 3 × 105), necessary for readout and high-fidelity two-qubit gates.

Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices., 21 pages, 12 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.

Noise that exhibits significant temporal and spatial correlations across multiple qubits can be especially harmful to both fault-tolerant quantum computation and quantum-enhanced metrology. However, a complete spectral characterization of the noise environment of even a two-qubit system has not been reported thus far. We propose and experimentally demonstrate a protocol for two-qubit dephasing noise spectroscopy based on continuous-control modulation. By combining ideas from spin-locking relaxometry with a statistically motivated robust estimation approach, our protocol allows for the simultaneous reconstruction of all the single-qubit and two-qubit cross-correlation spectra, including access to their distinctive nonclassical features. Only single-qubit control manipulations and state-tomography measurements are employed, with no need for entangled-state preparation or readout of two-qubit observables. While our experimental demonstration uses two superconducting qubits coupled to a shared, colored engineered noise source, our methodology is portable to a variety of dephasing-dominated qubit architectures. By pushing quantum noise spectroscopy beyond the single-qubit setting, our work heralds the characterization of spatiotemporal correlations in both engineered and naturally occurring noise environments., PRX Quantum, 1 (1), ISSN:2691-3399

© 2000-2012 IEEE. Quantum processing has the potential to transform the computing landscape by enabling efficient solutions to problems that are intractable using classical processors. The field was sparked by a suggestion from physicist Richard Feynman in 1981 that a controllable quantum system can be used to simulate other quantum systems, such as the energy band structure of complex materials or the chemical reaction rates of intricate molecules. In the 1990s, interest in quantum computing grew rapidly with the introduction of the first quantum "killer app"-the potential of a large-scale quantum processor to break certain types of public encryption schemes [1]. Recently, there has been growing consensus that myriad other fields besides data security could be impacted by the development of a quantum processor, including machine learning [2], many optimization problems [3], and Feynman's original idea of the simulation of materials properties [4]. In recent years, the field has progressed rapidly, but many technical challenges must be overcome before a large-scale quantum processor can be built. This article focuses on the development of packaging for solid-state qubits and the use of 3D integration to address this challenge.

Resonant transverse driving of a two-level system as viewed in the rotating frame couples two degenerate states at the Rabi frequency, an amazing equivalence that emerges in quantum mechanics. While spectacularly successful at controlling natural and artificial quantum systems, certain limitations may arise (e.g., the achievable gate speed) due to non-idealities like the counter-rotating term. Here, we explore a complementary approach to quantum control based on non-resonant, non-adiabatic driving of a longitudinal parameter in the presence of a fixed transverse coupling. We introduce a superconducting composite qubit (CQB), formed from two capacitively coupled transmon qubits, which features a small avoided crossing -- smaller than the environmental temperature -- between two energy levels. We control this low-frequency CQB using solely baseband pulses, non-adiabatic transitions, and coherent Landau-Zener interference to achieve fast, high-fidelity, single-qubit operations with Clifford fidelities exceeding $99.7\%$. We also perform coupled qubit operations between two low-frequency CQBs. This work demonstrates that universal non-adiabatic control of low-frequency qubits is feasible using solely baseband pulses.

The dominant source of decoherence in contemporary frequency-tunable superconducting qubits is 1/$f$ flux noise. To understand its origin and find ways to minimize its impact, we systematically study flux noise amplitudes in more than 50 flux qubits with varied SQUID geometry parameters and compare our results to a microscopic model of magnetic spin defects located at the interfaces surrounding the SQUID loops. Our data are in agreement with an extension of the previously proposed model, based on numerical simulations of the current distribution in the investigated SQUIDs. Our results and detailed model provide a guide for minimizing the flux noise susceptibility in future circuits., 14 pages, 6 figures

Solid-state qubits with transition frequencies in the microwave regime, such as superconducting qubits, are at the forefront of quantum information processing. However, high-fidelity, simultaneous control of superconducting qubits at even a moderate scale remains a challenge, partly due to the complexities of packaging these devices. Here, we present an approach to microwave package design focusing on material choices, signal line engineering, and spurious mode suppression. We describe design guidelines validated using simulations and measurements used to develop a 24-port microwave package. Analyzing the qubit environment reveals no spurious modes up to 11GHz. The material and geometric design choices enable the package to support qubits with lifetimes exceeding 350 {\mu}s. The microwave package design guidelines presented here address many issues relevant for near-term quantum processors., Comment: 15 pages, 9 figures

