Chiral groundstate currents of interacting photons in a synthetic magnetic field

  1. P. Roushan,
  2. C. Neill,
  3. A. Megrant,
  4. Y. Chen,
  5. R. Babbush,
  6. R. Barends,
  7. B. Campbell,
  8. Z. Chen,
  9. B. Chiaro,
  10. A. Dunsworth,
  11. A. Fowler,
  12. E. Jeffrey,
  13. J. Kelly,
  14. E. Lucero,
  15. J. Mutus,
  16. P. J. J. O'Malley,
  17. M. Neeley,
  18. C. Quintana,
  19. D. Sank,
  20. A. Vainsencher,
  21. J. Wenner,
  22. T. White,
  23. E. Kapit,
  24. and J. Martinis
The intriguing many-body phases of quantum matter arise from the interplay of particle interactions, spatial symmetries, and external fields. Generating these phases in an engineered
system could provide deeper insight into their nature and the potential for harnessing their unique properties. However, concurrently bringing together the main ingredients for realizing many-body phenomena in a single experimental platform is a major challenge. Using superconducting qubits, we simultaneously realize synthetic magnetic fields and strong particle interactions, which are among the essential elements for studying quantum magnetism and fractional quantum Hall (FQH) phenomena. The artificial magnetic fields are synthesized by sinusoidally modulating the qubit couplings. In a closed loop formed by the three qubits, we observe the directional circulation of photons, a signature of broken time-reversal symmetry. We demonstrate strong interactions via the creation of photon-vacancies, or „holes“, which circulate in the opposite direction. The combination of these key elements results in chiral groundstate currents, the first direct measurement of persistent currents in low-lying eigenstates of strongly interacting bosons. The observation of chiral currents at such a small scale is interesting and suggests that the rich many-body physics could survive to smaller scales. We also motivate the feasibility of creating FQH states with near future superconducting technologies. Our work introduces an experimental platform for engineering quantum phases of strongly interacting photons and highlight a path toward realization of bosonic FQH states.

Scalable in-situ qubit calibration during repetitive error detection

  1. J. Kelly,
  2. R. Barends,
  3. A. G. Fowler,
  4. A. Megrant,
  5. E. Jeffrey,
  6. T. C. White,
  7. D. Sank,
  8. J. Y. Mutus,
  9. B. Campbell,
  10. Yu Chen,
  11. Z. Chen,
  12. B. Chiaro,
  13. A. Dunsworth,
  14. E. Lucero,
  15. M. Neeley,
  16. C. Neill,
  17. P. J. J. O'Malley,
  18. C. Quintana,
  19. P. Roushan,
  20. A. Vainsencher,
  21. J. Wenner,
  22. and John M. Martinis
We present a method to optimize qubit control parameters during error detection which is compatible with large-scale qubit arrays. We demonstrate our method to optimize single or two-qubit
gates in parallel on a nine-qubit system. Additionally, we show how parameter drift can be compensated for during computation by inserting a frequency drift and using our method to remove it. We remove both drift on a single qubit and independent drifts on all qubits simultaneously. We believe this method will be useful in keeping error rates low on all physical qubits throughout the course of a computation. Our method is O(1) scalable to systems of arbitrary size, providing a path towards controlling the large numbers of qubits needed for a fault-tolerant quantum computer

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.

Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit

  1. Zijun Chen,
  2. Julian Kelly,
  3. Chis Quintana,
  4. R. Barends,
  5. B. Camppbell,
  6. Yu Chen,
  7. B. Chiaro,
  8. A. Dunsworth,
  9. A. Fowler,
  10. E. Lucero,
  11. E. Jeffrey,
  12. A. Megrant,
  13. J. Mutus,
  14. M. Neeley,
  15. C. Neill,
  16. P. J. J. O'malley,
  17. P. Roushan,
  18. D. Sank,
  19. A. Vainsencher,
  20. J. Wenner,
  21. T. C. White,
  22. A. N. Korotkov,
  23. and John M. Martinis
Leakage errors occur when a quantum system leaves the two-level qubit subspace. Reducing these errors is critically important for quantum error correction to be viable. To quantify
leakage errors, we use randomized benchmarking in conjunction with measurement of the leakage population. We characterize single qubit gates in a superconducting qubit, and by refining our use of Derivative Reduction by Adiabatic Gate (DRAG) pulse shaping along with detuning of the pulses, we obtain gate errors consistently below 10−3 and leakage rates at the 10−5 level. With the control optimized, we find that a significant portion of the remaining leakage is due to incoherent heating of the qubit.

