Session V26: Focus Session: Superconducting Qubits

Design improvements for superconducting qubits

Rapid understanding of decoherence processes, both energy and phase relaxation, for superconducting qubits led to novel design modifications with which various qubit performance metrics were improved dramatically. One example of a successfully redesigned qubit is the Transmon qubit. Here we show that there are other modifications that can made bestowing qubits with properties which we believe are advantageous for multi-qubit applications. Specifically we highlight two modifications for two types of qubits and compare these with experimental results. The first is a modified flux qubit which is less sensitive to some of the known decoherence sources. The second is a microwave-based read-out for phase qubits which completely avoids some of the decoherence mechanisms that were recently shown to limit qubit performance.   

Dipole to quadrapole interactions in a transmon qubit: Purcell protection and tunable coupling

In a recent experiment Houck et al [Phys. Rev. Lett. 101, 080502 (2008)] showed that the major source of decoherence in the transmon qubit was relaxation through the resonator. This relaxation is known as the Purcell effect and arises from the dipole interaction between the transmon qubit and the resonators electromagnetic field. In this talk I will present a modification of the transmon qubit that allows us to tune the transmon-resonator interaction from dipole to quadrapole, and hence turn the Purcell effect off with surprisingly little effect on the control and measurement.   

Tunable coupling between three qubits as a building block for a superconducting quantum computer

Large scale quantum computers will need to consist of many interacting qubits. In this talk we expand the two flux qubit coupling scheme first devised in [1] and realized in [2] to a three qubit, two coupler scenario. We study L-shaped and line-shaped coupler geometries, and show how the interaction strength between qubits changes in terms of the couplers' dimensions. We explore two cases: the ``on state" where the interaction energy between two nearest-neighbor qubits is high, and the ``off state'' where it is turned off. In both situations we study the undesirable crosstalk with the third qubit. Finally we use the GRAPE algorithm to find efficient pulse sequences for two qubit gates subject to physical constraints on the coupling strength.   

A superconducting flux qubit with tunable tunnel coupling

We present measurements on a superconducting flux qubit where the tunnel coupling Delta can be varied from 0.8 to 4.8 GHz. This allows for both ZZ and XZ qubit-qubit coupling architectures. The device is realized by replacing one of the Josephson junctions in the qubit with an additional loop which forms a dc SQUID. By applying different fluxes in the main loop and in the additional SQUID loop, we can change the qubit energy-level separation and the tunnel coupling independently [1]. This allows us to measure the energy relaxation (T1) and coherence (T2) times of the qubit at different tunnel couplings and operating points. We find that T1 varies between 1-2 us, and a spin-echo T2 decay of 700 ns. We analyze these results in terms of flux noise coupling into the two loops [2]. [1] Paauw et al., PRL 102, 090501 (2009) [2] Yoshihara et al., PRL 97, 167001 (2006)   

Theory of tunable coupling of phase qubits

We theoretically analyze a scheme for tunable coupling of two phase qubits, which has been recently realized experimentally. In this scheme, two inductors create a direct magnetic interaction between the qubits via mutual inductance, and an additional Josephson junction creates an indirect interaction which may be tuned via the bias current of the junction. These two contributions to $\sigma _{x}\sigma _{x}$ coupling of qubits have opposite signs and for some value of the bias current cancel each other, thus producing zero coupling. However, a small $\sigma _{z}\sigma _{z}$ coupling, which originates due to qubit anharmonicity, gets cancelled at a slightly different bias current, that leads to a small residual coupling. We calculate the residual coupling and the corresponding ON/OFF ratio analytically and numerically. We also discuss a minor modification of the scheme, for which the residual coupling may be zeroed.   

Straddling Regime of a Transmon Qubit

We investigate the straddling regime of a superconducting transmon qubit coupled to a microwave resonator in a circuit QED architecture. In this regime, effects of higher levels of the transmon qubit add constructively to improve single shot measurement. This regime requires significantly lower coupling between qubit and cavity than has previously been reported, but paradoxically, this reduced coupling leads to an increased measurement signal. We report on a qubit designed to substantially reduce coupling and access this straddling regime.   

dc SQUID Phase Qubit with Sub-Micron Junction and Interdigitated Capacitor

We have designed an Al/AlO$_{x}$/Al dc SQUID phase qubit on sapphire that minimizes the effects from sources of loss and dephasing, with the goal of reaching a coherence time of 10 micro-seconds. Loss from the Josephson junction's tunnel barrier and other neighboring dielectric layers is believed to be the dominant sources of decoherence in most phase qubits. To minimize the number of charge two-level systems in the barrier and the effect of dielectric loss, our phase qubit employs a 300 x 300 nm junction with a designed critical current of 150 nA and a 1 pF interdigitated capacitor that is added in parallel. The capacitor is made on the sapphire substrate and has 100 fingers that are about 1.2 microns wide with a 1.2 micron spacing between them. To minimize loss from the bias leads, the qubit is isolated from the leads by a tunable inductive isolation network and an on-chip LC filter. We will discuss the design as well as on-going research into the effect that these parameters have on the coherence time of such a device.   

