Skip to main content
SpringerLink
Log in

Fast two-quadrature adiabatic quantum gates for weakly nonlinear qubits: a tight-binding approach

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Adiabatic gate operations required to remain within the qubit subspace in an anharmonic oscillator can be slow when compared to qubit decoherence times. However, significant gate speedups are possible using methods such as derivative-removal-by-adiabatic-gate (DRAG) (Motzoi et al. in Phys Rev Lett 103:110501, 2009), which creates spectral-holes near unwanted transitions. We analyze the effect of DRAG on the transmon qubit in some detail for cosine and truncated Gaussian pulses. An accurate tight-binding multi-level transmon model is presented here along with a multi-level Lindblad model and time-evolution methods to remove phase oscillations. It is shown that in addition to DRAG, the simultaneous optimization of the pulse truncation, detuning and the pulse norm significantly reduces leakage errors. For sharply truncated Gaussian pulses, DRAG leads to faster gates that are also stable against pulse jitter. However, for slow rising pulse envelopes, DRAG is not effective. This is explained using spectral analysis. Overall this can lead to much faster reverse-engineered qubit gates soon.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998)

    Article  ADS  Google Scholar 

  2. Weber, J.R., Koehl, W.F., Varley, J.B., Janotti, A., Buckley, B.B., Van de Walle, C.G., Awschalom, D.D.: Quantum computing with defects. Proc. Natl. Acad. Sci. 107, 8513–8518 (2010)

    Article  ADS  Google Scholar 

  3. Imamo\(\bar{\rm g}\)lu, A., Awschalom, D.D., Burkard, G., DiVincenzo, D.P., Loss, D., Sherwin, M., Small, A.: Quantum information processing using quantum dot spins and cavity qed. Phys. Rev. Lett. 83, 4204–4207 (1999)

    Article  ADS  Google Scholar 

  4. Petta, J.R., Johnson, A.C., Taylor, J.M., Laird, E.A., Yacoby, A., Lukin, M.D., Marcus, C.M., Hanson, M.P., Gossard, A.C.: Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005)

    Article  ADS  Google Scholar 

  5. Hennessy, K., Badolato, A., Winger, M., Gerace, D., Atature, M., Gulde, S., Falt, S., Hu, E.L., Imamoglu, A.: Quantum nature of a strongly coupled single quantum dot-cavity system. Nature 445, 896–899 (2007)

    Article  ADS  Google Scholar 

  6. Devoret, M.H., Esteve, D., Martinis, J.M., Urbina, C.: Effect of an adjustable admittance on the macroscopic energy levels of a current biased Josephson junction. Phys. Scr. 1989, 118 (1989)

    Article  Google Scholar 

  7. Schoelkopf, R.J., Girvin, S.M.: Wiring up quantum systems. Nature 451, 664–669 (2008)

    Article  ADS  Google Scholar 

  8. Martinis, J.M.: Superconducting phase qubits. Quantum Inf. Process. 8, 81–103 (2009)

    Article  Google Scholar 

  9. Khaetskii, A.V., Loss, D., Glazman, L.: Electron spin decoherence in quantum dots due to interaction with nuclei. Phys. Rev. Lett. 88, 186802 (2002)

    Article  ADS  Google Scholar 

  10. de Sousa, R., Das Sarma, S.: Theory of nuclear-induced spectral diffusion: spin decoherence of phosphorus donors in Si and GaAs quantum dots. Phys. Rev. B 68, 115322 (2003)

    Article  ADS  Google Scholar 

  11. Yao, W., Liu, R.-B., Sham, L.J.: Theory of electron spin decoherence by interacting nuclear spins in a quantum dot. Phys. Rev. B 74, 195301 (2006)

    Article  ADS  Google Scholar 

  12. Yu, T., Eberly, J.H.: Phonon decoherence of quantum entanglement: robust and fragile states. Phys. Rev. B 66, 193306 (2002)

    Article  ADS  Google Scholar 

  13. Golovach, V.N., Khaetskii, A., Loss, D.: Phonon-induced decay of the electron spin in quantum dots. Phys. Rev. Lett. 93, 016601 (2004)

    Article  ADS  Google Scholar 

  14. Stano, P., Fabian, J.: Theory of phonon-induced spin relaxation in laterally coupled quantum dots. Phys. Rev. Lett. 96, 186602 (2006)

    Article  ADS  Google Scholar 

  15. Pellizzari, T., Gardiner, S.A., Cirac, J.I., Zoller, P.: Decoherence, continuous observation, and quantum computing: a cavity qed model. Phys. Rev. Lett. 75, 3788 (1995)

