Energy-participation quantization of Josephson circuits

  1. Zlatko K. Minev,
  2. Zaki Leghtas,
  3. Shantanu O. Mundhada,
  4. Lysander Christakis,
  5. Ioan M. Pop,
  6. and Michel H. Devoret
Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are one of the leading platforms for emerging quantum technologies. Increasing circuit
complexity further requires efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here, we present a method based on the energy-participation ratio (EPR) of a dissipative or nonlinear element in an electromagnetic mode. The EPR, a number between zero and one, quantifies how much of the energy of a mode is stored in each element. It obeys universal constraints—valid regardless of the circuit topology and nature of the nonlinear elements. The EPR of the elements are calculated from a unique, efficient electromagnetic eigenmode simulation of the linearized circuit, including lossy elements. Their set is the key input to the determination of the quantum Hamiltonian of the system. The method provides an intuitive and simple-to-use tool to quantize multi-junction circuits. It is especially well-suited for finding the Hamiltonian and dissipative parameters of weakly anharmonic systems, such as transmon qubits coupled to resonators, or Josephson transmission lines. We experimentally tested this method on a variety of Josephson circuits, and demonstrated agreement within several percents for nonlinear couplings and modal Hamiltonian parameters, spanning five-orders of magnitude in energy, across a dozen samples.

Quantum non-demolition dispersive readout of a superconducting artificial atom using large photon numbers

  1. Daria Gusenkova,
  2. Martin Spiecker,
  3. Richard Gebauer,
  4. Madita Willsch,
  5. Francesco Valenti,
  6. Nick Karcher,
  7. Lukas Grünhaupt,
  8. Ivan Takmakov,
  9. Patrick Winkel,
  10. Dennis Rieger,
  11. Alexey V. Ustinov,
  12. Nicolas Roch,
  13. Wolfgang Wernsdorfer,
  14. Kristel Michielsen,
  15. Oliver Sander,
  16. and Ioan M. Pop
Reading out the state of superconducting artificial atoms typically relies on dispersive coupling to a readout resonator. For a given system noise temperature, increasing the circulating
photon number n¯ in the resonator enables a shorter measurement time and is therefore expected to reduce readout errors caused by spontaneous atom transitions. However, increasing n¯ is generally observed to also increase these transition rates. Here we present a fluxonium artificial atom in which we measure an overall flat dependence of the transition rates between its first two states as a function of n¯, up to n¯≈200. Despite the fact that we observe the expected decrease of the dispersive shift with increasing readout power, the signal-to-noise ratio continuously improves with increasing n¯. Even without the use of a parametric amplifier, at n¯=74, we measure fidelities of 99% and 93% for feedback-assisted ground and excited state preparation, respectively.

Reducing the impact of radioactivity on quantum circuits in a deep-underground facility

  1. Laura Cardani,
  2. Francesco Valenti,
  3. Nicola Casali,
  4. Gianluigi Catelani,
  5. Thibault Charpentier,
  6. Massimiliano Clemenza,
  7. Ivan Colantoni,
  8. Angelo Cruciani,
  9. Luca Gironi,
  10. Lukas Grünhaupt,
  11. Daria Gusenkova,
  12. Fabio Henriques,
  13. Marc Lagoin,
  14. Maria Martinez,
  15. Giorgio Pettinari,
  16. Claudia Rusconi,
  17. Oliver Sander,
  18. Alexey V. Ustinov,
  19. Marc Weber,
  20. Wolfgang Wernsdorfer,
  21. Marco Vignati,
  22. Stefano Pirro,
  23. and Ioan M. Pop
As quantum coherence times of superconducting circuits have increased from nanoseconds to hundreds of microseconds, they are currently one of the leading platforms for quantum information
processing. However, coherence needs to further improve by orders of magnitude to reduce the prohibitive hardware overhead of current error correction schemes. Reaching this goal hinges on reducing the density of broken Cooper pairs, so-called quasiparticles. Here, we show that environmental radioactivity is a significant source of nonequilibrium quasiparticles. Moreover, ionizing radiation introduces time-correlated quasiparticle bursts in resonators on the same chip, further complicating quantum error correction. Operating in a deep-underground lead-shielded cryostat decreases the quasiparticle burst rate by a factor fifty and reduces dissipation up to a factor four, showcasing the importance of radiation abatement in future solid-state quantum hardware.

