We demonstrate a planar, tunable superconducting qubit with energy relaxation times up to 44 μs. This is achieved by using a geometry designed to both minimize radiative loss and reduce coupling to materials-related defects. At these levels of coherence, we find a fine structure in the qubit energy lifetime as a function of frequency, indicating the presence of a sparse population of incoherent, weakly coupled two-level defects. We elucidate this defect physics by experimentally varying the geometry and by a model analysis. Our "Xmon" qubit combines facile fabrication, straightforward connectivity, fast control, and long coherence, opening a viable route to constructing a chip-based quantum computer.

We describe the fabrication and measurement of microwave coplanar waveguide resonators with internal quality factors above 10 7 at high microwave powers and over 10 6 at low powers, with the best low power results approaching 2 × 10 6 , 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.High quality factor microwave resonators provide critical elements for superconducting electromagnetic radiation detectors 1 , quantum memories 2,3 , and quantum computer architectures 4 . Good performance and stability can be achieved for such applications using aluminum resonators patterned on sapphire substrates. Aluminum is a favored material due to its robust oxide and reasonable transition temperature, and sapphire provides an excellent substrate due to its very low microwave loss tangent 5 δ ∼ 10 −8 and its chemical inertness. However, the quality factors measured in such resonators is lower than expected; recent simulations 6 and experiments 7 suggest that the unexplained loss arises mostly from imperfections at the metal-substrate interface. Using an experimental apparatus with minimal stray magnetic fields and infrared light at the sample 8 , here we show that careful substrate preparation and cleaning yields aluminumon-sapphire resonators with significantly higher internal quality factors Q i . We also introduce a new method for evaluating the resonator microwave response.The aluminum for the resonators was deposited on cplane sapphire substrates in one of three deposition systems: A high vacuum DC sputter system (base pressure P base = 6 × 10 −8 Torr), a high vacuum electron-beam evaporator (P base = 5 × 10 −8 Torr) or an ultra-high vacuum (UHV) molecular beam epitaxy (MBE) system (P base = 6 × 10 −10 Torr) with electron-beam deposition. The sapphire substrates were first sonicated in a bath of acetone then isopropanol followed by a deionized water rinse. For the sputter-deposited and e-beam evaporated samples, we further cleaned the substrates prior to Al de-

Entanglement is one of the key resources required for quantum computation, so the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers. In superconducting devices, two-qubit entangled states have been demonstrated and used to show violations of Bell's inequality and to implement simple quantum algorithms. Unlike the two-qubit case, where all maximally entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways. These are typified by the states |GHZ>= (|000+ |111>)/ sqrt [2] and |W>= (|001> + |010> + |100>)/ sqrt [3]. Here we demonstrate the operation of three coupled superconducting phase qubits and use them to create and measure |GHZ> and |W>states. The states are fully characterized using quantum state tomography and are shown to satisfy entanglement witnesses, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.

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.

A quantum processor (QuP) can be used to exploit quantum mechanics to find the prime factors of composite numbers [1]. Compiled versions of Shor's algorithm have been demonstrated on ensemble quantum systems [2] and photonic systems [3][4][5], however this has yet to be shown using solid state quantum bits (qubits). Two advantages of superconducting qubit architectures are the use of conventional microfabrication techniques, which allow straightforward scaling to large numbers of qubits, and a toolkit of circuit elements that can be used to engineer a variety of qubit types and interactions [6,7]. Using a number of recent qubit control and hardware advances [7][8][9][10][11][12][13], here we demonstrate a nine-quantum-element solid-state QuP and show three experiments to highlight its capabilities. We begin by characterizing the device with spectroscopy. Next, we produces coherent interactions between five qubits and verify bi-and tripartite entanglement via quantum state tomography (QST) [8,12,14,15]. In the final experiment, we run a three-qubit compiled version of Shor's algorithm to factor the number 15, and successfully find the prime factors 48 % of the time. Improvements in the superconducting qubit coherence times and more complex circuits should provide the resources necessary to factor larger composite numbers and run more intricate quantum algorithms.In this experiment, we scaled-up from an architecture initially implemented with two qubits and three resonators [7] to a nine-element quantum processor (QuP) capable of realizing rapid entanglement and a compiled version of Shor's algorithm. The device is composed of four phase qubits and five superconducting coplanar waveguide (CPW) resonators, where the resonators are used as qubits by accessing only the two lowest levels. Four of the five CPWs can be used as quantum memory elements as in Ref. [7] and the fifth can be used to mediate entangling operations.The QuP can create entanglement and execute quantum circuits [16,17] with high-fidelity single-qubit gates (X, Y , Z, and H), [18,19]combined with swaps and controlled-phase (C φ ) gates [7,13,20], where one qubit interacts with a resonator at a time. The QuP can also utilize "fast-entangling logic" by bringing all participating qubits on resonance with the resonator at the same time to generate simultaneous entanglement [21]. At present, this combination of entangling capabilities has not been demonstrated on a single device. Previous examples have shown: spectroscopic evidence of the increased coupling for up to three qubits coupled to a resonator [14], as well as coherent interactions between two and three qubits with a resonator [12], although these lacked tomographic evidence of entanglement.Here we show coherent interactions for up to four qubits with a resonator and verify genuine bi-and tripartite entanglement including Bell [9] and |W -states [10] with quantum state tomography (QST). This QuP has the further advantage of creating entanglement at a rate more than twice that of previous demonst...