    Article  ADS  Google Scholar 

  16. Blais, A., Huang, R.-S., Wallraff, A., Girvin, S.M., Schoelkopf, R.J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)

    Article  ADS  Google Scholar 

  17. Wellstood, F., Urbina, C., Clarke, J.: Excess noise in dc SQUIDs from 4.2k to 0.022k. IEEE Trans. Mag. 23, 1662–1665 (1987)

    Article  ADS  Google Scholar 

  18. MacLean, K., Amasha, S., Radu, I.P., Zumbuhl, D.M., Kastner, M.A., Hanson, M.P., Gossard, A.C.: Energy-dependent tunneling in a quantum dot. Phys. Rev. Lett. 98, 036802 (2007)

    Article  ADS  Google Scholar 

  19. Clarke, J., Wilhelm, F.K.: Superconducting quantum bits. Nature 453, 1031–1042 (2008)

    Article  ADS  Google Scholar 

  20. Sendelbach, S., Hover, D., Kittel, A., Mück, M., Martinis, J.M., McDermott, R.: Magnetism in squids at millikelvin temperatures. Phys. Rev. Lett. 100, 227006 (2008)

    Article  ADS  Google Scholar 

  21. Paladino, E., Galperin, Y.M., Falci, G., Altshuler, B.L.: 1/f noise: implications for solid-state quantum information. Rev. Mod. Phys. 86, 361–418 (2014)

    Article  ADS  Google Scholar 

  22. De, A.: Ising-glauber spin cluster model for temperature-dependent magnetization noise in squids. Phys. Rev. Lett. 113, 217002 (2014)

    Article  ADS  Google Scholar 

  23. De, A.: 1/\(f\) flux noise in low-\(T_c\) squids due to superparamagnetic phase transitions in defect clusters. Phys. Rev. B 99, 024305 (2019)

    Article  ADS  Google Scholar 

  24. Knill, E., Laflamme, R., Zurek, W.H.: Resilient quantum computation. Science 279, 342 (1998)

    Article  ADS  Google Scholar 

  25. Steane, A.M.: Overhead and noise threshold of fault-tolerant quantum error correction. Phys. Rev. A 68, 042322 (2003)

    Article  ADS  Google Scholar 

  26. Gottesman, D., Aliferis, P., Preskill, J.: Quantum accuracy threshold for concatenated distance-3 code. Quant. Inf. Comput. 6, 97–165 (2006)

    MathSciNet  MATH  Google Scholar 

  27. Aharonov, D., Kitaev, A., Preskill, J.: Fault-tolerant quantum computation with long-range correlated noise. Phys. Rev. Lett. 96, 050504 (2006)

    Article  ADS  Google Scholar 

  28. Dennis, E., Kitaev, A., Landahl, A., Preskill, J.: Topological quantum memory. J. Math. Phys. 43, 4452 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  29. Raussendorf, R., Harrington, J.: Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007)

    Article  ADS  Google Scholar 

  30. Kitaev, A.Y.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  31. Letokhov, VS, and Chebotaev, V.P.: Nonlinear Laser Spectroscopy, vol. 4, 1st edn. Springer-Verlag Berlin Heidelberg (1977)

  32. Vitanov, N.V., Halfmann, T., Shore, B.W., Bergmann, K.: Laser-induced population transfer by adiabatic passage techniques. Ann. Rev. Phys. Chem. 52, 763–809 (2001)

    Article  ADS  Google Scholar 

  33. Unanyan, R., Fleischhauer, M., Shore, B.W., Bergmann, K.: Robust creation and phase-sensitive probing of superposition states via stimulated raman adiabatic passage (stirap) with degenerate dark states. Opt. Commun. 155, 144–154 (1998)

    Article  ADS  Google Scholar 

  34. Sugny, D., Ndong, M., Lauvergnat, D., Justum, Y., Desouter-Lecomte, M.: Laser control in open molecular systems: stirap and optimal control. J. Photochem. Photobiol. A Chem. 190, 359–371 (2007)

    Article  Google Scholar 

  35. Kis, Z., Renzoni, F.: Qubit rotation by stimulated raman adiabatic passage. Phys. Rev. A 65, 032318 (2002)

    Article  ADS  Google Scholar 

  36. Kai Eckert, M., Lewenstein, R.C., Birkl, G., Ertmer, W., Mompart, J.: Three-level atom optics via the tunneling interaction. Phys. Rev. A 70, 023606 (2004)

    Article  ADS  Google Scholar 

  37. Greentree, A.D., Cole, J.H., Hamilton, A.R., Hollenberg, L.C.L.: Coherent electronic transfer in quantum dot systems using adiabatic passage. Phys. Rev. B 70, 235317 (2004)

