Noise and loss of superconducting aluminium resonators at single photon energies

  1. Jonathan Burnett,
  2. Andreas Bengtsson,
  3. David Niepce,
  4. and Jonas Bylander
The loss and noise mechanisms of superconducting resonators are useful tools for understanding decoherence in superconducting circuits. While the loss mechanisms have been heavily studied,
noise in superconducting resonators has only recently been investigated. In particular, there is an absence of literature on noise in the single photon limit. Here, we measure the loss and noise of an aluminium on silicon quarter-wavelength (λ/4) resonator in the single photon regime.

Nondegenerate parametric oscillations in a tunable superconducting resonator

  1. Andreas Bengtsson,
  2. Philip Krantz,
  3. Michaël Simoen,
  4. Ida-Maria Svensson,
  5. Ben Schneider,
  6. Vitaly Shumeiko,
  7. Per Delsing,
  8. and Jonas Bylander
We investigate nondegenerate parametric oscillations in a multimode superconducting microwave resonator that is terminated by a SQUID. The parametric effect is achieved by modulating
magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonance tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.

Subharmonic oscillations in a driven superconducting resonator

  1. Ida-Maria Svensson,
  2. Andreas Bengtsson,
  3. Philip Krantz,
  4. Jonas Bylander,
  5. Vitaly Shumeiko,
  6. and Per Delsing
We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, kBT≪ℏω. The resonator is terminated
by a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, ω/2π∼5GHz, when the resonator was driven by a current at 3ω with an amplitude exceeding an instability threshold. The output radiation was red-detuned from the fundamental mode. We observed three stable radiative states with equal amplitudes and phase-shifted by 120∘. The downconversion from 3ω to ω is strongly enhanced by resonant excitation of the second mode of the resonator, and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.

Suppressing relaxation in superconducting qubits by quasiparticle pumping

  1. Simon Gustavsson,
  2. Fei Yan,
  3. Gianluigi Catelani,
  4. Jonas Bylander,
  5. Archana Kamal,
  6. Jeffrey Birenbaum,
  7. David Hover,
  8. Danna Rosenberg,
  9. Gabriel Samach,
  10. Adam P. Sears,
  11. Steven J. Weber,
  12. Jonilyn L. Yoder,
  13. John Clarke,
  14. Andrew J. Kerman,
  15. Fumiki Yoshihara,
  16. Yasunobu Nakamura,
  17. Terry P. Orlando,
  18. and William D. Oliver
Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneous
coherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation. In this work, we investigate a complementary, stochastic approach to reducing errors: instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement a pumping sequence to reduce the number of unpaired electrons (quasiparticles) in close proximity to the device. We report a 70% reduction in the quasiparticle density, resulting in a threefold enhancement in qubit relaxation times, and a comparable reduction in coherence variability.

Single-shot Readout of a Superconducting Qubit using a Josephson Parametric Oscillator

  1. Philip Krantz,
  2. Andreas Bengtsson,
  3. Michaël Simoen,
  4. Simon Gustavsson,
  5. Vitaly Shumeiko,
  6. W. D. Oliver,
  7. C. M. Wilson,
  8. Per Delsing,
  9. and Jonas Bylander
We present a new read-out technique for a superconducting qubit dispersively coupled to a Josephson parametric oscillator. We perform degenerate parametric flux pumping of the Josephson
inductance with a pump amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillations: one oscillating state, with on average 180 photons in the resonator, and one with zero oscillation amplitude. We demonstrate single-shot readout performance, with a total state discrimination of 81.5%. When accounting for qubit errors, this gives a corrected fidelity of 98.7%, obviating the need for a following quantum-limited amplifier. An error budget indicates that the readout fidelity is currently limited by spurious switching events between two bistable states of the resonator.

