Session T25: Superconducting Qubits: Qubit Design

Dispersive measurement of a metastable phase qubit using a tunable cavity

A metastable phase qubit was measured using a tunable cavity by two methods: a tunneling measurement followed by magnetometry readout by the cavity, and a non-destructive dispersive measurement of the qubit by the cavity. The cavity was also used to directly observe the photons radiated by a tunneling measurement. Using a tunable cavity to dispersively measure a metastable phase qubit avoids tunneling measurement radiation and allows for further post-measurement qubit manipulations, two characteristics useful in a quantum processor. The tunable nature of the cavity allows it to be detuned during any single qubit or multi-qubit gate operations in order to main long qubit lifetimes by avoiding loss via the Purcell Effect. This architecture is readily expanded for multiplexed readout of many qubits.   

Large Dispersive Shift of Cavity Resonance Induced by a Superconducting Flux Qubit in the Straddling Regime

We demonstrate enhancement of the dispersive frequency shift in a coplanar waveguide resonator induced by a capacitively coupled superconducting flux qubit in the straddling regime. The magnitude of the observed shift, 80~MHz for the qubit-resonator detuning of 5~GHz, is quantitatively explained by the generalized Rabi model which takes into account the contribution of the qubit higher energy levels. By applying the enhanced dispersive shift to the qubit readout, we achieved 90$\%$ contrast of the Rabi oscillations which is mainly limited by the energy relaxation of the qubit. We also discuss the qubit readout using a Josephson parametric amplifier.   

Strong Coupling of a Scannable Transmon to a Coplanar Waveguide Resonator

We report measurements of the coupling between a superconducting microwave resonator and a transmon qubit fabricated on a separate chip and mounted to a three-dimensional cryogenic translation stage. The qubit-resonator system reached the strong coupling regime with a coupling strength in excess of 180 MHz, while qubit and resonator linewidths were roughly 0.4 and 10 MHz respectively. We map out the coupling strength in the plane of the resonator and find good agreement with finite element simulation. Such a scannable qubit could be used as a part of a local probe of a large array of microwave cavities and superconducting qubits.   

Circuit QED with multi-pole microwave cavity filters

Circuit QED has proven to be a successful architecture for quantum computing and quantum optics. In this architecture multiple superconducting qubits are coupled to a high-Q microwave resonator, allowing for control, coupling and readout of qubit states. However, as we scale to larger systems and longer coherence times, reducing residual couplings become more important. We discuss multi-pole cavity filters as isolating elements between qubits, used as a technique for producing improved gates.   

Characterization of Multipole Microwave Cavity Filters

An essential requirement for a quantum information processor is the ability to controllably couple and decouple individual qubits with each other. With superconducting circuit QED, this can be implemented by coupling multiple qubits to a transmission line cavity bus, and can be controlled by moving the qubit frequencies in and out of resonance with the bus. As coherence times increase, and the number of qubits attached to a bus grows larger, the problem of spurious coupling while detuned will become more important. We propose using principles from microwave filter design to create new couplers with higher contrast ratios in the effective qubit-qubit coupling. We present progress towards circuit implementations of multipole qubit coupling architectures.   

Extracting an Effective Jaynes-Cummings Model for an LC Filtered dc SQUID

Spectroscopy of an Al/AlOx/Al dc SQUID phase qubit revealed peaks suggestive of dispersive photon shifts in a Jaynes-Cummings model, where the role of the resonator is played by an on-chip rf LC filter. A lumped element analysis of the filter-qubit system reveals qubit and resonator modes at the expected frequencies (330 MHz and 8.7 GHz) but an isolation junction mode at $\sim$100 GHz and qubit-filter coupling that is smaller than observed. As an alternative to the lumped element picture, we examine a transmission line model of the SQUID and the first order correction to the lumped element model. We discuss Jaynes-Cummings approximations to these various models.   

rf Photon Peaks of a dc SQUID Phase Qubit Coupled to On-Chip LC Filter

We have fabricated and tested an Al/AlO$_x$ /Al dc SQUID phase qubit on a sapphire substrate. The qubit is shunted by an interdigitated capacitor and isolated from the bias leads by an inductive isolation network using a larger Josephson junction. Additional high frequency filtering is provided by an on-chip LC filter which consists of square spiral inductors and parallel plate SiN$_x$ capacitors, with $\sim$330 MHz cutoff frequency. Spectroscopy of the qubit transition frequency at 8.7 GHz shows multiple equally spaced subpeaks. These subpeaks are caused by coupling between the qubit and the LC filter, forming a system that can be described by Jaynes-Cummings model. The individual subpeaks correspond to transitions with different photon numbers in the LC filter.   

Quantum Superinductor with Tunable Nonlinearity

We report on the realization of a superinductor, a dissipationless element whose microwave impedance greatly exceeds the resistance quantum R$_{Q}$. The design of the superinductor, implemented as a ladder of nanoscale Josephson junctions, enables tuning of the inductance and its nonlinearity by a weak magnetic field. The Rabi decay time of the superinductor-based qubit exceeds 1 $\mu$s. The high kinetic inductance and strong nonlinearity offer new types of functionality, including the development of qubits protected from both flux and charge noises, fault tolerant quantum computing, and high-impedance isolation for electrical current standards based on Bloch oscillations.   