Violating the Bell-Leggett-Garg inequality with weak measurement of an entangled state

  1. T. C. White,
  2. J. Y. Mutus,
  3. J. Dressel,
  4. J. Kelly,
  5. R. Barends,
  6. E. Jeffrey,
  7. D. Sank,
  8. A. Megrant,
  9. B. Campbell,
  10. Yu Chen,
  11. Z. Chen,
  12. B. Chiaro,
  13. A. Dunsworth,
  14. I.-C. Hoi,
  15. C. Neill,
  16. P. J. J. O'Malley,
  17. P. Roushan,
  18. A. Vainsencher,
  19. J. Wenner,
  20. A. N. Korotkov,
  21. and John M. Martinis
Since the inception of quantum mechanics, its validity as a complete description of reality has been challenged due to predictions that defy classical intuition. For many years it was
unclear whether predictions like entanglement and projective measurement represented real phenomena or artifacts of an incomplete model. Bell inequalities (BI) provided the first quantitative test to distinguish between quantum entanglement and a yet undiscovered classical hidden variable theory. The Leggett-Garg inequality (LGI) provides a similar test for projective measurement, and more recently has been adapted to include variable strength measurements to study the process of measurement itself. Here we probe the intersection of both entanglement and measurement through the lens of the hybrid Bell-Leggett-Garg inequality (BLGI). By correlating data from ancilla-based weak measurements and direct projective measurements, we for the first time quantify the effect of measurement strength on entanglement collapse. Violation of the BLGI, which we achieve only at the weakest measurement strengths, offers compelling evidence of the completeness of quantum mechanics while avoiding several loopholes common to previous experimental tests. This uniquely quantum result significantly constrains the nature of any possible classical theory of reality. Additionally, we demonstrate that with sufficient scale and fidelity, a universal quantum processor can be used to study richer fundamental physics.

Traveling wave parametric amplifier with Josephson junctions using minimal resonator phase matching

  1. T. C. White,
  2. J. Y. Mutus,
  3. I.-C. Hoi,
  4. R. Barends,
  5. B. Campbell,
  6. Yu Chen,
  7. Z. Chen,
  8. B. Chiaro,
  9. A. Dunsworth,
  10. E. Jeffrey,
  11. J. Kelly,
  12. A. Megrant,
  13. C. Neill,
  14. P. J. J. O'Malley,
  15. P. Roushan,
  16. D. Sank,
  17. A. Vainsencher,
  18. J. Wenner,
  19. S. Chaudhuri,
  20. J. Gao,
  21. and John M. Martinis
Josephson parametric amplifiers have become a critical tool in superconducting device physics due to their high gain and quantum-limited noise. Traveling wave parametric amplifiers
(TWPAs) promise similar noise performance while allowing for significant increases in both bandwidth and dynamic range. We present a TWPA device based on an LC-ladder transmission line of Josephson junctions and parallel plate capacitors using low-loss amorphous silicon dielectric. Crucially, we have inserted λ/4 resonators at regular intervals along the transmission line in order to maintain the phase matching condition between pump, signal, and idler and increase gain. We achieve an average gain of 12\,dB across a 4\,GHz span, along with an average saturation power of -92\,dBm with noise approaching the quantum limit.