Flux qubit noise spectroscopy using Rabi oscillations under strong driving conditions

  1. Fumiki Yoshihara,
  2. Yasunobu Nakamura,
  3. Fei Yan,
  4. Simon Gustavsson,
  5. Jonas Bylander,
  6. William D. Oliver,
  7. and Jaw-Shen Tsai
We infer the high-frequency flux noise spectrum in a superconducting flux qubit by studying the decay of Rabi oscillations under strong driving conditions. The large anharmonicity of
the qubit and its strong inductive coupling to a microwave line enabled high-amplitude driving without causing significant additional decoherence. Rabi frequencies up to 1.7 GHz were achieved, approaching the qubit’s level splitting of 4.8 GHz, a regime where the rotating-wave approximation breaks down as a model for the driven dynamics. The spectral density of flux noise observed in the wide frequency range decreases with increasing frequency up to 300 MHz, where the spectral density is not very far from the extrapolation of the 1/f spectrum obtained from the free-induction-decay measurements. We discuss a possible origin of the flux noise due to surface electron spins.

Investigation of nonlinear effects in Josephson parametric oscillators used in circuit QED

  1. Philip Krantz,
  2. Yarema Reshitnyk,
  3. Waltraut Wustmann,
  4. Jonas Bylander,
  5. Simon Gustavsson,
  6. William D. Oliver,
  7. Timothy Duty,
  8. Vitaly Shumeiko,
  9. and Per Delsing
We experimentally study the behavior of a parametrically pumped nonlinear oscillator, which is based on a superconducting lambda /4 resonator, and is terminated by a flux-tunable SQUID.
We extract parameters for two devices. In particular, we study the effect of the nonlinearities in the system and compare to theory. The Duffing nonlinearity, \alpha, is determined from the probe-power dependent frequency shift of the oscillator, and the nonlinearity, \beta, related to the parametric flux pumping, is determined from the pump amplitude for the onset of parametric oscillations. Both nonlinearities depend on the parameters of the device and can be tuned in-situ by the applied dc flux. We also suggest how to cancel the effect of \beta by adding a small dc flux and a pump tone at twice the pump frequency.

Improving quantum gate fidelities by using a qubit to measure microwave pulse distortions

  1. Simon Gustavsson,
  2. Olger Zwier,
  3. Jonas Bylander,
  4. Fei Yan,
  5. Fumiki Yoshihara,
  6. Yasunobu Nakamura,
  7. Terry P. Orlando,
  8. and William D. Oliver
We present a new method for determining pulse imperfections and improving the single-gate fidelity in a superconducting qubit. By applying consecutive positive and negative $pi$ pulses,
we amplify the qubit evolution due to microwave pulse distortion, which causes the qubit state to rotate around an axis perpendicular to the intended rotation axis. Measuring these rotations as a function of pulse period allows us to reconstruct the shape of the microwave pulse arriving at the sample. Using the extracted response to predistort the input signal, we are able to improve the pulse shapes and to reach an average single-qubit gate fidelity higher than 99.8%.

Time-Reversal Symmetry and Universal Conductance Fluctuations in a Driven Two-Level System

  1. Simon Gustavsson,
  2. Jonas Bylander,
  3. and William D. Oliver
In the presence of time-reversal symmetry, quantum interference gives strong corrections to the electric conductivity of disordered systems. The self-interference of an electron wavefunction
traveling time-reversed paths leads to effects such as weak localization and universal conductance fluctuations. Here, we investigate the effects of broken time-reversal symmetry in a driven artificial two-level system. Using a superconducting flux qubit, we implement scattering events as multiple Landau-Zener transitions by driving the qubit periodically back and forth through an avoided crossing. Interference between different qubit trajectories give rise to a speckle pattern in the qubit transition rate, similar to the interference patterns created when coherent light is scattered off a disordered potential. Since the scattering events are imposed by the driving protocol, we can control the time-reversal symmetry of the system by making the drive waveform symmetric or asymmetric in time. We find that the fluctuations of the transition rate exhibit a sharp peak when the drive is time-symmetric, similar to universal conductance fluctuations in electronic transport through mesoscopic systems.

Dynamical decoupling and dephasing in interacting two-level systems

  1. Simon Gustavsson,
  2. Fei Yan,
  3. Jonas Bylander,
  4. Fumiki Yoshihara,
  5. Yasunobu Nakamura,
  6. Terry P. Orlando,
  7. and William D. Oliver
We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic
two-level system. By rapidly changing the qubit’s transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our $1/f$ noise model. The results are applicable to any two-qubit system with transverse coupling, and they highlight the potential of decoupling techniques for improving two-qubit gate fidelities, an essential prerequisite for implementing fault-tolerant quantum computing.