    Article  ADS  Google Scholar 

  38. Greentree, A.D., Hamilton, A.R., Green, F.: Charge shelving and bias spectroscopy for the readout of a charge qubit on the basis of superposition states. Phys. Rev. B 70, 041305 (2004)

    Article  ADS  Google Scholar 

  39. Motzoi, F., Gambetta, J.M., Rebentrost, P., Wilhelm, F.K.: Simple pulses for elimination of leakage in weakly nonlinear qubits. Phys. Rev. Lett. 103, 110501 (2009)

    Article  ADS  Google Scholar 

  40. Gambetta, J.M., Motzoi, F., Merkel, S.T., Wilhelm, F.K.: Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator. Phys. Rev. A 83, 012308 (2011)

    Article  ADS  Google Scholar 

  41. Motzoi, F., Wilhelm, F.K.: Improving frequency selection of driven pulses using derivative-based transition suppression. Phys. Rev. A 88, 062318 (2013)

    Article  ADS  Google Scholar 

  42. Poudel, A., Vavilov, M.G.: Effect of an ohmic environment on an optimally controlled flux-biased phase qubit. Phys. Rev. B 82, 144528 (2010)

    Article  ADS  Google Scholar 

  43. Chow, J.M., DiCarlo, L., Gambetta, J.M., Motzoi, F., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Optimized driving of superconducting artificial atoms for improved single-qubit gates. Phys. Rev. A 82, 040305 (2010)

    Article  ADS  Google Scholar 

  44. Martinis, J.M., Geller, M.R.: Fast adiabatic qubit gates using only \(\sigma _z\) control. Phys. Rev. A 90, 022307 (2014)

    Article  ADS  Google Scholar 

  45. Wood, C.J., Gambetta, J.M.: Quantification and characterization of leakage errors. Phys. Rev. A 97, 032306 (2018)

    Article  ADS  Google Scholar 

  46. Koch, J., Yu, T.M., Jay Gambetta, A.A., Houck, D.I., Schuster, J.M., Alexandre Blais, M.H., Devoret, S.M., Girvin, R.J.S.: Charge-insensitive qubit design derived from the cooper pair box. Phys. Rev. A 76, 042319 (2007)

    Article  ADS  Google Scholar 

  47. Weides, M.P., Kline, J.S., Vissers, M.R., Sandberg, M.O., Wisbey, D.S., Johnson, B.R., Ohki, T.A., Pappas, D.P.: Coherence in a transmon qubit with epitaxial tunnel junctions. Appl. Phys. Lett. 99, 262502 (2011)

    Article  ADS  Google Scholar 

  48. Rigetti, C., Gambetta, J.M., Stefano Poletto, B.L.T., Plourde, J.M., Chow, A.D., Córcoles, J.A., Smolin, S.T., Merkel, J.R., Rozen, G.A., Keefe, M.B., Rothwell, M.B., Ketchen, M.S.: Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms. Phys. Rev. B 86, 100506 (2012)

    Article  ADS  Google Scholar 

  49. Yoshihara, F., Harrabi, K., Niskanen, A.O., Nakamura, Y., Tsai, J.S.: Decoherence of flux qubits due to 1/f flux noise. Phys. Rev. Lett. 97, 167001 (2006)

    Article  ADS  Google Scholar 

  50. Sank, D., Barends, R., Bialczak, R.C., Chen, Y., Kelly, J., Lenander, M., Lucero, E., Mariantoni, M., Megrant, A., Neeley, M., O’Malley, P.J.J., Vainsencher, A., Wang, H., Wenner, J., White, T.C., Yamamoto, T., Yin, Y., Cleland, A.N., Martinis, J.M.: Flux noise probed with real time qubit tomography in a Josephson phase qubit. Phys. Rev. Lett. 109, 067001 (2012)

    Article  ADS  Google Scholar 

  51. Ithier, G., Collin, E., Joyez, P., Meeson, P.J., Vion, D., Es-teve, D., Chiarello, F., Shnirman, A., Makhlin, Y., Schriefl, J., Schön, G.: Decoherence in a superconducting quantum bit circuit. Phys. Rev. B 72, 134519 (2005)

    Article  ADS  Google Scholar 

  52. McDermott, R.: Materials origins of decoherence in superconducting qubits. IEEE Trans. Appl. Supercond. 19, 2–13 (2009)