In condensed matter systems, coherent backscattering and quantum interference in the presence of time-reversal symmetry lead to well-known phenomena such as weak localization (WL) and universal conductance fluctuations (UCF). Here we use multi-pass Landau-Zener transitions at the avoided crossing of a highly-coherent superconducting qubit to emulate these phenomena. The average and standard deviation of the qubit transition rate exhibit a dip and peak when the driving waveform is time-reversal symmetric, analogous to WL and UCF, respectively. The higher coherence of this qubit enabled the realization of both effects, in contrast to earlier work arXiv:1204.6428, which successfully emulated UCF, but did not observe WL. This demonstration illustrates the use of non-adiabatic control to implement quantum emulation with superconducting qubits., 14 pages, 7 figures; two reference added; figure 4 changed; 2 more figures added in Suppl. Info

© 2019 IEEE. As designs for superconducting qubits become more complex, 3D integration of two or more vertically bonded chips will become necessary to enable increased density and connectivity. Precise control of the spacing between these chips is required for accurate prediction of circuit performance. In this paper, we demonstrate an improvement in the planarity of bonded superconducting qubit chips while retaining device performance by utilizing hard-stop silicon spacer posts. These silicon spacers are defined by etching several microns into a silicon substrate and are compatible with 3D-integrated qubit fabrication. This includes fabrication of Josephson junctions, superconducting air-bridge crossovers, underbump metallization and indium bumps. To qualify the integrated process, we demonstrate high-quality factor resonators on the etched surface and measure qubit coherence (T1, T2,echo > 40 μs) in the presence of silicon posts as near as 350 μm to the qubit.

Extending qubit lifetime through a shaped environment Qubits are the quantum two-level systems that encode and process information in quantum computing. Kept in isolation, qubits can be stable. In a practical setting, however, qubits must be addressed and interact with each other. Such an environment is typically viewed as a source of decoherence and has a detrimental effect on a qubit's ability to retain encoded information. Gustavsson et al. used a sequence of pulses as a source of “environment shaping” that could substantially increase the coherence time of a superconducting qubit. Science , this issue p. 1573

© 2019 IEEE. Over the past two decades, the performance of superconducting quantum circuits has tremendously improved. The progress of superconducting qubits enabled a new industry branch to emerge from global technology enterprises to quantum computing startups. Here, an overview of superconducting quantum circuit microwave control is presented. Furthermore, we discuss one of the persistent engineering challenges in the field - how to control the electromagnetic environment of increasingly complex superconducting circuits such that they are simultaneously protected and efficiently controllable.

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

Single photon detection is a requisite technique in quantum-optics experiments in both the optical and the microwave domains. However, the energy of microwave quanta are four to five orders of magnitude less than their optical counterpart, making the efficient detection of single microwave photon extremely challenging. Here, we demonstrate the detection of a single microwave photon propagating through a waveguide. The detector is implemented with an "impedance-matched" artificial Λ system comprising the dressed states of a driven superconducting qubit coupled to a microwave resonator. We attain a single-photon detection efficiency of 0.66±0.06 with a reset time of ~400 ns. This detector can be exploited for various applications in quantum sensing, quantum communication and quantum information processing.

As superconducting qubit circuits become more complex, addressing a large array of qubits becomes a challenging engineering problem. Dense arrays of qubits benefit from, and may require, access via the third dimension to alleviate interconnect crowding. Through-silicon vias (TSVs) represent a promising approach to three-dimensional (3D) integration in superconducting qubit arrays -- provided they are compact enough to support densely-packed qubit systems without compromising qubit performance or low-loss signal and control routing. In this work, we demonstrate the integration of superconducting, high-aspect ratio TSVs -- 10 $\mu$m wide by 20 $\mu$m long by 200 $\mu$m deep -- with superconducting qubits. We utilize TSVs for baseband control and high-fidelity microwave readout of qubits using a two-chip, bump-bonded architecture. We also validate the fabrication of qubits directly upon the surface of a TSV-integrated chip. These key 3D integration milestones pave the way for the control and readout of high-density superconducting qubit arrays using superconducting TSVs., Comment: 8 pages; 4 figures

