Observation of topological transitions in interacting quantum circuits

  1. P. Roushan,
  2. C. Neill,
  3. Yu Chen,
  4. M. Kolodrubetz,
  5. C. Quintana,
  6. N. Leung,
  7. M. Fang,
  8. R. Barends,
  9. B. Campbell,
  10. Z. Chen,
  11. B. Chiaro,
  12. A. Dunsworth,
  13. E. Jeffrey,
  14. J. Kelly,
  15. A. Megrant,
  16. J. Mutus,
  17. P. O'Malley,
  18. D. Sank,
  19. A. Vainsencher,
  20. J. Wenner,
  21. T. White,
  22. A. Polkovnikov,
  23. A. N. Cleland,
  24. and J.M. Martinis
The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust
and hence promising for applications. However, the non-locality of this ordering makes direct experimental studies an outstanding challenge, even in the simplest model topological systems, and interactions among the constituent particles adds to this challenge. Here we demonstrate a novel dynamical method to explore topological phases in both interacting and non-interacting systems, by employing the exquisite control afforded by state-of-the-art superconducting quantum circuits. We utilize this method to experimentally explore the well-known Haldane model of topological phase transitions by directly measuring the topological invariants of the system. We construct the topological phase diagram of this model and visualize the microscopic evolution of states across the phase transition, tasks whose experimental realizations have remained elusive. Furthermore, we developed a new qubit architecture that allows simultaneous control over every term in a two-qubit Hamiltonian, with which we extend our studies to an interacting Hamiltonian and discover the emergence of an interaction-induced topological phase. Our implementation, involving the measurement of both global and local textures of quantum systems, is close to the original idea of quantum simulation as envisioned by R. Feynman, where a controllable quantum system is used to investigate otherwise inaccessible quantum phenomena. This approach demonstrates the potential of superconducting qubits for quantum simulation and establishes a powerful platform for the study of topological phases in quantum systems.

Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing

  1. R. Barends,
  2. J. Kelly,
  3. A. Megrant,
  4. A. Veitia,
  5. D. Sank,
  6. E. Jeffrey,
  7. T. C. White,
  8. J. Mutus,
  9. A. G. Fowler,
  10. B. Campbell,
  11. Y. Chen,
  12. Z. Chen,
  13. B. Chiaro,
  14. A. Dunsworth,
  15. C. Neill,
  16. P. O'Malley,
  17. P. Roushan,
  18. A. Vainsencher,
  19. J. Wenner,
  20. A. N. Korotkov,
  21. A. N. Cleland,
  22. and John M. Martinis
A quantum computer can solve hard problems – such as prime factoring, database searching, and quantum simulation – at the cost of needing to protect fragile quantum states
from error. Quantum error correction provides this protection, by distributing a logical state among many physical qubits via quantum entanglement. Superconductivity is an appealing platform, as it allows for constructing large quantum circuits, and is compatible with microfabrication. For superconducting qubits the surface code is a natural choice for error correction, as it uses only nearest-neighbour coupling and rapidly-cycled entangling gates. The gate fidelity requirements are modest: The per-step fidelity threshold is only about 99%. Here, we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity up to 99.4%. This places Josephson quantum computing at the fault-tolerant threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger (GHZ) state using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

Coherent Josephson qubit suitable for scalable quantum integrated circuits

  1. R. Barends,
  2. J. Kelly,
  3. A. Megrant,
  4. D. Sank,
  5. E. Jeffrey,
  6. Y. Chen,
  7. Y. Yin,
  8. B. Chiaro,
  9. J. Mutus,
  10. C. Neill,
  11. P. O'Malley,
  12. P. Roushan,
  13. J. Wenner,
  14. T. C. White,
  15. A. N. Cleland,
  16. and John M. Martinis
We demonstrate a planar, tunable superconducting qubit with energy relaxation times up to 44 microseconds. This is achieved by using a geometry designed to both minimize radiative loss
and reduce coupling to materials-related defects. At these levels of coherence, we find a fine structure in the qubit energy lifetime as a function of frequency, indicating the presence of a sparse population of incoherent, weakly coupled two-level defects. This is supported by a model analysis as well as experimental variations in the geometry. Our `Xmon‘ qubit combines facile fabrication, straightforward connectivity, fast control, and long coherence, opening a viable route to constructing a chip-based quantum computer.

Multiplexed dispersive readout of superconducting phase qubits

  1. Yu Chen,
  2. D. Sank,
  3. P. O'Malley,
  4. T. White,
  5. R. Barends,
  6. B. Chiaro,
  7. J. Kelly,
  8. E. Lucero,
  9. M. Mariantoni,
  10. A. Megrant,
  11. C. Neill,
  12. A. Vainsencher,
  13. J. Wenner,
  14. Yi Yin,
  15. A. N. Cleland,
  16. and John M. Martinis
We introduce a frequency-multiplexed readout scheme for superconducting phase qubits. Using a quantum circuit with four phase qubits, we couple each qubit to a separate lumped-element
superconducting readout resonator, with the readout resonators connected in parallel to a single measurement line. The readout resonators and control electronics are designed so that all four qubits can be read out simultaneously using frequency multiplexing on the one measurement line. This technology provides a highly efficient and compact means for reading out multiple qubits, a significant advantage for scaling up to larger numbers of qubits.