Fluctuations of Energy-Relaxation Times in Superconducting Qubits

  1. P. V. Klimov,
  2. J. Kelly,
  3. Z. Chen,
  4. M. Neeley,
  5. A. Megrant,
  6. B. Burkett,
  7. R. Barends,
  8. K. Arya,
  9. B. Chiaro,
  10. Yu Chen,
  11. A. Dunsworth,
  12. A. Fowler,
  13. B. Foxen,
  14. C. Gidney,
  15. M. Giustina,
  16. R. Graff,
  17. T. Huang,
  18. E. Jeffrey,
  19. Erik Lucero,
  20. J. Y. Mutus,
  21. O. Naaman,
  22. C. Neill,
  23. C. Quintana,
  24. P. Roushan,
  25. Daniel Sank,
  26. A. Vainsencher,
  27. J. Wenner,
  28. T. C. White,
  29. S. Boixo,
  30. R. Babbush,
  31. V. N. Smelyanskiy,
  32. H. Neven,
  33. and John M. Martinis
Superconducting qubits are an attractive platform for quantum computing since they have demonstrated high-fidelity quantum gates and extensibility to modest system sizes. Nonetheless,
an outstanding challenge is stabilizing their energy-relaxation times, which can fluctuate unpredictably in frequency and time. Here, we use qubits as spectral and temporal probes of individual two-level-system defects to provide direct evidence that they are responsible for the largest fluctuations. This research lays the foundation for stabilizing qubit performance through calibration, design, and fabrication.

High speed flux sampling for tunable superconducting qubits with an embedded cryogenic transducer

  1. B. Foxen,
  2. J. Y. Mutus,
  3. E. Lucero,
  4. E. Jeffrey,
  5. D. Sank,
  6. R. Barends,
  7. K. Arya,
  8. B. Burkett,
  9. Yu Chen,
  10. Zijun Chen,
  11. B. Chiaro,
  12. A. Dunsworth,
  13. A. Fowler,
  14. C. Gidney,
  15. M. Giustina,
  16. R. Graff,
  17. T. Huang,
  18. J. Kelly,
  19. P. Klimov,
  20. A. Megrant,
  21. O. Naaman,
  22. M. Neeley,
  23. C. Neill,
  24. C. Quintana,
  25. P. Roushan,
  26. A. Vainsencher,
  27. J. Wenner,
  28. T. C. White,
  29. and John M. Martinis
We develop a high speed on-chip flux measurement using a capacitively shunted SQUID as an embedded cryogenic transducer and apply this technique to the qualification of a near-term
scalable printed circuit board (PCB) package for frequency tunable superconducting qubits. The transducer is a flux tunable LC resonator where applied flux changes the resonant frequency. We apply a microwave tone to probe this frequency and use a time-domain homodyne measurement to extract the reflected phase as a function of flux applied to the SQUID. The transducer response bandwidth is 2.6 GHz with a maximum gain of 1200∘/Φ0 allowing us to study the settling amplitude to better than 0.1%. We use this technique to characterize on-chip bias line routing and a variety of PCB based packages and demonstrate that step response settling can vary by orders of magnitude in both settling time and amplitude depending on if normal or superconducting materials are used. By plating copper PCBs in aluminum we measure a step response consistent with the packaging used for existing high-fidelity qubits.

