Session A25: Superconducting Qubits: Magnetic Flux and Vortex Noise on Qubits and Resonators, Quasiparticles, and Qubit-Resonator Designs

Simulations of Noise in the 2D XY Spin Model

Experiments implicate spins on the surface of metals as the source of flux and inductance noise in SQUIDs. There is experimental evidence that interactions between these surface spins cannot be ignored. As a candidate model of the surface spins, we present Monte Carlo simulations of the classical 2D XY spin model on a square lattice. We investigate the magnetization noise as a function of frequency and temperature. Finite size effects are considered through studies of different size systems.   

Surface spins in superconducting qubits: noise of noise and noise of inductance

In the last several years a growing bulk of experimental evidence has emerged explaining the 1/f magnetic flux noise in superconducting circuits, e.g., qubits, by a very high density of paramagnetic impurities on the surfaces or interfaces of the superconducting metal. A theoretical picture of this phenomenon is still missing. Here we study a model of weakly interacting dissipative spins or spin clusters with the aim to determine their noise properties. In particular we compare the noise of noise (second spectrum) with the noise of the magnetic susceptibility measured as noise of inductance. Both of these were recently studied in experiments. We argue that the noise of noise is dominated by a simple gaussian background, whereas the noise of susceptibility can provide a hint about the microscopic nature of the spins. In particular we discuss the influence of the spin-spin interactions on the susceptibility noise.   

Experimental results on decoherence and readout of coupled superconducting flux qubits in a circuit-QED setup

We present the results of experiments with two superconducting flux qubits coupled to a high-quality factor aluminum coplanar waveguide resonator. The flux qubits have a loop area of $\sim$ 24 $\mu$m$^2$. The coupling to the resonator is implemented using the inductance of a shared line. The qubits are independently controlled via on-chip fast flux bias lines. Readout is performed by homodyne detection at large resonator driving power. Readout contrast exceeds 70\% for each qubit. We observed long relaxation times, approaching 10 microseconds. The coherence time at the symmetry point exceeds 1 microsecond. Away from the symmetry point, decoherence is due to $1/f$ flux noise, with a measured density of $2.6 \times 10^{-6}$ $\Phi_0$ $/\sqrt{\mathrm{Hz}}$ at 1 Hz. We discuss the implementation of a two-qubit controlled-NOT gate using the selective darkening technique [1]. [1] P. C. de Groot, J. Lisenfeld, R. N. Schouten, S. Ashhab, A. Lupascu, C. J. P. M. Harmans, and J. E. Mooij. Nat. Phys., 6(10):763-766, October 2010.   

Ultrasensitive detection of magnetic field using a single artificial atom

We employ a single artificial atom to implement ultrasensitive magnetic field detection. The artificial atom is a persistent current qubit with a size in the micron range, which couples very strongly to magnetic field, with an equivalent magnetic moment of $3.8\times 10^5$ Bohr magnetons. Sensitive detection is realized by employing the field-dependent coherent evolution of the artificial atom and high-fidelity quantum measurement, in a way similar to atomic magnetometry. Using an operation mode based on spin-echo manipulation and qubit reset by energy relaxation, we demonstrate a magnetic field detection sensitivity of $7.5\, pT/\sqrt{Hz}$ for an AC field at $10 MHz$. The sensitivity is further improved if the reset step is eliminated and the correlation of consecutive projective measurements is used instead, reaching $3.3\, pT/\sqrt{Hz}$. The intrinsic sensitivity of this method to AC fields at frequencies in the $100\, kHz - 10\, MHz$ range compares favourably with DC-SQUIDs and atomic magnetometers of equivalent spatial resolution. More than an order of magnitude increase in sensitivity is possible using feasible improvements of qubit design and readout. This result illustrates the potential of artificial quantum systems for sensitive detection and related applications.   

Magnetic Field Effects on High Quality Factor Superconducting Coplanar Resonators

Superconducting coplanar waveguide resonators have proven to be invaluable tools in studying some of the same decoherence mechanisms as those found in superconducting qubits. Prior improvements in fabrication led to resonator internal quality factors (Qi's) in excess of 10 million at high power, enabling us to sensitively probe environmental effects on the resonance frequency and Qi. We have found these resonators to be very susceptible to applied and stray magnetic fields, with measurable changes in the resonator's Qi and resonance frequency from fields as small as a few milligauss. I will present more recent measurements of resonators in magnetic fields.   

Effects of vortices trapped in superconducting microwave resonators

The microwave response of superconductors can be influenced by the presence of vortices and the dynamics they exhibit at high frequencies. We present measurements of vortices trapped in coplanar waveguide superconducting resonators fabricated from thin aluminum films, a common material for superconducting qubit circuits. In particular, by adjusting the geometry of our resonators we are able to trap only a few vortices in certain regions of the resonators. We perform field-cooled measurements to study the dependence of the microwave vortex response on magnetic field and frequency for various resonator modes. In most cases, the addition of vortices results in a downward shift in resonant frequency and a reduction in the quality factor. However, under certain circumstances, the presence of trapped vortices can actually lead to an enhancement of the resonator quality factor.   