Single-photon detection is a requisite technique in quantum-optics experiments in both the optical and the microwave domains. However, the energy of microwave quanta are four to five orders of magnitude less than their optical counterpart, making the efficient detection of single microwave photons extremely challenging. Here we demonstrate the detection of a single microwave photon propagating through a waveguide. The detector is implemented with an impedance-matched artificial Λ system comprising the dressed states of a driven superconducting qubit coupled to a microwave resonator. Each signal photon deterministically induces a Raman transition in the Λ system and excites the qubit. The subsequent dispersive readout of the qubit produces a discrete ‘click’. We attain a high single-photon-detection efficiency of 0.66±0.06 with a low dark-count probability of 0.014±0.001 and a reset time of ∼400 ns. This detector can be exploited for various applications in quantum sensing, quantum communication and quantum information processing., Japan Society for the Promotion of Science (KAKENHI Grants 25400417, 26220601 and 15K17731), Japan. Science and Technology Agency. ImPACT Program of Council for Science, National Institute of Information and Communications Technology (Japan)

Universal quantum computing relies on high-fidelity entangling operations. Here, we demonstrate that four coupled qubits can operate as a quantum gate, where two qubits control the operation on two target qubits (a four-qubit gate). This configuration can implement four different controlled two-qubit gates: two different entangling swap and phase operations, a phase operation distinguishing states of different parity, and the identity operation (idle quantum gate), where the choice of gate is set by the state of the control qubits. The device exploits quantum interference to control the operation on the target qubits by coupling them to each other via the control qubits. By connecting several four-qubit devices in a two-dimensional lattice, one can achieve a highly connected quantum computer. We consider an implementation of the four-qubit gate with superconducting qubits, using capacitively coupled qubits arranged in a diamond-shaped architecture., npj Quantum Information, 6 (1), ISSN:2056-6387

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.

Granular aluminium — a superconductor with high kinetic inductance — has been used to create a superinductor for a fluxonium superconducting qubit.

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.

Experimentalists seeking to improve the coherent lifetimes of quantum bits have generally focused on mitigating decoherence mechanisms through, for example, improvements to qubit designs and materials, and system isolation from environmental perturbations. In the case of the phase degree of freedom in a quantum superposition, however, the coherence that must be preserved is not solely internal to the qubit, but rather necessarily includes that of the qubit relative to the ‘master clock’ (e.g., a local oscillator) that governs its control system. In this manuscript, we articulate the impact of instabilities in the master clock on qubit phase coherence and provide tools to calculate the contributions to qubit error arising from these processes. We first connect standard oscillator phase-noise metrics to their corresponding qubit dephasing spectral densities. We then use representative lab-grade and performance-grade oscillator specifications to calculate operational fidelity bounds on trapped-ion and superconducting qubits with relatively slow and fast operation times. We discuss the relevance of these bounds for quantum error correction in contemporary experiments and future large-scale quantum information systems, and consider potential means to improve master clock stability.

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

Superconducting qubits are electronic circuits comprising lithographically defined Josephson tunnel junctions, inductors, capacitors, and interconnects. When cooled to dilution refrigerator temperatures, these circuits behave as quantum mechanical “artificial atoms,” exhibiting quantized states of electronic charge, magnetic flux, or junction phase depending on the design parameters of the constituent circuit elements. Their potential for lithographic scalability, compatibility with microwave control, and operability at nanosecond time scales place superconducting qubits among the leading modalities being considered for quantum information science and technology applications. Over the past decade, the quantum coherence of superconducting qubits has increased more than five orders of magnitude, due primarily to improvements in their design, fabrication, and, importantly, their constituent materials and interfaces. In this article, we review superconducting qubits, articulate the important role of materials research in their development, and provide a prospectus for the future as these devices transition from scientific curiosity to the threshold of technical reality.