State preparation of a fluxonium qubit with feedback from a custom FPGA-based platform

  1. Richard Gebauer,
  2. Nick Karcher,
  3. Daria Gusenkova,
  4. Martin Spiecker,
  5. Lukas Grünhaupt,
  6. Ivan Takmakov,
  7. Patrick Winkel,
  8. Luca Planat,
  9. Nicolas Roch,
  10. Wolfgang Wernsdorfer,
  11. Alexey V. Ustinov,
  12. Marc Weber,
  13. Martin Weides,
  14. Ioan M. Pop,
  15. and Oliver Sander
We developed a versatile integrated control and readout instrument for experiments with superconducting quantum bits (qubits), based on a field-programmable gate array (FPGA) platform.
Using this platform, we perform measurement-based, closed-loop feedback operations with 428ns platform latency. The feedback capability is instrumental in realizing active reset initialization of the qubit into the ground state in a time much shorter than its energy relaxation time T1. We show experimental results demonstrating reset of a fluxonium qubit with 99.4% fidelity, using a readout-and-drive pulse sequence approximately 1.5μs long. Compared to passive ground state initialization through thermalization, with the time constant given by T1= 80μs, the use of the FPGA-based platform allows us to improve both the fidelity and the time of the qubit initialization by an order of magnitude.

Implementation of a transmon qubit using superconducting granular aluminum

  1. Patrick Winkel,
  2. Kiril Borisov,
  3. Lukas Grünhaupt,
  4. Dennis Rieger,
  5. Martin Spiecker,
  6. Francesco Valenti,
  7. Alexey V. Ustinov,
  8. Wolfgang Wernsdorfer,
  9. and Ioan M. Pop
The high kinetic inductance offered by granular aluminum (grAl) has recently been employed for linear inductors in superconducting high-impedance qubits and kinetic inductance detectors.
Due to its large critical current density compared to typical Josephson junctions, its resilience to external magnetic fields, and its low dissipation, grAl may also provide a robust source of non-linearity for strongly driven quantum circuits, topological superconductivity, and hybrid systems. Having said that, can the grAl non-linearity be sufficient to build a qubit? Here we show that a small grAl volume (10×200×500nm3) shunted by a thin film aluminum capacitor results in a microwave oscillator with anharmonicity α two orders of magnitude larger than its spectral linewidth Γ01, effectively forming a transmon qubit. With increasing drive power, we observe several multi-photon transitions starting from the ground state, from which we extract α=2π×4.48MHz. Resonance fluorescence measurements of the |0>→|1> transition yield an intrinsic qubit linewidth γ=2π×10kHz, corresponding to a lifetime of 16μs. This linewidth remains below 2π×150kHz for in-plane magnetic fields up to ∼70mT.

Microscopic charging and in-gap states in superconducting granular aluminum

  1. Fang Yang,
  2. Tim Storbeck,
  3. Thomas Gozlinski,
  4. Lukas Grünhaupt,
  5. Ioan M. Pop,
  6. and Wulf Wulfhekel
Following the emergence of superconducting granular aluminum (grAl) as a material for high-impedance quantum circuits, future development hinges on a microscopic understanding of its
phase diagram, and whether the superconductor-to-insulator transition (SIT) is driven by disorder or charging effects. Beyond fundamental relevance, these mechanisms govern noise and dissipation in microwave circuits. Although the enhancement of the critical temperature, and the SIT in granular superconductors have been studied for more than fifty years, experimental studies have so far provided incomplete information on the microscopic phenomena. Here we present scanning tunneling microscope measurements of the local electronic structure of superconducting grAl. We confirm an increased superconducting gap in individual grains both near and above the Mott resistivity ρM≈400 μΩcm. Above ρM we find Coulomb charging effects, a first indication for decoupling, and in-gap states on individual grains, which could contribute to flux noise and dielectric loss in quantum devices. We also observe multiple low-energy states outside the gap, which may indicate bosonic excitations of the superconducting order parameter.

Non-degenerate parametric amplifiers based on dispersion engineered Josephson junction arrays

  1. Patrick Winkel,
  2. Ivan Takmakov,
  3. Dennis Rieger,
  4. Luca Planat,
  5. Wiebke Hasch-Guichard,
  6. Lukas Grünhaupt,
  7. Nataliya Maleeva,
  8. Farshad Foroughi,
  9. Fabio Henriques,
  10. Kiril Borisov,
  11. Julian Ferrero,
  12. Alexey V. Ustinov,
  13. Wolfgang Wernsdorfer,
  14. Nicolas Roch,
  15. and Ioan M. Pop
Determining the state of a qubit on a timescale much shorter than its relaxation time is an essential requirement for quantum information processing. With the aid of a new type of non-degenerate
parametric amplifier, we demonstrate the continuous detection of quantum jumps of a transmon qubit with 90% fidelity in state discrimination. Entirely fabricated with standard two-step optical lithography techniques, this type of parametric amplifier consists of a dispersion engineered Josephson junction (JJ) array. By using long arrays, containing 103 JJs, we can obtain amplification at multiple eigenmodes with frequencies below 10 GHz, which is the typical range for qubit readout. Moreover, by introducing a moderate flux tunability of each mode, employing superconducting quantum interference device (SQUID) junctions, a single amplifier device could potentially cover the entire frequency band between 1 and 10 GHz.

