Planar superconducting resonators with internal quality factors above one million
TL;DR: In this paper, the authors describe the fabrication and measurement of microwave coplanar waveguide resonators with internal quality factors above 107 at high microwave powers and over 106 at low powers, with the best low power results approaching 2×106.
Abstract: We describe the fabrication and measurement of microwave coplanar waveguide resonators with internal quality factors above 107 at high microwave powers and over 106 at low powers, with the best low power results approaching 2×106, corresponding to ∼1 photon in the resonator. These quality factors are achieved by controllably producing very smooth and clean interfaces between the resonators’ aluminum metallization and the underlying single crystal sapphire substrate. Additionally, we describe a method for analyzing the resonator microwave response, with which we can directly determine the internal quality factor and frequency of a resonator embedded in an imperfect measurement circuit.
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TL;DR: For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely.
Abstract: The performance of superconducting qubits has improved by several orders of magnitude in the past decade. These circuits benefit from the robustness of superconductivity and the Josephson effect, and at present they have not encountered any hard physical limits. However, building an error-corrected information processor with many such qubits will require solving specific architecture problems that constitute a new field of research. For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely. We offer a view on some directions for the field and speculate on its future.
2,013 citations
TL;DR: The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.
Abstract: A quantum computer can solve hard problems, such as prime factoring, database searching and quantum simulation, at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection by distributing a logical state among many physical quantum bits (qubits) by means of quantum entanglement. Superconductivity is a useful phenomenon in this regard, because it allows the construction of large quantum circuits and is compatible with microfabrication. For superconducting qubits, the surface code approach to quantum computing is a natural choice for error correction, because it uses only nearest-neighbour coupling and rapidly cycled entangling gates. The gate fidelity requirements are modest: the per-step fidelity threshold is only about 99 per cent. Here we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92 per cent and a two-qubit gate fidelity of up to 99.4 per cent. This places Josephson quantum computing at the fault-tolerance threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger state using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.
1,710 citations
TL;DR: In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons as mentioned in this paper, and many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed.
909 citations
TL;DR: The field of circuit quantum electrodynamics (QED) as discussed by the authors was initiated by Josephson-junction-based superconducting circuits and has become an independent and thriving field of research in its own right.
Abstract: Quantum-mechanical effects at the macroscopic level were first explored in Josephson-junction-based superconducting circuits in the 1980s. In recent decades, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to gate-based digital quantum information processing with superconducting circuits. In addition, circuit QED provides a framework for the study of hybrid quantum systems, such as quantum dots, magnons, Rydberg atoms, surface acoustic waves, and mechanical systems interacting with microwave photons. Here the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focusing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system are reviewed. Also discussed is coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, important use cases of these ideas in quantum information processing and in quantum optics are discussed. Circuit QED realizes a broad set of concepts that open up new possibilities for the study of quantum physics at the macro scale with superconducting circuits and applications to quantum information science in the widest sense.
773 citations
TL;DR: In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons as mentioned in this paper, and many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed.
Abstract: In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed, e.g., giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments may lead to improved understanding of the counterintuitive properties of quantum mechanics, and speed up applications ranging from microwave photonics to superconducting quantum information processing. In this article, we review experimental and theoretical progress in microwave photonics with superconducting quantum circuits. We hope that this global review can provide a useful roadmap for this rapidly developing field.
700 citations
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TL;DR: The demonstration of a superconducting detector that is easily fabricated and can readily be incorporated into large arrays, and its sensitivity is already within an order of magnitude of that needed for CMB observations, and the energy resolution is similarly close to the targets required for future X-ray astronomy missions.
Abstract: Cryogenic detectors are extremely sensitive and have a wide variety of applications (particularly in astronomy), but are difficult to integrate into large arrays like a modern CCD (charge-coupled device) camera. As current detectors of the cosmic microwave background (CMB) already have sensitivities comparable to the noise arising from the random arrival of CMB photons, the further gains in sensitivity needed to probe the very early Universe will have to arise from large arrays. A similar situation is encountered at other wavelengths. Single-pixel X-ray detectors now have a resolving power of ΔE < 5 eV for single 6-keV photons, and future X-ray astronomy missions anticipate the need for 1,000-pixel arrays. Here we report the demonstration of a superconducting detector that is easily fabricated and can readily be incorporated into such an array. Its sensitivity is already within an order of magnitude of that needed for CMB observations, and its energy resolution is similarly close to the targets required for future X-ray astronomy missions.