Low Loss Multi-Layer Wiring for Superconducting Microwave Devices

  1. A. Dunsworth,
  2. A. Megrant,
  3. R. Barends,
  4. Yu Chen,
  5. Zijun Chen,
  6. B. Chiaro,
  7. A. Fowler,
  8. B. Foxen,
  9. E. Jeffrey,
  10. J. Kelly,
  11. P. V. Klimov,
  12. E. Lucero,
  13. J. Y. Mutus,
  14. M. Neeley,
  15. C. Neill,
  16. C. Quintana,
  17. P. Roushan,
  18. D. Sank,
  19. A. Vainsencher,
  20. J. Wenner,
  21. T. C. White,
  22. H. Neven,
  23. and John M. Martinis
Complex integrated circuits require multiple wiring layers. In complementary metal-oxide-semiconductor (CMOS) processing, these layers are robustly separated by amorphous dielectrics.
These dielectrics would dominate energy loss in superconducting integrated circuits. Here we demonstrate a procedure that capitalizes on the structural benefits of inter-layer dielectrics during fabrication and mitigates the added loss. We separate and support multiple wiring layers throughout fabrication using SiO2 scaffolding, then remove it post-fabrication. This technique is compatible with foundry level processing and the can be generalized to make many different forms of low-loss multi-layer wiring. We use this technique to create freestanding aluminum vacuum gap crossovers (airbridges). We characterize the added capacitive loss of these airbridges by connecting ground planes over microwave frequency λ/4 coplanar waveguide resonators and measuring resonator loss. We measure a low power resonator loss of ∼3.9×10−8 per bridge, which is 100 times lower than dielectric supported bridges. We further characterize these airbridges as crossovers, control line jumpers, and as part of a coupling network in gmon and fuxmon qubits. We measure qubit characteristic lifetimes (T1’s) in excess of 30 μs in gmon devices.

Spectral signatures of many-body localization with interacting photons

  1. P. Roushan,
  2. C. Neill,
  3. J. Tangpanitanon,
  4. V.M. Bastidas,
  5. A. Megrant,
  6. R. Barends,
  7. Y. Chen,
  8. Z. Chen,
  9. B. Chiaro,
  10. A. Dunsworth,
  11. A. Fowler,
  12. B. Foxen,
  13. M. Giustina,
  14. E. Jeffrey,
  15. J. Kelly,
  16. E. Lucero,
  17. J. Mutus,
  18. M. Neeley,
  19. C. Quintana,
  20. D. Sank,
  21. A. Vainsencher,
  22. J. Wenner,
  23. T. White,
  24. H. Neven,
  25. D. G. Angelakis,
  26. and J. Martinis
Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization,
but, can interacting systems always equilibrate regardless of parameter values\,? The energy spectrum of a system can answer this question and reveal the nature of the underlying phases. However, most experimental techniques only indirectly probe the many-body energy spectrum. Using a chain of nine superconducting qubits, we implement a novel technique for directly resolving the energy levels of interacting photons. We benchmark this method by capturing the intricate energy spectrum predicted for 2D electrons in a magnetic field, the Hofstadter butterfly. By increasing disorder, the spatial extent of energy eigenstates at the edge of the energy band shrink, suggesting the formation of a mobility edge. At strong disorder, the energy levels cease to repel one another and their statistics approaches a Poisson distribution – the hallmark of transition from the thermalized to the many-body localized phase. Our work introduces a new many-body spectroscopy technique to study quantum phases of matter.

A blueprint for demonstrating quantum supremacy with superconducting qubits

  1. C. Neill,
  2. P. Roushan,
  3. K. Kechedzhi,
  4. S. Boixo,
  5. S. V. Isakov,
  6. V. Smelyanskiy,
  7. R. Barends,
  8. B. Burkett,
  9. Y. Chen,
  10. Z. Chen,
  11. B. Chiaro,
  12. A. Dunsworth,
  13. A. Fowler,
  14. B. Foxen,
  15. R. Graff,
  16. E. Jeffrey,
  17. J. Kelly,
  18. E. Lucero,
  19. A. Megrant,
  20. J. Mutus,
  21. M. Neeley,
  22. C. Quintana,
  23. D. Sank,
  24. A. Vainsencher,
  25. J. Wenner,
  26. T. C. White,
  27. H. Neven,
  28. and J.M. Martinis
Fundamental questions in chemistry and physics may never be answered due to the exponential complexity of the underlying quantum phenomena. A desire to overcome this challenge has sparked
a new industry of quantum technologies with the promise that engineered quantum systems can address these hard problems. A key step towards demonstrating such a system will be performing a computation beyond the capabilities of any classical computer, achieving so-called quantum supremacy. Here, using 9 superconducting qubits, we demonstrate an immediate path towards quantum supremacy. By individually tuning the qubit parameters, we are able to generate thousands of unique Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert-space. As the number of qubits in the algorithm is varied, the system continues to explore the exponentially growing number of states. Combining these large datasets with techniques from machine learning allows us to construct a model which accurately predicts the measured probabilities. We demonstrate an application of these algorithms by systematically increasing the disorder and observing a transition from delocalized states to localized states. By extending these results to a system of 50 qubits, we hope to address scientific questions that are beyond the capabilities of any classical computer.

