Readout of a quantum processor with high dynamic range Josephson parametric amplifiers

  1. T. C. White,
  2. Alex Opremcak,
  3. George Sterling,
  4. Alexander Korotkov,
  5. Daniel Sank,
  6. Rajeev Acharya,
  7. Markus Ansmann,
  8. Frank Arute,
  9. Kunal Arya,
  10. Joseph C Bardin,
  11. Andreas Bengtsson,
  12. Alexandre Bourassa,
  13. Jenna Bovaird,
  14. Leon Brill,
  15. Bob B. Buckley,
  16. David A. Buell,
  17. Tim Burger,
  18. Brian Burkett,
  19. Nicholas Bushnell,
  20. Zijun Chen,
  21. Ben Chiaro,
  22. Josh Cogan,
  23. Roberto Collins,
  24. Alexander L. Crook,
  25. Ben Curtin,
  26. Sean Demura,
  27. Andrew Dunsworth,
  28. Catherine Erickson,
  29. Reza Fatemi,
  30. Leslie Flores-Burgos,
  31. Ebrahim Forati,
  32. Brooks Foxen,
  33. William Giang,
  34. Marissa Giustina,
  35. Alejandro Grajales Dau,
  36. Michael C. Hamilton,
  37. Sean D. Harrington,
  38. Jeremy Hilton,
  39. Markus Hoffmann,
  40. Sabrina Hong,
  41. Trent Huang,
  42. Ashley Huff,
  43. Justin Iveland,
  44. Evan Jeffrey,
  45. Mária Kieferová,
  46. Seon Kim,
  47. Paul V. Klimov,
  48. Fedor Kostritsa,
  49. John Mark Kreikebaum,
  50. David Landhuis,
  51. Pavel Laptev,
  52. Lily Laws,
  53. Kenny Lee,
  54. Brian J. Lester,
  55. Alexander Lill,
  56. Wayne Liu,
  57. Aditya Locharla,
  58. Erik Lucero,
  59. Trevor McCourt,
  60. Matt McEwen,
  61. Xiao Mi,
  62. Kevin C. Miao,
  63. Shirin Montazeri,
  64. Alexis Morvan,
  65. Matthew Neeley,
  66. Charles Neill,
  67. Ani Nersisyan,
  68. Jiun How Ng,
  69. Anthony Nguyen,
  70. Murray Nguyen,
  71. Rebecca Potter,
  72. Chris Quintana,
  73. Pedram Roushan,
  74. Kannan Sankaragomathi,
  75. Kevin J. Satzinger,
  76. Christopher Schuster,
  77. Michael J. Shearn,
  78. Aaron Shorter,
  79. Vladimir Shvarts,
  80. Jindra Skruzny,
  81. W. Clarke Smith,
  82. Marco Szalay,
  83. Alfredo Torres,
  84. Bryan Woo,
  85. Z. Jamie Yao,
  86. Ping Yeh,
  87. Juhwan Yoo,
  88. Grayson Young,
  89. Ningfeng Zhu,
  90. Nicholas Zobrist,
  91. Yu Chen,
  92. Anthony Megrant,
  93. Julian Kelly,
  94. and Ofer Naaman
We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in which the active nonlinear element is implemented using an array of rf-SQUIDs. The device is matched to the
50 Ω environment with a Klopfenstein-taper impedance transformer and achieves a bandwidth of 250-300 MHz, with input saturation powers up to -95 dBm at 20 dB gain. A 54-qubit Sycamore processor was used to benchmark these devices, providing a calibration for readout power, an estimate of amplifier added noise, and a platform for comparison against standard impedance matched parametric amplifiers with a single dc-SQUID. We find that the high power rf-SQUID array design has no adverse effect on system noise, readout fidelity, or qubit dephasing, and we estimate an upper bound on amplifier added noise at 1.6 times the quantum limit. Lastly, amplifiers with this design show no degradation in readout fidelity due to gain compression, which can occur in multi-tone multiplexed readout with traditional JPAs.

Removing leakage-induced correlated errors in superconducting quantum error correction

  1. M. McEwen,
  2. D. Kafri,
  3. Z. Chen,
  4. J. Atalaya,
  5. K. J. Satzinger,
  6. C. Quintana,
  7. P. V. Klimov,
  8. D. Sank,
  9. C. Gidney,
  10. A. G. Fowler,
  11. F. Arute,
  12. K. Arya,
  13. B. Buckley,
  14. B. Burkett,
  15. N. Bushnell,
  16. B. Chiaro,
  17. R. Collins,
  18. S.Demura,
  19. A. Dunsworth,
  20. C. Erickson,
  21. B. Foxen,
  22. M. Giustina,
  23. T. Huang,
  24. S. Hong,
  25. E. Jeffrey,
  26. S. Kim,
  27. K. Kechedzhi,
  28. F. Kostritsa,
  29. P. Laptev,
  30. A. Megrant,
  31. X. Mi,
  32. J. Mutus,
  33. O. Naaman,
  34. M. Neeley,
  35. C. Neill,
  36. M.Niu,
  37. A. Paler,
  38. N. Redd,
  39. P. Roushan,
  40. T. C. White,
  41. J. Yao,
  42. P. Yeh,
  43. A. Zalcman,
  44. Yu Chen,
  45. V. N. Smelyanskiy,
  46. John M. Martinis,
  47. H. Neven,
  48. J. Kelly,
  49. A. N. Korotkov,
  50. A. G. Petukhov,
  51. and R. Barends
Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation,
unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing.

High-Fidelity Measurement of a Superconducting Qubit using an On-Chip Microwave Photon Counter

  1. A. Opremcak,
  2. C. H. Liu,
  3. C. Wilen,
  4. K. Okubo,
  5. B. G. Christensen,
  6. D. Sank,
  7. T. C. White,
  8. A. Vainsencher,
  9. M. Giustina,
  10. A. Megrant,
  11. B. Burkett,
  12. B. L. T. Plourde,
  13. and R. McDermott
We describe an approach to the high-fidelity measurement of a superconducting qubit using an on-chip microwave photon counter. The protocol relies on the transient response of a dispersively
coupled measurement resonator to map the state of the qubit to „bright“ and „dark“ cavity pointer states that are characterized by a large differential photon occupation. Following this mapping, we photodetect the resonator using the Josephson Photomultipler (JPM), which transitions between classically distinguishable flux states when cavity photon occupation exceeds a certain threshold. Our technique provides access to the binary outcome of projective quantum measurement at the millikelvin stage without the need for quantum-limited preamplification and thresholding at room temperature. We achieve raw single-shot measurement fidelity in excess of 98% across multiple samples using this approach in total measurement times under 500 ns. In addition, we show that the backaction and crosstalk associated with our measurement protocol can be mitigated by exploiting the intrinsic damping of the JPM itself.

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.

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.