We present an experimental realization of resonance fluorescence in squeezed vacuum. We strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detect the resulting fluorescence with high resolution enabled by a broadband traveling-wave parametric amplifier. We investigate the fluorescence spectra in the weak and strong driving regimes, observing up to 3.1 dB of reduction of the fluorescence linewidth below the ordinary vacuum level and a dramatic dependence of the Mollow triplet spectrum on the relative phase of the driving and squeezed vacuum fields. Our results are in excellent agreement with predictions for spectra produced by a two-level atom in squeezed vacuum [Phys. Rev. Lett. 58, 2539 (1987)], demonstrating that resonance fluorescence offers a resource-efficient means to characterize squeezing in cryogenic environments., United States. Army Research Office (W911NF-14-1-0078), United States. Office of Naval Research (N00014-13-1-0150), United States. Office of the Director of National Intelligence, United States. Intelligence Advanced Research Projects Activity, United States. Air Force (Contract No. FA8721-05-C-0002), United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant No. FA9550-12-1-0488)

Coherent circuits based on superconducting elements hold tremendous promise for the practical implementation of quantum information technology: advanced computation, cryptography, and hardware simulation of complex materials systems are envisioned applications. Such circuits are essentially engineered atoms with level transitions in the 4–8 GHz regime; as such “read” and “write” operations are performed with the aid of fast microwave pulses and low-noise amplifiers, respectively. Recent advances in cavity-based superconducting parametric amplifiers have enabled real-time measurement and feedback in one and two qubits. We demonstrate a novel Josephson junction transmission-line based traveling-wave amplifier which employs sub-wavelength phase matching resonators to achieve high gain, several GHz of bandwidth, and near quantum-noise limited performance. Such devices will enable multiplexed qubit readout in integrated architectures comprised of a variety of microwave frequency analog and digital superconducting technologies: signal sources, multiplexers, ADCs, DACs, mixers, and amplifiers.

Superconducting persistent-current qubits are quantum-coherent artificial atoms with multiple, tunable energy levels. In the presence of large-amplitude harmonic excitation, the qubit state can be driven through one or more of the constituent energy-level avoided crossings. The resulting Landau-Zener-Stueckelberg (LZS) transitions mediate a rich array of quantum-coherent phenomena. We review here three experimental works based on LZS transitions: Mach-Zehnder-type interferometry between repeated LZS transitions, microwave-induced cooling, and amplitude spectroscopy. These experiments exhibit a remarkable agreement with theory, and are extensible to other solid-state and atomic qubit modalities. We anticipate they will find application to qubit state-preparation and control methods for quantum information science and technology., Comment: 13 pages, 5 figures

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

The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad-frequency tunability, strong anharmonicity, high reproducibility and relaxation times in excess of 40 μs at its flux-insensitive point. Qubit relaxation times T1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise and 1/f-flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal-photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T2≈85 μs, approximately the 2T1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T2 in contemporary qubits based on transverse qubit–resonator interaction., Scalable quantum information processing requires controllable high-coherence qubits. Here, the authors present superconducting flux qubits with broad frequency tunability, strong anharmonicity and high reproducibility, identifying photon shot noise as the main source of dephasing for further improvements.

Detuning a superconducting qubit from its rotating frame is one means to implement a Z-gate operation. In this work, we implement a Z gate by pulsing a current through the qubit’s readout dc SQUID. While the dc SQUID acts as a magnetic flux sensor for qubit readout, we in turn may use it as a flux actuator with tunable strength to impose a qubit frequency shift. Using this approach, we demonstrate Ramsey-type free-induction experiments with time constants as long as 280 ns and rotation frequencies as high as 1.4 GHz. We experimentally demonstrate an inferred Z-gate fidelity of approximately 90%, limited largely by the bandwidth of our system. In the absence of this limitation, we argue that the inferred fidelity may be improved to as high as 99%.