Large kinetic inductance microwave resonators in magnetic field

Superconducting resonators of high quality factors are of great interest for photon detection and quantum computation. Conventionally, they operate in or close to the magnetic vacuum. However, for some circuits -for instance resonators coupled to spin ensemble crystals or Majorana fermions- the magnetic field is not negligible and the resonator's field robustness has to be well engineered. The magnetic field dependencies of resonance frequency and quality factor are of considerable interest to improve resonant quantum devices. In this presentation we will discuss thin film titanium nitride resonators operating in a homogeneous magnetic field. Titanium nitride has remarkably high internal microwave quality factors down to single photon levels, and a significant kinetic inductance contribution for thin film resonators. The microwave scattering data of frequency multiplexed resonators was taken in a Helium-3 refrigerator over a large range of photon number levels, temperatures, and magnetic fields. The resonators exhibit strong magnetic hysteresis effects in frequency and quality factor. The magnetic memory -caused by a spatial distribution of trapped vortices- is related to the resonator geometry.   

Flux-dependent loss in aluminum nanobridge SQUID resonators

Unlike traditional tunnel junctions, nanobridge Josephson junctions have weaker nonlinearity, higher transmittivity, and relatively few conduction channels. These parameters carry with them their own intrinsic loss mechanisms. In particular, quasiparticle trapping has been recently shown [1] to be prevalent in quantum point contact junctions operating in a similar parameter regime. We investigate losses in resonant circuits comprised of nanobridge SQUIDs. We observe an increase in loss and an anomalous frequency shift as the SQUIDs are flux-biased, which we speculate to be the result of quasiparticle trapping in a phase-biased nanobridge. We present detailed measurements of this effect, and discuss efforts towards eliminating it. [1] Bretheau et al., PRL 106, 257003 (2011)   

Random frequency modulation of a superconducting qubit

Superconducting circuits with Josephson junctions are a promising platform not only for developing quantum technologies, but, importantly, also for the study of effects that typically occur in complex condensed-matter systems. Here, we employ a transmon qubit to conduct an analog simulation of motional averaging, a phenomenon initially observed in nuclear magnetic resonance spectroscopy. To realize this effect, the flux bias of the transmon is modulated by a controllable pseudo-random telegraph noise, which results in stochastic jumping of the energy separation (frequency) between two discrete values. This can also be seen as a simulated fast-fluctuation environment under direct experimental control. Additionally, we discuss the population dynamics using an analytical master equation, and apply the motional averaging analysis on phenomena where the fluctuation of the energy is due to quasiparticles or to photon shot noise.   

Driven Dynamics and Rotary Echo of a Qubit Tunably Coupled to a Harmonic Oscillator

We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.   

Effect of environmental coupling on tunneling of quasiparticles in Josephson junctions

We study quasiparticle tunneling in Josephson tunnel junctions embedded in an electromagnetic environment. We identify tunneling processes that transfer electrical charge and couple to the environment in a way similar to that of normal electrons, and processes that mix electrons and holes and are thus creating charge superpositions. The latter are sensitive for the phase difference between the superconductor and are thus limited by phase diffusion even at zero temperature. We show that that term is suppressed in many environments, thus leading to lower quasiparticle decay rates and thus better qubit coherence than previously expected.   

Real-time measurement of quasiparticle tunneling in a single-junction transmon qubit using feedback

With coherence times of superconducting qubits now exceeding $100~\mathrm{\mu s}$, the contribution of quasiparticle (QP) tunneling to qubit relaxation and dephasing becomes potentially relevant. We report the real-time measurement of QP tunneling across the single junction of a 3D transmon qubit. We integrate recent developments in projective qubit readout with $99\%$ fidelity and feedback-based reset to transform the qubit into a charge-parity detector with $6~\mathrm{\mu s}$ resolution. We detect a symmetric random telegraph signal matching a QP tunneling time of $0.8~\mathrm{ms}$. By measuring the correlation function of charge parity conditioned on specific initial and final qubit states, we determine that most QP tunneling does not induce qubit transitions, in contradiction with recent theory [1]. We extract a QP-induced qubit relaxation time $T_1^{\mathrm{qp}} \sim 3~\mathrm{ms}$, decidedly not limiting the measured $T_1 = 0.14~\mathrm{ms}$.\\[4pt] [1] G. Catelani et al., Phys. Rev. B 84, 064517 (2011).   

Interfacing Superconducting Qubits and Resonator Qudit

We consider methods to transfer multi-qubit states into the higher-dimensional state space of a superconducting resonator, acting as a qudit. Several methods are proposed, using different combinations of resonant, dispersive, and auxiliary interactions. The complexity of such schemes are explored using analytical and numerically optimized control sequences. Extension to resonator measurement and qudit logic will be also be described.   

Frequency multiplexed dispersive readout of transmon qubits with the UCSB paramp

Our new Xmon qubit shows good coherence, controllability and simplified coupling to other circuit elements, making it a good candidate for a large scale quantum computer. Like all qubits, it requires high fidelity readout. To this end we have developed a new parametric amplifier circuit. Simplified input coupling of the amplifier allows straightforward interfacing with our frequency multiplexed dispersive readout circuitry. The amplifier features five different modes of pump power delivery, some of which allow us to reduce the microwave component count in our readout chain. We characterize our readout system using each of these modes of operation, as well as multi qubit readout.   

Engineering and control of coupled superconducting qubits arrays for quantum simulation

Superconducting qubit technology allows for engineering experimentally accessible, macroscopic quantum systems to arbitrary specifications within a large parameter space. By coupling multiple superconducting qubits in a periodic array, it is possible to fabricate physical objects which mimic the properties of naturally occurring systems not readily accessible to measurement or parameter variation, or theoretical systems not occurring in nature. We discuss design, fabrication, and measurement of a physical realization of the quantum Ising model in zero and one dimension. This is accomplished using a chain of identical transmon qubits acting as artificial spins whose interaction is dominated by nearest neighbor coupling. Control and readout of the system is accomplished by coupling only one of the artificial spins to a microwave resonator in a circuit QED architecture.