We present an atomic resolution scanning tunneling spectroscopy study of superconducting BaFe1.8Co0.2As2 single crystals in magnetic fields up to 9 T. At zero field, a single gap with coherence peaks at Delta=6.25 meV is observed in the density of states. At 9 and 6 T, we image a disordered vortex lattice, consistent with isotropic, single flux quantum vortices. Vortex locations are uncorrelated with strong-scattering surface impurities, demonstrating bulk pinning. The vortex-induced subgap density of states fits an exponential decay from the vortex center, from which we extract a coherence length xi=27.6+/-2.9 A, corresponding to an upper critical field Hc2=43 T.

We find that stray infrared light from the 4 K stage in a cryostat can cause significant loss in superconducting resonators and qubits. For devices shielded in only a metal box, we measured resonators with quality factors Q = 10 5 and qubits with energy relaxation times T1 = 120 ns, consistent with a stray light-induced quasiparticle density of 170-230 µm −3 . By adding a second black shield at the sample temperature, we found about an order of magnitude improvement in performance and no sensitivity to the 4 K radiation. We also tested various shielding methods, implying a lower limit of Q = 10 8 due to stray light in the light-tight configuration.Quantum information processing in superconducting circuits is performed at very low temperatures, so energy loss due to quasiparticles is expected to vanish because their density diminishes exponentially with decreasing temperature. As energy relaxation times saturate for superconducting quantum circuits and planar resonators, reaching values on the order of 1-10 µs [1-4], recent experiments have suggested that this may be due to excess non-equilibrium quasiparticles; measurements on phase qubit coherence [5,6], tunneling in charge qubits [7], resonator quality factors [3,4] and quasiparticle recombination times [8,9] are compatible with an excess quasiparticle density on the order of 10-100 µm −3 , possibly arising from stray light, cosmic rays, background radioactivity, or the slow heat release of defects.In this Letter, we demonstrate that stray infrared light gives significant loss in resonators and qubits, and is sometimes the dominant limitation in our present experiments. We also show quantitatively how a combination of infrared shielding techniques removes the influence of stray infrared light, and that the required shielding is beyond what is generally used. The effectiveness of the various techniques is investigated by methodically changing and testing them. With our new light-tight setup, the quality factors of Al superconducting resonators improve dramatically by a factor of 20, as shown in Fig. 1. We also show that shielding improves phase qubit coherence.Loss in a superconducting resonator with frequency f is controlled by the quasiparticle density n qp [10] (for kT ≪ hf )with ∆ the energy gap, D(E F ) the two-spin density of states, and α the kinetic inductance fraction, which depends on geometry. Importantly, excess quasiparticles can limit quality factors, in particular at the low temperatures at which resonators and qubits are operated.Measurements on the temperature dependence of resonator quality factors indicate the presence of an additional loss term, as shown in Fig. 1. Here we plot quality factors of coplanar waveguide (CPW) Al resonators. The open symbols are measured when simply placing the sample in a sample box in a cryostat, with no special measures against stray light. Above a temperature of 200 mK the quality factors decrease exponentially, consistent with a thermal quasiparticle density (dashed line, Eq. 1). At low temperatures a plateau ...

Losses in superconducting planar resonators are presently assumed to predominantly arise from surfaceoxide dissipation, due to experimental losses varying with choice of materials. We model and simulate the magnitude of the loss from interface surfaces in the resonator, and investigate the dependence on power, resonator geometry, and dimensions. Surprisingly, the dominant surface loss is found to arise from the metalsubstrate and substrate-air interfaces. This result will be useful in guiding device optimization, even with conventional materials.