We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities, and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circuit quantum electrodynamics., Comment: 5 pages, 4 figures, Supplemental Material

Stringing together a powerful amplifier Amplifying microwave signals with high gain and across a broad range of frequencies is crucial in solid-state quantum information processing (QIP). Achieving broadband operation is especially tricky. Macklin et al. engineered an amplifier that contains a long chain of so-called Josephson junctions (see the Perspective by Cleland). The amplifier exhibited high gain over a gigahertz-sized bandwidth and was able to perform high-fidelity qubit readout. Because the amplifier will be capable of reading out as many as 20 qubits simultaneously, it may help to scale up QIP protocols. Science , this issue p. 307 ; see also p. 280

Gate operations in a quantum information processor are generally realized by tailoring specific periods of free and driven evolution of a quantum system. Unwanted environmental noise, which may in principle be distinct during these two periods, acts to decohere the system and increase the gate error rate. Although there has been significant progress characterizing noise processes during free evolution, the corresponding driven-evolution case is more challenging as the noise being probed is also extant during the characterization protocol. Here we demonstrate the noise spectroscopy (0.1-200 MHz) of a superconducting flux qubit during driven evolution by using a robust spin-locking pulse sequence to measure relaxation (T1ρ) in the rotating frame. In the case of flux noise, we resolve spectral features due to coherent fluctuators, and further identify a signature of the 1 MHz defect in a time-domain spin-echo experiment. The driven-evolution noise spectroscopy complements free-evolution methods, enabling the means to characterize and distinguish various noise processes relevant for universal quantum control. © 2013 Macmillan Publishers Limited. All rights reserved.

Remarkable advancements in coherence and control fidelity have been achieved in recent years with cryogenic solid-state qubits. Nonetheless, thermalizing such devices to their milliKelvin environments has remained a long-standing fundamental and technical challenge. In this context, we present a systematic study of the first-excited-state population in a 3D transmon superconducting qubit mounted in a dilution refrigerator with a variable temperature. Using a modified version of the protocol developed by Geerlings et al., we observe the excited-state population to be consistent with a Maxwell-Boltzmann distribution, i.e., a qubit in thermal equilibrium with the refrigerator, over the temperature range 35-150 mK. Below 35 mK, the excited-state population saturates at approximately 0.1%. We verified this result using a flux qubit with ten times stronger coupling to its readout resonator. We conclude that these qubits have effective temperature T(eff)=35 mK. Assuming T(eff) is due solely to hot quasiparticles, the inferred qubit lifetime is 108 μs and in plausible agreement with the measured 80 μs.

We measured the energy relaxation time in a Nb superconducting persistent current qubit using a time-resolved fast measurement scheme. The energy relaxation time is longer than 10/spl mu/s, showing a strong potential of realizing quantum computation with Nb-based superconducting qubits.

We infer the high-frequency flux noise spectrum in a superconducting flux qubit by studying the decay of Rabi oscillations under strong driving conditions. The large anharmonicity of the qubit and its strong inductive coupling to a microwave line enabled high-amplitude driving without causing significant additional decoherence. Rabi frequencies up to 1.7 GHz were achieved, approaching the qubit's level splitting of 4.8 GHz, a regime where the rotating-wave approximation breaks down as a model for the driven dynamics. The spectral density of flux noise observed in the wide frequency range decreases with increasing frequency up to 300 MHz, where the spectral density is not very far from the extrapolation of the 1/f spectrum obtained from the free-induction-decay measurements. We discuss a possible origin of the flux noise due to surface electron spins., 6 pages, 3 figures, and one Supplemental Material

We present measurements of coherence and successive decay dynamics of higher energy levels of a superconducting transmon qubit. By applying consecutive $\pi$-pulses for each sequential transition frequency, we excite the qubit from the ground state up to its fourth excited level and characterize the decay and coherence of each state. We find the decay to proceed mainly sequentially, with relaxation times in excess of 20 $\mu$s for all transitions. We also provide a direct measurement of the charge dispersion of these levels by analyzing beating patterns in Ramsey fringes. The results demonstrate the feasibility of using higher levels in transmon qubits for encoding quantum information., Comment: Minor corrections. Added two plots in Figure 2. Added figures of the setup and the Ramsey fits in the supplemental material, as as more details on the device characterization. Rephrased last paragraph on charge dissipation. Added some references

We present a new method for determining pulse imperfections and improving the single-gate fidelity in a superconducting qubit. By applying consecutive positive and negative pi pulses, we amplify the qubit evolution due to microwave pulse distortions, which causes the qubit state to rotate around an axis perpendicular to the intended rotation axis. Measuring these rotations as a function of pulse period allows us to reconstruct the shape of the microwave pulse arriving at the sample. Using the extracted response to predistort the input signal, we are able to reduce the average error per gate by 37%, which enables us to reach an average single-qubit gate fidelity higher than 0.998. DOI: 10.1103/PhysRevLett.110.040502

We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our $1/f$ noise model. The results are applicable to any two-qubit system with transverse coupling, and they highlight the potential of decoupling techniques for improving two-qubit gate fidelities, an essential prerequisite for implementing fault-tolerant quantum computing.