Improved Phase Qubit with Low-Loss Shunt Capacitance

Superconducting circuits containing Josephson junctions are a leading candidate for scalable quantum information processing in the solid state. Qubit energy relaxation times are limited by microwave loss induced by a continuum of two-level state (TLS) defects in the dielectric materials of the circuit. State-of-the-art phase qubit circuits employ a micron-scale Josephson junction shunted by an external capacitor. In this case, the qubit $T_1$ time is directly proportional to the density of TLS defects in the capacitor dielectric. Here, we explore an alternative design that replaces the lossy lumped-element capacitor with a loss-loss effective capacitance. By minimizing the presence of the offending lossy amorphous dielectrics, we can extend the qubit $T_1$ times significantly. Here we show the results of this redesign and discuss it's impact on qubit performance.   

Measurements of coherence times on a transmon qubit with superconducting bandgap engineering

A practical quantum computer requires qubits to have long enough coherence times to perform many quantum gates. For a superconducting transmon qubit, non-equilibrium quasiparticles are one possible source for decoherence. Although the origin of these non-equilibrium quasiparticles remains unclear, the poisoning effect of quasiparticles is expected to be reduced by lowering the quasiparticle density near the tunnel junctions of the qubits. Potential approaches to reducing the quasiparticle density include using a higher-gap superconductor and fabricating quasiparticle traps near the tunnel junctions. We will present preliminary data of the coherence times measured on a transmon qubit fabricated by engineered Al bandgap profiles and compare them with those obtained on regular transmon qubits.   

Long coherence time in a superconducting persistent-current qubit

We report relaxation times $T_1$ in excess of 10 $\mu$s in aluminum persistent-current qubits (flux qubits), read out by a switching dc SQUID. At the sweet spot in flux bias, spin-echo refocusing gives a relaxation-limited coherence time $T_2=2T_1 $. The free-induction decay time constant $T_2^*$ reaches 2.5 $\mu$s. Detuning the quantization axis away from this optimal point, the much-increased sensitivity to flux noise enhances the phase-decay rate. We confirm the Gaussian phase decay indicative of flux noise with a nearly $1/f$ spectral density, as well as the magnitude of the noise reported in ref.\@ [1]. Contrary to dephasing, the relaxation rate has weak dependence on quantization axis (flux-bias). Finding the microscopic mechanism for $T_1$ relaxation remains one of the most important topics in superconducting qubit research. \newline[1] Yoshihara \emph{et al.}, PRL \textbf{97}, 167001 (2006)   

Experimental bring-up procedures with metrology to improve superconducting qubit performance

Demonstrating complex algorithms on a quantum computer will require high fidelity single qubit and coupled qubit gates. Current superconducting architectures have demonstrated high fidelity single qubit gates, entangling gates through novel coupling schemes, and small scale algorithms. Building on these achievements, we present progress towards scalable implementations of high fidelity gates that will enable more complex quantum algorithms. In particular, we present a detailed experimental bring-up procedure complete with improved single qubit gates that use Derivative Reduction by Adiabatic Gates (DRAG), calibrated Z-gates to cancel the AC Stark effect, and metrological techniques to quantify errors.   

Development of on-chip passive microwave components towards a continuous variables implementation of Quantum Information Processing

Quantum information processing aims to exploit entanglement, the unique feature of quantum mechanics, to enhance our abilities for communication and computation. In the strategy of continuous-variables quantum information processing, an entangled state of the electromagnetic field, similar to the famous EPR state, can be generated by combining two squeezed states on a beam splitter. Our group has already demonstrated the ability to generate these highly non classical squeezed states at microwave frequencies using a Josephson Parametric Amplifier. However, generating EPR states is more demanding. Passive elements, like directional couplers and 90-degree-hybrid couplers (the microwave analogue of beam splitters), have to be developed such that they can be integrated on the same chip as the JPA. In addition, they must be low-loss to preserve the entanglement. In this talk we will present the design and test of an on-chip 20dB directional coupler and a 90-degree-hybrid coupler. Their performance will be carefully analyzed by the use of the Through-Reflect-Line calibration method.