We have characterized the temperature dependence of the flux threading dc SQUIDs cooled to millikelvin temperatures. The flux increases as 1/T as temperature is lowered; moreover, the flux change is proportional to the density of trapped vortices. The data are compatible with the thermal polarization of surface spins in the trapped fields of the vortices. In the absence of trapped flux, we observe evidence of spin-glass freezing at low temperature. These results suggest an explanation for the universal 1/f flux noise in SQUIDs and superconducting qubits.

We describe a microwave photon counter based on the current-biased Josephson junction. The junction is tuned to absorb single microwave photons from the incident field, after which it tunnels into a classically observable voltage state. Using two such detectors, we have performed a microwave version of the Hanbury Brown-Twiss experiment at 4 GHz and demonstrated a clear signature of photon bunching for a thermal source. The design is readily scalable to tens of parallelized junctions, a configuration that would allow number-resolved counting of microwave photons.

Magnetic flux noise is a dominant source of dephasing and energy relaxation in superconducting qubits. The noise power spectral density varies with frequency as 1/f α with α ∼ < 1 and spans 13 orders of magnitude. Recent work indicates that the noise is from unpaired magnetic defects on the surfaces of the superconducting devices. Here, we demonstrate that adsorbed molecular O2 is the dominant contributor to magnetism in superconducting thin films. We show that this magnetism can be suppressed by appropriate surface treatment or improvement in the sample vacuum environment. We observe a suppression of static spin susceptibility by more than an order of magnitude and a suppression of 1/f magnetic flux noise power spectral density by more than a factor of 5. These advances open the door to realization of superconducting qubits with improved quantum coherence.A quantum computer will allow efficient solutions for certain problems that are intractable on conventional, classical computers, including factoring and quantum simulation. Superconducting quantum bits ("qubits") based on Josephson junctions are a leading candidate for scalable quantum information processing in the solid state [1, 2]. Gate and measurement operations have attained a level of fidelity that should enable quantum error correction [3, 4], and there is interest in scaling to larger systems [5, 6]. However, qubit performance is limited by dephasing [7,8]. The dominant source of dephasing is low-frequency 1/f magnetic flux noise [9][10][11]. Uncontrolled variation of the flux bias of the qubit leads to the accumulation of spurious phase during periods of free evolution, resulting in a rapid decay of qubit coherence. Magnetic flux noise was first identified in the 1980s [12,13]. Efforts to avoid flux noise include operation at a "sweet spot" where the device is insensitive to first order to magnetic flux fluctuations [14], or elimination of superconducting loops that allow the frequency of the qubit to be tuned in situ [15]. However, restriction to fixedfrequency qubits results in longer gate times, and static disorder in the junction critical currents makes it difficult to target specific frequencies, leading to frequency clashes in larger multiqubit circuits. In the context of a quantum annealer [16,17], flux noise degrades performance by limiting the number of qubits that can tunnel coherently. For these reasons, there is strong motivation to understand and eliminate the flux noise.Recent experiments indicate that there is a high density of unpaired surface spins in superconducting integrated circuits [18] and it is believed that fluctuations of * Present address: Northrop Grumman Corporation, Linthicum, Maryland 21203, USA † Electronic address: rfmcdermott@wisc.edu these spins give rise to the 1/f flux noise [19][20][21]. There is experimental evidence that interactions between the surface spins are significant [22]. To date, however, there has been no experimental data pointing toward the microscopic nature of the surface magnetic defects, althou...

We have characterized the complex inductance of dc SQUIDs cooled to millikelvin temperatures. The SQUID inductance displays a rich, history-dependent structure as a function of temperature, with fluctuations of order 1 fH. At a fixed temperature, the SQUID inductance fluctuates with a 1/f power spectrum; the inductance noise is highly correlated with the conventional 1/f flux noise. The data are interpreted in terms of the reconfiguration of clusters of surface spins, with correlated fluctuations of effective magnetic moments and relaxation times.