Long-lived, radiation-suppressed superconducting quantum bit in a planar geometry

We present a superconducting qubit design that is fabricated in a 2D geometry over a super-conducting ground plane to enhance the lifetime. The qubit is coupled to a microstrip resonator for readout. The circuit is fabricated on a silicon substrate using low loss, stoichiometric titanium nitride for capacitor pads and small, shadow-evaporated aluminum/aluminum-oxide junctions. We observe qubit relaxation and coherence times (T$_{\mathrm{1}}$ and T$_{\mathrm{2}})$ of 11.7 $\pm $ 0.2 $\mu $s and 8.7 $\pm $ 0.3 $\mu $s, respectively. Calculations show that the proximity of the superconducting plane suppresses the otherwise high radiation loss of the qubit. A significant increase in T$_{\mathrm{1}}$ is projected for a reduced qubit-to-superconducting plane separation.   

Towards Tunable Transitions in 2-D Transmons

We have developed a design for a tunable transmon qubit with an on-chip flux bias. The transmon is fabricated with two sub-micron Al/AlO$_{x}$/Al tunnel junctions and coupled to a superconducting planar lumped-element resonator. A coplanar transmission line provides flux coupling and tuning of the qubit's transition energies. We will discuss the design and fabrication strategy and present preliminary measurements of coherence and tunability in these devices.   

Tuning qubit interactions with asymmetric transmons

Superconducting transmon qubits have been used in numerous key experiments in the field of quantum information processing. We are exploring a variation of this circuit, the asymmetric transmon, where the two Josephson junctions making up the qubit have substantially different critical currents. This results in a second sweet spot with respect to magnetic flux at odd half-integer flux-quantum bias points. The corresponding reduction in energy-modulation depth makes the qubit less sensitive to dephasing due to flux noise for bias points away from the sweet spots. At the same time, the tunability of the qubit energy allows for novel qubit-cavity processes, including flux-driven sideband transitions, as well as adjustable interactions between multiple qubits.   

Investigation of Single and Coupled Flux Qubit Energy Spectra Using Tunneling Spectroscopy

We present the results of our investigation of the energy levels of systems of flux qubits using tunneling spectroscopy. Tunneling spectroscopy is a technique by which we use macroscopic resonant tunneling processes of a neighboring qubit to probe the energy spectrum of a system of flux qubits. We used this technique to measure the energy gap of a single qubit near its degeneracy point where it is in a superposition of left and right circulating current states. Furthermore, we applied this technique to systems of up to 8 coupled qubits that were biased at degeneracy and observed energy spectra that agree with theoretical predictions based on independently determined device parameters.   

Phase versus flux coupling between resonator and superconducting flux qubit

The dispersive coupling of qubits to microwave resonators has become widely used for qubit readout. Recent advances in coupling qubits to 3D resonators have demonstrated the importance of the nature of the qubit-resonator coupling in determining the qubit relaxation and decoherence times, $T_1$ and $T_2^*$. We study the effect of phase versus flux coupling on flux qubits coupled to planar resonators. Using an aluminum shadow evaporation technique we fabricate a low-loss planar resonator, consisting of a meandering inductor and interdigitated capacitor, and a flux qubit, all in a single processing step. Whereas the qubit and resonator are always flux coupled via a geometric mutual inductance, a phase coupling can be added by including a shared trace between the qubit and resonator. This technique allows us to control both the magnitude and nature of the qubit-resonator coupling without significantly affecting either the qubit or resonator design. We characterize the dependence of the qubit parameters $T_1$, $T_2^*$, and spin echo time $T_{echo}$ on the resonator coupling parameters to gain insight into possible sources of decoherence and loss.   

Solid-state quantum metamaterials

Quantum metamaterials provide a promising potential test bed for probing the quantum-classical transition. We propose a scalable and feasible architecture for a solid-state quantum metamaterial. This consists of an ensemble of superconducting flux qubits inductively coupled to a superconducting transmission line. We make use of fully quantum mechanical models which account for decoherence, input and readout to study the behaviour of prototypical 1D and 2D quantum metamaterials. In addition to demonstrating some of the novel phenomena that arise in these systems, such as ``quantum birefringence,'' we will also discuss potential applications.   

Development of superconducting transmission-line metamaterials

In recent years, various metamaterials have received substantial attention for their ability to exhibit simultaneous negative permittivity and permeability. Such systems are commonly referred to as left-handed materials and display a variety of counterintuitive properties. We are investigating one-dimensional metamaterials consisting of superconducting circuit elements that operate in the microwave regime. In this talk, we will discuss our efforts to develop a superconducting left-handed transmission line (LHTL) coupled to a coplanar waveguide resonator (right-handed line --RHTL) to create a composite transmission line. Such a structure is predicted to exhibit an intriguing mode structure and we will discuss possible schemes for coupling superconducting qubits to these metamaterials.