IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 19, NO. 3, JUNE 2009 957 Dc SQUID Phase Qubit With an LC Filter Hyeokshin Kwon, A. J. Przybysz, T. A. Palomaki, R. M. Lewis, B. S. Palmer, H. Paik, S. K. Dutta, B. K. Cooper, J. R. Anderson, C. J. Lobb, and F. C. Wellstood Abstract—We describe the design of an inductor-capacitor (LC) network to increase the isolation of a dc SQUID phase qubit from its current bias leads and thereby increase the relaxation time and coherence time . One junction in the SQUID acts as an ideal phase qubit while the second junction and the SQUID loop induc- tance act as a broadband inductive filter to isolate the first junction from the current bias leads. The LC isolation network provides an additional isolation factor at the junction plasma frequency and al- lows flexibility in the choice of SQUID parameters. Our thin-film on-chip LC isolation network has a 10 nH inductor and an 80 pF capacitor. The combination of the broadband filter and LC filter provides a maximum nominal isolation factor of about at a qubit plasma frequency of about 6.7 GHz. To reduce dielectric loss and two level systems in the qubit junction, we use a relatively small area (4 ) qubit junction built on sapphire and add an external capacitor with 100 nm thick dielectric layers. Measurements revealed Rabi oscillations with an envelope decay time constant of about 42 ns, and an energy relaxation time of 32 ns, consistent with a loss tangent in the . Index Terms—Decoherence, dissipation, filter, Josephson junc- tion, qubit. I. INTRODUCTION R ESEARCH in quantum computing has led to substantial advances in the performance of superconducting qubits in the last decade [1]–[14]. For example, Martinis et al. found that dielectric loss and two-level fluctuators were a significant source of decoherence in phase qubits and that large improvements in the coherence time could be obtained by replacing lossy dielec- tric insulation layers with low-loss materials [11]–[13]. While the coherence times of phase qubits are still not as long as de- sired, a major obstacle has been identified and significant effort is now being directed at resolving the problem. One of the difficulties with phase qubits is that they are poten- tially sensitive to several distinct types of decoherence mecha- nisms. Dissipation and current noise from the bias leads was ini- tially suspected as a source of decoherence [2]–[4], [14]. This motivated designs for networks that isolated the qubit junction by stepping up the impedance of the bias leads and attenuating current noise before it could reach the qubit. In particular, Mar- tinis et al. introduced a broadband inductive isolation scheme Manuscript received August 26, 2008. First published June 30, 2009; current version published July 10, 2009. This work was funded by the NSA, the Joint Quantum Institute (JQI), and the Center for Nanophysics and Advanced Mate- rials (CNAM). H. Kwon, A. J. Przybysz, T. A. Palomaki, R. M. Lewis, S. K. Dutta, B. K. Cooper, J. R. Anderson, C. J. Lobb, and F. C. Wellstood are with the JQI, CNAM and the Department of Physics at the University of Maryland, College Park, Maryland 20742-4111 USA (e-mail: hskwon@umd.edu). B. S. Palmer and H. Paik are with the JQI, CNAM and the Laboratory for Physical Sciences, College Park, Maryland 20742-4111 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2009.2019424 (the dc SQUID phase qubit). In this scheme one junction in the SQUID acts as an ideal phase qubit while the second junction and the SQUID loop inductance act as an inductive filter that isolates the first junction from the current bias leads [4]. In prac- tice, we have found that it is difficult to achieve a large degree of isolation with this scheme due to constraints in the design. Increasing the loop inductance or the isolation junction critical current improves the isolation of the qubit junction. However, this leads to more metastable flux states and requires us to apply an additional initialization procedure to select the starting flux state [14], [15]. In this paper, we describe an isolation scheme for the phase qubit that combines the broadband inductive iso- lation of the dc SQUID phase qubit [4] with a low-pass resonant inductor-capacitor (LC) network [9], [16]. II. LC ISOLATION Fig. 1 shows a schematic of our LC-isolated dc SQUID phase qubit. The LC filter network is formed by inductor and ca- pacitor , and the broad band inductive isolation network is formed by inductors and and the isolation junction . For frequencies f which are much larger than the resonance fre- quency of the filter, the two networks act together to step up the characteristic impedance of the bias leads to an ef- fective shunting resistance across the junction given by (1) where is the current power isolation factor (2) and where is the filter resonance, is the Josephson inductance of the qubit junction , is the Josephson inductance of the isolation junction , and . The first factor in (2) is due to the LC-filter network and causes the isolation to increase rapidly as the frequency in- creases; the LC network acts as a low-pass filter. With a filter resonance frequency of 180 MHz and a qubit operating fre- quency of 6.7 GHz, this factor is about . This factor is only approximate. In particular, parasitic capacitance between the coils of the filter’s inductor and stray inductance in the leads to the filter capacitor will cause self-resonances in both the filter inductor and capacitor and reduce the isolation above the self-resonances. Also, at a frequency of 10 GHz the wavelength is comparable to the overall size of our filter and we expect our lumped circuit model to fail. In this limit, detailed electro- magnetic simulations would be needed to predict the isolation. Finally, the filter is not effective for frequencies or frequencies near the filter resonance frequency; current 1051-8223/$25.00 © 2009 IEEE