We describe a microwave amplifier based on the Superconducting Low-inductance Undulatory Galvanometer (SLUG). The SLUG is embedded in a microstrip resonator, and the signal current is injected directly into the device loop. Measurements at 30 mK show gains of 25 dB at 3 GHz and 15 dB at 9 GHz. Amplifier performance is well described by a simple numerical model based on the Josephson junction phase dynamics. We expect optimized devices based on high critical current junctions to achieve gain greater than 15 dB, bandwidth of several hundred MHz, and added noise of order one quantum in the frequency range of 5-10 GHz.PACS numbers: 85.25. Am, 85.25.Dq, 84.30.Le, 84.40.Lj Recent progress in the superconducting quantum circuit community has motivated a search for ultralow-noise microwave amplifiers for the readout of qubits and linear cavity resonators [1,2]. It has long been recognized that the dc Superconducting QUantum Interference Device (SQUID) can achieve noise performance approaching the standard quantum limit of half a quantum [3]. While in principle the SQUID should be able to amplify signals approaching the Josephson frequency (typically several tens of GHz), it remains challenging to integrate the SQUID into a 50 Ω environment and to provide for efficient coupling of the microwave signal to the device. In one arrangement, a multiturn input coil has been configured as a microstrip resonator, with the SQUID washer acting as a groundplane [4]. This so-called microstrip SQUID amplifier has achieved noise performance within a factor of two of the standard quantum limit at 600 MHz [5,6]; however, performance degrades at higher frequencies due to the reduced coupling associated with the shorter microstrip input line [7]. An alternative approach accesses the GHz regime by integrating a high-gain SQUID gradiometer into a coplanar transmission line resonator at a current antinode [8,9]. In other work, Jospehson circuits have been driven by an external microwave tone to enable ultralow-noise parametric amplification of microwave frequency signals [10][11][12]; however, Josephson parametric amplifiers provide limited bandwidth and dynamic range, and the external microwave bias circuitry introduces an additional layer of complexity.In this Letter we describe a new device configuration that provides efficient coupling of a GHz-frequency signal to a compact Superconducting Low-inductance Undulatory Galvanometer (SLUG). In contrast to the dc SQUID, which relies on a separate inductive element to transform the input signal into a magnetic flux, the SLUG samples the magnetic flux generated by a current that is directly injected into the device loop [13]. The compact geometry of the SLUG makes the device straightforward to model at microwave frequencies and * Electronic address: rfmcdermott@wisc.edu easy to integrate into a microwave transmission line. Moreover, it is simple to decouple the SLUG modes from the input modes, allowing for separate optimization of the gain element and the matching network.The layer stackup of ...

We have incorporated a single crystal silicon shunt capacitor into a Josephson phase qubit. The capacitor is derived from a commercial silicon-on-insulator wafer. Bosch reactive ion etching is used to create a suspended silicon membrane; subsequent metallization on both sides is used to form the capacitor. The superior dielectric loss of the crystalline silicon leads to a significant increase in qubit energy relaxation times. T1 times up to 1.6 µs were measured, more than a factor of two greater than those seen in amorphous phase qubits. The design is readily scalable to larger integrated circuits incorporating multiple qubits and resonators.PACS numbers: 85.25. Cp,77.22.Gm,74.50.+r The Josephson phase qubit is an attractive candidate for scalable quantum information processing in the solid state [1][2][3][4][5]. This qubit has achieved several important milestones, including realization of high-fidelity entangling gates in two and three qubit circuits [4], violation of a Bell's inequality [5], and full characterization of highly non-classical states in linear microwave resonators [6]. However, qubit performance is limited by relatively short coherence times, under 1 µs. It has been shown that the dominant energy relaxation mechanism is dielectric loss induced by a continuum of low-energy defect states in the amorphous thin films of the circuit [7]. In the most common approach to qubit realization, a ∼ 1 µm 2 Josephson junction is shunted by an external thin film capacitor of order 1 pF [8]; in this case, qubit T 1 is determined solely by the loss tangent of the bulk capacitor dielectric: T 1 = 1/ω 10 tan δ, where ω 10 /2π is the qubit frequency. There have been efforts to develop amorphous dielectrics with improved intrinsic (low-temperature, low power) loss for superconducting qubit applications [9]. An alternative approach is to incorporate crystalline, defectfree dielectrics into the qubit circuit. Molecular beam epitaxy techniques have been used to grow single-crystal Al 2 O 3 tunnel barriers on crystalline Re underlayers, and phase qubit circuits incorporating these barriers demonstrate a significant reduction in the density of spurious microwave resonances [10,11]. Moreover, there has been progress in the incorporation of epitaxial Josephson junctions into transmon qubits, although T 1 times were under 1 µs [12,13]. Other work involves the development of grown bulk crystalline Al 2 O 3 for phase qubit shunt capacitors [14]. However, the robust, repeatable growth of crystalline dielectrics for superconducting qubit circuits remains a daunting challenge.In this work, we demonstrate the realization of a Josephson phase qubit incorporating a crystalline silicon shunt capacitor. Silicon growth has been perfected over decades by the integrated circuit industry, and commercial-grade intrinsic silicon displays an internal quality factor in excess of 10 6 in the low-power, lowtemperature regime relevant to qubit operation. More- over, silicon-on-insulator (SOI) technology provides a path to the incorporation of...

We present the results of measurements of the scattering parameters of microstrip amplifiers ͑MSAs͒ based on the dc superconducting quantum interference device. The amplifier input impedance is poorly matched to typical transmission line impedances, resulting in high input return loss around Ϫ2 dB. We show that negative feedback can lower the MSA input impedance to achieve a robust match to 50 ⍀. In the presence of capacitive and inductive feedback, the input return loss of the MSA can be reduced below Ϫ10 dB, opening the door to the practical use of the MSA for a variety of demanding applications.

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