Qubit compatible superconducting interconnects

  1. B. Foxen,
  2. J. Y. Mutus,
  3. E. Lucero,
  4. R. Graff,
  5. A. Megrant,
  6. Yu Chen,
  7. C. Quintana,
  8. B. Burkett,
  9. J. Kelly,
  10. E. Jeffrey,
  11. Yan Yang,
  12. Anthony Yu,
  13. K. Arya,
  14. R. Barends,
  15. Zijun Chen,
  16. B. Chiaro,
  17. A. Dunsworth,
  18. A. Fowler,
  19. C. Gidney,
  20. M. Giustina,
  21. T. Huang,
  22. P. Klimov,
  23. M. Neeley,
  24. C. Neill,
  25. P. Roushan,
  26. D. Sank,
  27. A. Vainsencher,
  28. J. Wenner,
  29. T. C. White,
  30. and John M. Martinis
We present a fabrication process for fully superconducting interconnects compatible with superconducting qubit technology. These interconnects allow for the 3D integration of quantum
circuits without introducing lossy amorphous dielectrics. They are composed of indium bumps several microns tall separated from an aluminum base layer by titanium nitride which serves as a diffusion barrier. We measure the whole structure to be superconducting (transition temperature of 1.1K), limited by the aluminum. These interconnects have an average critical current of 26.8mA, and mechanical shear and thermal cycle testing indicate that these devices are mechanically robust. Our process provides a method that reliably yields superconducting interconnects suitable for use with superconducting qubits.

Characterization and Reduction of Capacitive Loss Induced by Sub-Micron Josephson Junction Fabrication in Superconducting Qubits

  1. A. Dunsworth,
  2. A. Megrant,
  3. C. Quintana,
  4. Zijun Chen,
  5. R. Barends,
  6. B. Burkett,
  7. B. Foxen,
  8. Yu Chen,
  9. B. Chiaro,
  10. A. Fowler,
  11. R. Graff,
  12. E. Jeffrey,
  13. J. Kelly,
  14. E. Lucero,
  15. J. Y. Mutus,
  16. M. Neeley,
  17. C. Neill,
  18. P. Roushan,
  19. D. Sank,
  20. A. Vainsencher,
  21. J. Wenner,
  22. T. C. White,
  23. and John M. Martinis
Josephson junctions form the essential non-linearity for almost all superconducting qubits. The junction is formed when two superconducting electrodes come within ∼1 nm of each other.
Although the capacitance of these electrodes is a small fraction of the total qubit capacitance, the nearby electric fields are more concentrated in dielectric surfaces and can contribute substantially to the total dissipation. We have developed a technique to experimentally investigate the effect of these electrodes on the quality of superconducting devices. We use λ/4 coplanar waveguide resonators to emulate lumped qubit capacitors. We add a variable number of these electrodes to the capacitive end of these resonators and measure how the additional loss scales with number of electrodes. We then reduce this loss with fabrication techniques that limit the amount of lossy dielectrics. We then apply these techniques to the fabrication of Xmon qubits on a silicon substrate to improve their energy relaxation times by a factor of 5.

Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence

  1. C. M. Quintana,
  2. Yu Chen,
  3. D. Sank,
  4. A. G. Petukhov,
  5. T. C. White,
  6. Dvir Kafri,
  7. B. Chiaro,
  8. A. Megrant,
  9. R. Barends,
  10. B. Campbell,
  11. Z. Chen,
  12. A. Dunsworth,
  13. A. G. Fowler,
  14. R. Graff,
  15. E. Jeffrey,
  16. J. Kelly,
  17. E. Lucero,
  18. J. Y. Mutus,
  19. M. Neeley,
  20. C. Neill,
  21. P. J. J. O'Malley,
  22. P. Roushan,
  23. A. Shabani,
  24. A. Vainsencher,
  25. J. Wenner,
  26. H. Neven,
  27. and John M. Martinis
By analyzing the dissipative dynamics of a tunable gap flux qubit, we extract both sides of its two-sided environmental flux noise spectral density over a range of frequencies around
2kBT/h≈1GHz, allowing for the observation of a classical-quantum crossover. Below the crossover point, the symmetric noise component follows a 1/f power law that matches the magnitude of the 1/f noise near 1Hz. The antisymmetric component displays a 1/T dependence below 100mK, providing dynamical evidence for a paramagnetic environment. Extrapolating the two-sided spectrum predicts the linewidth and reorganization energy of incoherent resonant tunneling between flux qubit wells.

Dielectric surface loss in superconducting resonators with flux-trapping holes

  1. B. Chiaro,
  2. A. Megrant,
  3. A. Dunsworth,
  4. Z. Chen,
  5. R. Barends,
  6. B. Campbell,
  7. Y. Chen,
  8. A. Fowler,
  9. I.-C. Hoi,
  10. E. Jeffrey,
  11. J. Kelly,
  12. J. Mutus,
  13. C. Neill,
  14. P. J. J. O'Malley,
  15. C. Quintana,
  16. P. Roushan,
  17. D. Sank,
  18. A. Vainsencher,
  19. J. Wenner,
  20. T. C. White,
  21. and John M. Martinis
Surface distributions of two level system (TLS) defects and magnetic vortices are limiting dissipation sources in superconducting quantum circuits. Arrays of flux-trapping holes arecommonly used to eliminate loss due to magnetic vortices, but may increase dielectric TLS loss. We find that dielectric TLS loss increases by approximately 25% for resonators with a hole array beginning 2 μm from the resonator edge, while the dielectric loss added by holes further away was below measurement sensitivity. Other forms of loss were not affected by the holes. Additionally, we bound the loss tangent due to residual magnetic effects to <9×10−11/mG for resonators patterned with flux-traps and operated in magnetic fields up to 50mG.[/expand]

Measurement-induced state transitions in a superconducting qubit: Beyond the rotating wave approximation

  1. Daniel Sank,
  2. Zijun Chen,
  3. Mostafa Khezri,
  4. J. Kelly,
  5. R. Barends,
  6. Y. Chen,
  7. A. Fowler,
  8. E. Jeffrey,
  9. E. Lucero,
  10. A. Megrant,
  11. J. Mutus,
  12. M. Neeley,
  13. P. Roushan,
  14. A. Vainsencher,
  15. T. White,
  16. B. Campbell,
  17. B. Chiaro,
  18. A. Dunsworth,
  19. C. Neill,
  20. P. J. J. O'Malley,
  21. C. Quintana,
  22. J. Wenner,
  23. Alexander N. Korotkov,
  24. and John M. Martinis
Many superconducting qubit systems use the dispersive interaction between the qubit and a coupled harmonic resonator to perform quantum state measurement. Previous works have found
that such measurements can induce state transitions in the qubit if the number of photons in the resonator is too high. We investigate these transitions and find that they can push the qubit out of the two-level subspace. Furthermore, these transitions show resonant behavior as a function of photon number. We develop a theory for these observations based on level crossings within the Jaynes-Cummings ladder, with transitions mediated by terms in the Hamiltonian which are typically ignored by the rotating wave approximation. We confirm the theory by measuring the photon occupation of the resonator when transitions occur while varying the detuning between the qubit and resonator.