1,429 citations
TL;DR: This work synthesizes the states using a superconducting phase qubit to phase-coherently pump photons into the resonator, making use of an algorithm that generalizes a previously demonstrated method of generating photon number (Fock) states in a resonator.
Abstract: The superposition principle is a fundamental tenet of quantum mechanics, allowing a quantum system to be 'in two places at the same time'. The preparation and use of superposed states forms the basis of quantum computation and simulation. Max Hofheinz and colleagues now demonstrate the technically challenging preparation and measurement of arbitrary quantum states in an electromagnetic resonator. States with different numbers of photons are superposed in a completely controlled and deterministic manner. The superposition principle is a fundamental tenet of quantum mechanics, allowing a quantum system to be 'in two places at the same time'. Here, the preparation and measurement of arbitrary quantum states in an electromagnetic resonator is demonstrated; states with different numbers of photons are superposed in a completely controlled and deterministic manner. The superposition principle is a fundamental tenet of quantum mechanics. It allows a quantum system to be ‘in two places at the same time’, because the quantum state of a physical system can simultaneously include measurably different physical states. The preparation and use of such superposed states forms the basis of quantum computation and simulation1. The creation of complex superpositions in harmonic systems (such as the motional state of trapped ions2, microwave resonators3,4,5 or optical cavities6) has presented a significant challenge because it cannot be achieved with classical control signals. Here we demonstrate the preparation and measurement of arbitrary quantum states in an electromagnetic resonator, superposing states with different numbers of photons in a completely controlled and deterministic manner. We synthesize the states using a superconducting phase qubit to phase-coherently pump photons into the resonator, making use of an algorithm7 that generalizes a previously demonstrated method of generating photon number (Fock) states in a resonator8. We completely characterize the resonator quantum state using Wigner tomography, which is equivalent to measuring the resonator’s full density matrix.
827 citations
TL;DR: In this paper, a wide range of experimental and theoretical studies of two-level or tunnelling states in glasses are discussed, focusing on fundamental physics rather than a detailed comparison of experiment and theory.
Abstract: This review covers a wide range of experimental and theoretical studies of two-level or tunnelling states in glasses. Emphasis is on fundamental physics rather than a detailed comparison of experiment and theory. Sections cover the static and dynamic properties of tunnelling states, their contribution to thermal properties and their response to weak and strong electric and acoustic fields, both steady state and pulsed. A section on metallic glasses focuses on the importance of electron tunnelling-state interactions, and a final section illustrates approaches to a microscopic description by means of selected examples.
711 citations
TL;DR: A quantum central processing unit that exchanges data with a quantum random-access memory integrated on a chip, with instructions stored on a classical computer is demonstrated.
Abstract: The von Neumann architecture for a classical computer comprises a central processing unit and a memory holding instructions and data. We demonstrate a quantum central processing unit that exchanges data with a quantum random-access memory integrated on a chip, with instructions stored on a classical computer. We test our quantum machine by executing codes that involve seven quantum elements: Two superconducting qubits coupled through a quantum bus, two quantum memories, and two zeroing registers. Two vital algorithms for quantum computing are demonstrated, the quantum Fourier transform, with 66% process fidelity, and the three-qubit Toffoli-class OR phase gate, with 98% phase fidelity. Our results, in combination especially with longer qubit coherence, illustrate a potentially viable approach to factoring numbers and implementing simple quantum error correction codes.
290 citations
TL;DR: In this paper, the surface composition, termination, and structure of the Al 2 O 3 {0001}-(1 × 1) surface have been determined through the use of time-of-flight scattering and recoiling spectrometry (TOF-SARS), low energy electron diffraction (LEED), and classical ion trajectory simulations.
265 citations