Onset of phase diffusion in high kinetic inductance granular aluminum micro-SQUIDs

  1. Felix Friedrich,
  2. Patrick Winkel,
  3. Kiril Borisov,
  4. Hannes Seeger,
  5. Christoph Sürgers,
  6. Ioan M. Pop,
  7. and Wolfgang Wernsdorfer
Superconducting granular aluminum is attracting increasing interest due to its high kinetic inductance and low dissipation, favoring its use in kinetic inductance particle detectors,
superconducting resonators or quantum bits. We perform switching current measurements on DC-SQUIDs, obtained by introducing two identical geometric constrictions in granular aluminum rings of various normal-state resistivities in the range from ρn=250μΩcm to 5550μΩcm. The relative high kinetic inductance of the SQUID loop, in the range of tens of nH, leads to a suppression of the modulation in the measured switching current versus magnetic flux, accompanied by a distortion towards a triangular shape. We observe a change in the temperature dependence of the switching current histograms with increasing normal-state film resistivity. This behavior suggests the onset of a diffusive motion of the superconducting phase across the constrictions in the two-dimensional washboard potential of the SQUIDs, which could be caused by a change of the local electromagnetic environment of films with increasing normal-state resistivities.

Phonon traps reduce the quasiparticle density in superconducting circuits

  1. Fabio Henriques,
  2. Francesco Valenti,
  3. Thibault Charpentier,
  4. Marc Lagoin,
  5. Clement Gouriou,
  6. Maria Martínez,
  7. Laura Cardani,
  8. Lukas Grünhaupt,
  9. Daria Gusenkova,
  10. Julian Ferrero,
  11. Sebastian T. Skacel,
  12. Wolfgang Wernsdorfer,
  13. Alexey V. Ustinov,
  14. Gianluigi Catelani,
  15. Oliver Sander,
  16. and Ioan M. Pop
Out of equilibrium quasiparticles (QPs) are one of the main sources of decoherence in superconducting quantum circuits, and are particularly detrimental in devices with high kinetic
inductance, such as high impedance resonators, qubits, and detectors. Despite significant progress in the understanding of QP dynamics, pinpointing their origin and decreasing their density remain outstanding tasks. The cyclic process of recombination and generation of QPs implies the exchange of phonons between the superconducting thin film and the underlying substrate. Reducing the number of substrate phonons with frequencies exceeding the spectral gap of the superconductor should result in a reduction of QPs. Indeed, we demonstrate that surrounding high impedance resonators made of granular aluminum (grAl) with lower gapped thin film aluminum islands increases the internal quality factors of the resonators in the single photon regime, suppresses the noise, and reduces the rate of observed QP bursts. The aluminum islands are positioned far enough from the resonators to be electromagnetically decoupled, thus not changing the resonator frequency, nor the loading. We therefore attribute the improvements observed in grAl resonators to phonon trapping at frequencies close to the spectral gap of aluminum, well below the grAl gap.

Granular aluminum: A superconducting material for high impedance quantum circuits

  1. Lukas Grünhaupt,
  2. Martin Spiecker,
  3. Daria Gusenkova,
  4. Nataliya Maleeva,
  5. Sebastian T. Skacel,
  6. Ivan Takmakov,
  7. Francesco Valenti,
  8. Patrick Winkel,
  9. Hannes Rotzinger,
  10. Alexey V. Ustinov,
  11. and Ioan M. Pop
Superconducting quantum information processing machines are predominantly based on microwave circuits with relatively low characteristic impedance, of about 100 Ohm, and small anharmonicity,
which can limit their coherence and logic gate fidelity. A promising alternative are circuits based on so-called superinductors, with characteristic impedances exceeding the resistance quantum RQ=6.4 kΩ. However, previous implementations of superinductors, consisting of mesoscopic Josephson junction arrays, can introduce unintended nonlinearity or parasitic resonant modes in the qubit vicinity, degrading its coherence. Here we present a fluxonium qubit design using a granular aluminum (grAl) superinductor strip. Granular aluminum is a particularly attractive material, as it self-assembles into an effective junction array with a remarkably high kinetic inductance, and its fabrication can be in-situ integrated with standard aluminum circuit processing. The measured qubit coherence time TR2 up to 30 μs illustrates the potential of grAl for applications ranging from protected qubit designs to quantum limited amplifiers and detectors.