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Implementation of XY entangling gates with a single calibrated pulse

Nature Electronics volume 3, pages 744–750 (2020)Cite this article

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Abstract

Near-term applications of quantum information processors will rely on optimized circuit implementations to minimize the circuit depth, reducing the negative impact of gate errors in noisy intermediate-scale quantum (NISQ) computers. One approach to minimize the circuit depth is the use of a more expressive gate set. The XY two-qubit gate set can offer reductions in circuit depth for generic circuits, as well as improved performance for problems with symmetries that match the gate set. Here we report an implementation of the family of XY entangling gates in a transmon-based superconducting qubit architecture using a gate decomposition strategy that requires only a single calibrated pulse. The approach allows us to implement XY gates with a median fidelity of 97.35 ± 0.17%, approaching the coherence-limited gate fidelity of the two-qubit pair. We also show that the XY gate can be used to implement instances of the quantum approximate optimization algorithm, achieving a reduction in circuit depth of ~30% compared with the use of CZ gates only. Finally, we extend our decomposition scheme to other gate families, which can allow for further reductions in circuit depth.

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Fig. 1: XY interaction chevrons.
Fig. 2: Gate fidelity for XY composed of one and two pulses.
Fig. 3: iRB fidelity scaling with number of XY gates.
Fig. 4: XY gate fidelity as function of θ.
Fig. 5: MAXCUT QAOA landscapes.

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Data availability

The experimental data and circuits used for the QAOA experiment are provided in ref. 54.

Code availability

The code used for data analysis is provided in ref. 54.

References

  1. Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).

    Google Scholar 

  2. Otterbach, J. S. et al. Unsupervised machine learning on a hybrid quantum computer. Preprint at https://arxiv.org/pdf/1712.05771.pdf (2017).

  3. McCaskey, A. J. et al. Quantum chemistry as a benchmark for near-term quantum computers. npj Quantum Inf. 5, 99 (2019).

    Google Scholar 

  4. Hong, S. S. et al. Demonstration of a parametrically activated entangling gate protected from flux noise. Phys. Rev. A 101, 012302 (2020).

    Google Scholar 

  5. Andersen, C. K. et al. Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits. npj Quantum Inf. 5, 69 (2019).

    Google Scholar 

  6. Quantum devices & simulators. IBM https://www.research.ibm.com/ibm-q/technology/devices/ibmqx4 (2018).

  7. Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014).

    Google Scholar 

  8. Sheldon, S., Magesan, E., Chow, J. M. & Gambetta, J. M. Procedure for systematically tuning up cross-talk in the cross-resonance gate. Phys. Rev. A 93, 060302 (2016).

    Google Scholar 

  9. Barends, R. et al. Diabatic gates for frequency-tunable superconducting qubits. Phys. Rev. Lett. 123, 210501 (2019).

    Google Scholar 

  10. Peterson, E. C., Crooks, G. E. & Smith, R. S. Two-qubit circuit depth and the monodromy polytope. Quantum 4, 247 (2020).

    Google Scholar 

  11. Vidal, G. & Dawson, C. M. Universal quantum circuit for two-qubit transformations with three controlled-NOT gates. Phys. Rev. A 69, 010301 (2004).

    Google Scholar 

  12. Shende, V. V., Markov, I. L. & Bullock, S. S. Minimal universal two-qubit controlled-NOT-based circuits. Phys. Rev. A 69, 062321 (2004).

    Google Scholar 

  13. Schuch, N. & Siewert, J. Natural two-qubit gate for quantum computation using the XY interaction. Phys. Rev. A 67, 032301 (2003).

    MathSciNet  Google Scholar 

  14. Siewert, J. & Fazio, R. Quantum algorithms for Josephson networks. Phys. Rev. Lett. 87, 257905 (2001).

    Google Scholar 

  15. Kempe, J., Bacon, D., DiVincenzo, D. P. & Whaley, K. B. Encoded universality from a single physical interaction. Quantum Inf. Comput. 1, 33–55 (2001).

    MathSciNet  MATH  Google Scholar 

  16. Echternach, P. et al. Universal quantum gates for single Cooper pair box based quantum computing. Quantum Inf. Comput. 1, 143–150 (2001).

    Google Scholar 

  17. Ganzhorn, M. et al. Gate-efficient simulation of molecular eigenstates on a quantum computer. Phys. Rev. Appl. 11, 044092 (2019).