We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.

We have measured flux-noise correlations in a tunable superconducting flux qubit. The device consists of two loops that independently control the qubit's energy splitting and tunnel coupling. Low frequency flux noise in the loops causes fluctuations of the qubit frequency and leads to dephasing. Since the noises in the two loops couple to different terms of the qubit Hamiltonian, a measurement of the dephasing rate at different bias points provides a way to extract both the amplitude and the sign of the noise correlations. We find that the flux fluctuations in the two loops are anti-correlated, consistent with a model where the flux noise is generated by randomly oriented unpaired spins on the metal surface., Comment: 7 pages, including supplementary material

We present a fabrication scheme and testing results for epitaxial sub-micrometer Josephson junctions. The junctions are made using a high-temperature (1170 K) 'via process' yielding junctions as small as 0.8 µm in diameter by use of optical lithography. Sapphire (Al2O3) tunnel-barriers are grown on an epitaxial Re/Ti multilayer base-electrode. We have fabricated devices with both Re and Al top-electrodes. While room temperature (295 K) resistance versus area data are favorable for both types of top-electrodes, the low-temperature (50 mK) data show that junctions with the Al top-electrode have a much higher subgap resistance. The microwave loss properties of the junctions have been measured by use of superconducting Josephson junction qubits. The results show that high subgap resistance correlates with improved qubit performance.

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY)., Transitions in an artificial atom, driven nonadiabatically through an energy-level avoided crossing, can be controlled by carefully engineering the driving protocol. We have driven a superconducting persistent-current qubit with a large-amplitude radio-frequency field. By applying a biharmonic wave form generated by a digital source, we demonstrate a mapping between the amplitude and phase of the harmonics produced at the source and those received by the device. This allows us to image the actual wave form at the device. This information is used to engineer a desired time dependence, as confirmed by the detailed comparison with a simulation. © 2009 The American Physical Society., This work was sponsored by the U.S. Government and the W. M. Keck Foundation Center for Extreme Quantum Information Theory. M.S.R. was supported by DOE CSGF, Grant No. DE-FG02-97ER25308, and the NSF. The work at Lincoln Laboratory was sponsored by the AFOSR under Air Force Contract No. FA8721-05-C-0002.

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY)., The interference between repeated Landau-Zener transitions in a qubit swept through an avoided level crossing results in Stückelberg oscillations in qubit magnetization, a hallmark of the coherent strongly driven regime in two-level systems. The two-dimensional Fourier transforms of the resulting oscillatory patterns are found to exhibit a family of one-dimensional curves in Fourier space, in agreement with recent observations in a superconducting qubit. We interpret these images in terms of time evolution of the quantum phase of the qubit state and show that they can be used to probe dephasing mechanisms., We acknowledge partial support from W. M. Keck Foundation Center for Extreme Quantum Information Theory, and from the United States Government. The work of M. S. R. was supported by DOE CSGF, Grant No. DE-FG02-97ER25308, and the NSF. The work at Lincoln Laboratory was sponsored by the U.S. DOD under Air Force Contract No. FA8721-05-C-0002.

We present a scheme for implementing quantum operations with superconducting qubits. Our approach uses a ``coupler'' qubit to mediate a controllable interaction between data qubits, pulse sequences which strongly mitigate the effects of $1/f$ flux noise, and a high-$Q$ resonator-based local memory. We develop a Monte Carlo simulation technique capable of describing arbitrary noise-induced dephasing and decay, and demonstrate in this system a set of universal gate operations with $O({10}^{\ensuremath{-}5})$ error probabilities in the presence of experimentally measured levels of $1/f$ noise. We then add relaxation and quantify the decay times required to maintain this error level.