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.

Diabatic gates for frequency-tunable superconducting qubits

  1. R. Barends,
  2. C. M. Quintana,
  3. A. G. Petukhov,
  4. Yu Chen,
  5. D. Kafri,
  6. K. Kechedzhi,
  7. R. Collins,
  8. O. Naaman,
  9. S. Boixo,
  10. F. Arute,
  11. K. Arya,
  12. D. Buell,
  13. B. Burkett,
  14. Z. Chen,
  15. B. Chiaro,
  16. A. Dunsworth,
  17. B. Foxen,
  18. A. Fowler,
  19. C. Gidney,
  20. M. Giustina,
  21. R. Graff,
  22. T. Huang,
  23. E. Jeffrey,
  24. J. Kelly,
  25. P. V. Klimov,
  26. F. Kostritsa,
  27. D. Landhuis,
  28. E. Lucero,
  29. M. McEwen,
  30. A. Megrant,
  31. X. Mi,
  32. J. Mutus,
  33. M. Neeley,
  34. C. Neill,
  35. E. Ostby,
  36. P. Roushan,
  37. D. Sank,
  38. K. J. Satzinger,
  39. A. Vainsencher,
  40. T. White,
  41. J. Yao,
  42. P. Yeh,
  43. A. Zalcman,
  44. H. Neven,
  45. V. N. Smelyanskiy,
  46. and John M. Martinis
We demonstrate diabatic two-qubit gates with Pauli error rates down to 4.3(2)⋅10−3 in as fast as 18 ns using frequency-tunable superconducting qubits. This is achieved by synchronizing
the entangling parameters with minima in the leakage channel. The synchronization shows a landscape in gate parameter space that agrees with model predictions and facilitates robust tune-up. We test both iSWAP-like and CPHASE gates with cross-entropy benchmarking. The presented approach can be extended to multibody operations as well.

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.

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.

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.

Scalable Quantum Simulation of Molecular Energies

  1. P. J. J. O'Malley,
  2. R. Babbush,
  3. I. D. Kivlichan,
  4. J. Romero,
  5. J. R. McClean,
  6. R. Barends,
  7. J. Kelly,
  8. P. Roushan,
  9. A. Tranter,
  10. N. Ding,
  11. B. Campbell,
  12. Y. Chen,
  13. Z. Chen,
  14. B. Chiaro,
  15. A. Dunsworth,
  16. A. G. Fowler,
  17. E. Jeffrey,
  18. A. Megrant,
  19. J. Y. Mutus,
  20. C. Neill,
  21. C. Quintana,
  22. D. Sank,
  23. A. Vainsencher,
  24. J. Wenner,
  25. T. C. White,
  26. P. V. Coveney,
  27. P. J. Love,
  28. H. Neven,
  29. A. Aspuru-Guzik,
  30. and J.M. Martinis
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits
to compute the energy surface of molecular hydrogen using two distinct quantum algorithms. First, we experimentally execute the unitary coupled cluster method using the variational quantum eigensolver. Our efficient implementation predicts the correct dissociation energy to within chemical accuracy of the numerically exact result. Next, we experimentally demonstrate the canonical quantum algorithm for chemistry, which consists of Trotterization and quantum phase estimation. We compare the experimental performance of these approaches to show clear evidence that the variational quantum eigensolver is robust to certain errors, inspiring hope that quantum simulation of classically intractable molecules may be viable in the near future.

Digitized adiabatic quantum computing with a superconducting circuit

  1. R. Barends,
  2. A. Shabani,
  3. L. Lamata,
  4. J. Kelly,
  5. A. Mezzacapo,
  6. U. Las Heras,
  7. R. Babbush,
  8. A. G. Fowler,
  9. B. Campbell,
  10. Yu Chen,
  11. Z. Chen,
  12. B. Chiaro,
  13. A. Dunsworth,
  14. E. Jeffrey,
  15. E. Lucero,
  16. A. Megrant,
  17. J. Y. Mutus,
  18. M. Neeley,
  19. C. Neill,
  20. P. J. J. O'Malley,
  21. C. Quintana,
  22. P. Roushan,
  23. D. Sank,
  24. A. Vainsencher,
  25. J. Wenner,
  26. T. C. White,
  27. E. Solano,
  28. H. Neven,
  29. and John M. Martinis
A major challenge in quantum computing is to solve general problems with limited physical hardware. Here, we implement digitized adiabatic quantum computing, combining the generality
of the adiabatic algorithm with the universality of the digital approach, using a superconducting circuit with nine qubits. We probe the adiabatic evolutions, and quantify the success of the algorithm for random spin problems. We find that the system can approximate the solutions to both frustrated Ising problems and problems with more complex interactions, with a performance that is comparable. The presented approach is compatible with small-scale systems as well as future error-corrected quantum computers.