    Google Scholar 

  18. Hadfield, S. et al. From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms 2019, 34 (2019).

    MathSciNet  MATH  Google Scholar 

  19. Wang, Z., Rubin, N. C., Dominy, J. M. & Rieffel, E. G. XY mixers: analytical and numerical results for the quantum alternating operator ansatz. Phys. Rev. A 101, 012320 (2020).

    MathSciNet  Google Scholar 

  20. Knill, E., Laflamme, R., Martinez, R. & Tseng, C. An algorithmic benchmark for quantum information processing. Nature 404, 368–370 (2000).

    Google Scholar 

  21. Strauch, F. W. et al. Quantum logic gates for coupled superconducting phase qubits. Phys. Rev. Lett. 91, 167005 (2003).

    Google Scholar 

  22. Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007).

    Google Scholar 

  23. Dewes, A. et al. Characterization of a two-transmon processor with individual single-shot qubit readout. Phys. Rev. Lett. 108, 057002 (2012).

    Google Scholar 

  24. Bertet, P., Harmans, C. J. P. M. & Mooij, J. E. Parametric coupling for superconducting qubits. Phys. Rev. B 73, 2–7 (2005).

    Google Scholar 

  25. Niskanen, A. O. et al. Quantum coherent tunable coupling of superconducting qubits. Science 316, 723–726 (2007).

    Google Scholar 

  26. McKay, D. C. et al. Universal gate for fixed-frequency qubits via a tunable bus. Phys. Rev. Appl. 6, 064007 (2016).

    Google Scholar 

  27. Roth, M. et al. Analysis of a parametrically driven exchange-type gate and a two-photon excitation gate between superconducting qubits. Phys. Rev. A 96, 062323 (2017).

    Google Scholar 

  28. Didier, N., Sete, E. A., da Silva, M. P. & Rigetti, C. Analytical modeling of parametrically modulated transmon qubits. Phys. Rev. A 97, 022330 (2018).

    Google Scholar 

  29. Caldwell, S. A. et al. Parametrically activated entangling gates using transmon qubits. Phys. Rev. Appl. 10, 034050 (2018).

    Google Scholar 

  30. Mundada, P., Zhang, G., Hazard, T. & Houck, A. Suppression of qubit crosstalk in a tunable coupling superconducting circuit. Phys. Rev. Appl. 12, 054023 (2019).

    Google Scholar 

  31. Naik, R. K. et al. Random access quantum information processors using multimode circuit quantum electrodynamics. Nat. Commun. 8, 1904 (2017).

    Google Scholar 

  32. Yan, F. et al. Tunable coupling scheme for implementing high-fidelity two-qubit gates. Phys. Rev. Appl. 10, 054062 (2018).

    Google Scholar 

  33. Vaughan, R. W., Elleman, D. D., Stacey, L. M., Rhim, W. & Lee, J. W. A simple, low power, multiple pulse NMR spectrometer. Rev. Sci. Instrum. 43, 1356–1364 (1972).

    Google Scholar 

  34. Kimmel, S., Low, G. H. & Yoder, T. J. Robust calibration of a universal single-qubit gate set via robust phase estimation. Phys. Rev. A 92, 062315 (2015).

    Google Scholar 

  35. Magesan, E. et al. Efficient measurement of quantum gate error by interleaved randomized benchmarking. Phys. Rev. Lett. 109, 080505 (2012).

    MATH  Google Scholar 

  36. Dvoretzky, A., Kiefer, J. & Wolfowitz, J. Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator. Ann. Math. Stat. 27, 642–669 (1956).

    MathSciNet  MATH  Google Scholar 

  37. Birnbaum, Z. W. & McCarty, R. C. A distribution-free upper confidence bound for Pr{Y < X}, based on independent samples of X and Y. Ann. Math. Stat. 29, 558–562 (1958).

    MathSciNet  MATH  Google Scholar 

  38. Massart, P. The tight constant in the Dvoretzky–Kiefer–Wolfowitz inequality. Ann. Probab. 18, 1269–1283 (1990).

    MathSciNet  MATH  Google Scholar 

  39. Didier, N., Sete, E. A., Combes, J. & da Silva, M. P. AC flux sweet spots in parametrically modulated superconducting qubits. Phys. Rev. Appl. 12, 054015 (2019).

    Google Scholar 

  40. Merkel, S. T. et al. Self-consistent quantum process tomography. Phys. Rev. A 87, 062119 (2013).

    Google Scholar 

  41. Farhi, E., Goldstone, J. & Gutmann, S. A quantum approximate optimization algorithm. Preprint at https://arxiv.org/pdf/1411.4028.pdf (2014).