Digital quantum simulation of fermionic models with a superconducting circuit

  1. R. Barends,
  2. L. Lamata,
  3. J. Kelly,
  4. L. García-Álvarez,
  5. A. G. Fowler,
  6. A. Megrant,
  7. E. Jeffrey,
  8. T. C. White,
  9. D. Sank,
  10. J. Y. Mutus,
  11. B. Campbell,
  12. Yu Chen,
  13. Z. Chen,
  14. B. Chiaro,
  15. A. Dunsworth,
  16. I.-C. Hoi,
  17. C. Neill,
  18. P. J. J. O'Malley,
  19. C. Quintana,
  20. P. Roushan,
  21. A. Vainsencher,
  22. J. Wenner,
  23. E. Solano,
  24. and John M. Martinis
Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universal
quantum simulation of fermionic systems is daunting due to their particle statistics, and Feynman left as an open question whether it could be done, because of the need for non-local control. Here, we implement fermionic interactions with digital techniques in a superconducting circuit. Focusing on the Hubbard model, we perform time evolution with constant interactions as well as a dynamic phase transition with up to four fermionic modes encoded in four qubits. The implemented digital approach is universal and allows for the efficient simulation of fermions in arbitrary spatial dimensions. We use in excess of 300 single-qubit and two-qubit gates, and reach global fidelities which are limited by gate errors. This demonstration highlights the feasibility of the digital approach and opens a viable route towards analog-digital quantum simulation of interacting fermions and bosons in large-scale solid state systems.

State preservation by repetitive error detection in a superconducting quantum circuit

  1. J. Kelly,
  2. R. Barends,
  3. A. G. Fowler,
  4. A. Megrant,
  5. E. Jeffrey,
  6. T. C. White,
  7. D. Sank,
  8. J. Y. Mutus,
  9. B. Campbell,
  10. Yu Chen,
  11. Z. Chen,
  12. B. Chiaro,
  13. A. Dunsworth,
  14. I.-C. Hoi,
  15. C. Neill,
  16. P. J. J. O'Malley,
  17. C. Quintana,
  18. P. Roushan,
  19. A. Vainsencher,
  20. J. Wenner,
  21. A. N. Cleland,
  22. and John M. Martinis
Quantum computing becomes viable when a quantum state can be preserved from environmentally-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and
quantum error correction (QEC) is capable of identifying and correcting them. Adding more qubits improves the preservation by guaranteeing increasingly larger clusters of errors will not cause logical failure – a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here, we report the protection of classical states from environmental bit-flip errors and demonstrate the suppression of these errors with increasing system size. We use a linear array of nine qubits, which is a natural precursor of the two-dimensional surface code QEC scheme, and track errors as they occur by repeatedly performing projective quantum non-demolition (QND) parity measurements. Relative to a single physical qubit, we reduce the failure rate in retrieving an input state by a factor of 2.7 for five qubits and a factor of 8.5 for nine qubits after eight cycles. Additionally, we tomographically verify preservation of the non-classical Greenberger-Horne-Zeilinger (GHZ) state. The successful suppression of environmentally-induced errors strongly motivates further research into the many exciting challenges associated with building a large-scale superconducting quantum computer.

Characterization and reduction of microfabrication-induced decoherence in superconducting quantum circuits

  1. C. M. Quintana,
  2. A. Megrant,
  3. Z. Chen,
  4. A. Dunsworth,
  5. B. Chiaro,
  6. R. Barends,
  7. B. Campbell,
  8. Yu Chen,
  9. I.-C. Hoi,
  10. E. Jeffrey,
  11. J. Kelly,
  12. J. Y. Mutus,
  13. P. J. J. O'Malley,
  14. C. Neill,
  15. P. Roushan,
  16. D. Sank,
  17. A. Vainsencher,
  18. J. Wenner,
  19. T. C. White,
  20. A. N. Cleland,
  21. and John M. Martinis
Many superconducting qubits are highly sensitive to dielectric loss, making the fabrication of coherent quantum circuits challenging. To elucidate this issue, we characterize the interfaces
and surfaces of superconducting coplanar waveguide resonators and study the associated microwave loss. We show that contamination induced by traditional qubit lift-off processing is particularly detrimental to quality factors without proper substrate cleaning, while roughness plays at most a small role. Aggressive surface treatment is shown to damage the crystalline substrate and degrade resonator quality. We also introduce methods to characterize and remove ultra-thin resist residue, providing a way to quantify and minimize remnant sources of loss on device surfaces.