  42. Abrams, D. M., Didier, N., Caldwell, S. A., Johnson, B. R. & Ryan, C. A. Methods for measuring magnetic flux crosstalk between tunable transmons. Phys. Rev. Appl. 12, 064022 (2019).

    Google Scholar 

  43. Wang, Z., Hadfield, S., Jiang, Z. & Rieffel, E. G. Quantum approximate optimization algorithm for maxcut: a fermionic view. Phys. Rev. A 97, 022304 (2018).

    Google Scholar 

  44. Qiang, X. et al. Large-scale silicon quantum photonics implementing arbitrary two-qubit processing. Nat. Photon. 12, 534–539 (2018).

    Google Scholar 

  45. Verdon, G. et al. Learning to learn with quantum neural networks via classical neural networks. Preprint at https://arxiv.org/pdf/1907.05415.pdf (2019).

  46. Babbush, R. et al. Low-depth quantum simulation of materials. Phys. Rev. X 8, 011044 (2018).

    Google Scholar 

  47. Kivlichan, I. D. et al. Quantum simulation of electronic structure with linear depth and connectivity. Phys. Rev. Lett. 120, 110501 (2018).

    MathSciNet  Google Scholar 

  48. Crooks, G. E. Performance of the quantum approximate optimization algorithm on the maximum cut problem. Preprint at https://arxiv.org/pdf/1811.08419.pdf (2018).

  49. O’Gorman, B., Huggins, W. J., Rieffel, E. G. & Whaley, K. B. Generalized swap networks for near-term quantum computing. Preprint at https://arxiv.org/pdf/1905.05118.pdf (2019).

  50. Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995).

    Google Scholar 

  51. Reed, M. D. et al. Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 382–385 (2012).

    Google Scholar 

  52. Fedorov, A., Steffen, L., Baur, M., da Silva, M. P. & Wallraff, A. Implementation of a Toffoli gate with superconducting circuits. Nature 481, 170–172 (2012).

    Google Scholar 

  53. Mariantoni, M. et al. Implementing the quantum von Neumann architecture with superconducting circuits. Science 334, 61–65 (2011).

    Google Scholar 

  54. Abrams, D., Didier, N., Johnson, B., da Silva, M. P. & Ryan, C. Ancillary files for paper: Implementation of the XY interaction family with calibration of a single pulse. Zenodo https://zenodo.org/record/3568420 (2019).

  55. Nersisyan, A. et al. Manufacturing low dissipation superconducting quantum processors. Preprint at https://arxiv.org/pdf/1901.08042.pdf (2019).

  56. Jones, G. et al. Scalable instrumentation for general purpose quantum computers. In American Physical Society March Meeting 2019 abstr. V26.00011 (APS, 2019).

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Acknowledgements

Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231. We thank the Rigetti quantum software team for providing tooling support, the Rigetti fabrication team for manufacturing the device, the Rigetti technical operations team for fridge build out and maintenance, the Rigetti cryogenic hardware team for providing the chip packaging, and the Rigetti control systems and embedded software teams for creating the Rigetti AWG control system. We additionally thank M. Scheer and E. Peterson for convincing us that the composite pulse decomposition would be a valid implementation of the XY gates. We thank P. Karalekas for his help in setting up the QAOA demo. Finally, we thank Z. Wang, N.C. Rubin, E.G. Rieffel and D. Venturelli for valuable conversations.

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Authors and Affiliations

  1. Rigetti Computing, Berkeley, CA, USA

    Deanna M. Abrams, Nicolas Didier, Blake R. Johnson, Marcus P. da Silva & Colm A. Ryan

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Contributions

D.M.A., C.A.R. and M.P.d.S. drafted the manuscript, puzzled out the implementation of frame phases and brainstormed effective ways to benchmark the gate. D.M.A. performed the experiments. N.D. provided theory to describe the turn-on phase of shaped flux pulses and the formula for the coherence-limited gate fidelity. B.R.J., C.A.R. and M.P.d.S. organized the effort.

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Correspondence to Nicolas Didier.

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N.D. is an employee of Rigetti Computing. All other authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Circuit identities.

Circuit diagrams visually representing equations (3)–(9) in the main text. The diagrams are numbered according to the corresponding equation. Time flows from left to right in these diagrams—that is, the leftmost operations are applied first.

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Abrams, D.M., Didier, N., Johnson, B.R. et al. Implementation of XY entangling gates with a single calibrated pulse. Nat Electron 3, 744–750 (2020). https://doi.org/10.1038/s41928-020-00498-1

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