    Article  ADS  Google Scholar 

  53. Chen, Z., Kelly, J., Quintana, C., Barends, R., Campbell, B., Chen, Y., Chiaro, B., Dunsworth, A., Fowler, A.G., Lucero, E., Jeffrey, E., Megrant, A., Mutus, J., Neeley, M., Neill, C., O’Malley, P.J.J., Roushan, P., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Korotkov, A.N., Martinis, J.M.: Measuring and suppressing quantum state leakage in a superconducting qubit. Phys. Rev. Lett. 116, 020501 (2016)

    Article  ADS  Google Scholar 

  54. Barends, R., Kelly, J., Megrant, A., Veitia, A., Sank, D., Jeffrey, E., White, T.C., Mutus, J., Fowler, A.G., Campbell, B., et al.: Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014)

    Article  ADS  Google Scholar 

  55. Kelly, J., Barends, R., Fowler, A.G., Megrant, A., Jeffrey, E., White, T.C., Sank, D., Mutus, J.Y., Campbell, B., Chen, Y., et al.: State preservation by repetitive error detection in a superconducting quantum circuit. Nature 519, 66–69 (2015)

    Article  ADS  Google Scholar 

  56. Córcoles, A.D., Magesan, E., Srinivasan, S.J., Cross, A.W., Steffen, M., Gambetta, J.M., Chow, J.M.: Demonstration of a quantum error detection code using a square lattice of four superconducting qubits. Nat. Commun. 6, 6979 (2015)

    Article  ADS  Google Scholar 

  57. Ghosh, J., Fowler, A.G., Martinis, J.M., Geller, M.R.: Understanding the effects of leakage in superconducting quantum-error-detection circuits. Phys. Rev. A 88, 062329 (2013)

    Article  ADS  Google Scholar 

  58. Fowler, A.G., Whiteside, A.C., Hollenberg, L.C.L.: Towards practical classical processing for the surface code. Phys. Rev. Lett. 108, 180501 (2012)

    Article  ADS  Google Scholar 

  59. Fowler, A.G., Mariantoni, M., Martinis, J.M., Cleland, A.N.: Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)

    Article  ADS  Google Scholar 

  60. Brif, C., Grace, M.D., Sarovar, M., Young, K.C.: Exploring adiabatic quantum trajectories via optimal control. New J. Phys. 16, 065013 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  61. Pryadko, L.P., Sengupta, P.: Second-order shaped pulses for solid-state quantum computation. Phys. Rev. A 78, 032336 (2008)

    Article  ADS  Google Scholar 

  62. Lucero, E., Kelly, J., Bialczak, R.C., Lenan-der, M., Mariantoni, M., Neeley, M., O’Connell, A.D., Sank, D., Wang, H., Weides, M., Wenner, J., Yamamoto, T., Cleland, A.N., Martinis, J.M.: Reduced phase error through optimized control of a superconducting qubit. Phys. Rev. A 82, 042339 (2010)

    Article  ADS  Google Scholar 

  63. Forney, A.M., Jackson, S.R., Strauch, F.W.: Multifrequency control pulses for multilevel superconducting quantum circuits. Phys. Rev. A 81, 012306 (2010)

    Article  ADS  Google Scholar 

  64. De, A., Pryadko, L.P.: Dynamically corrected gates for qubits with always-on ising couplings: error model and fault tolerance with the toric code. Phys. Rev. A 89, 032332 (2014)

    Article  ADS  Google Scholar 

  65. De, A., Pryadko, L.P.: Universal set of dynamically protected gates for bipartite qubit networks: soft pulse implementation of the [[5, 1, 3]] quantum error-correcting code. Phys. Rev. A 93, 042333 (2016)

    Article  ADS  Google Scholar 

  66. Kofman, A.G., Kurizki, G.: Universal dynamical control of quantum mechanical decay: modulation of the coupling to the continuum. Phys. Rev. Lett. 87, 270405 (2001)

    Article  Google Scholar 

  67. Khodjasteh, K., Lidar, D.A.: Fault-tolerant quantum dynamical decoupling. Phys. Rev. Lett. 95, 180501 (2005)

    Article  ADS  Google Scholar 

  68. Götz, S.: Keeping a quantum bit alive by optimized \(\pi \)-pulse sequences. Phys. Rev. Lett. 98, 100504 (2007)

    Article  Google Scholar 

  69. Lee, B., Witzel, W.M., Das Sarma, S.: Universal pulse sequence to minimize spin dephasing in the central spin decoherence problem. Phys. Rev. Lett. 100, 160505 (2008)

    Article  ADS  Google Scholar 

  70. Bacon, D., Kempe, J., Lidar, D.A., Whaley, K.B.: Universal fault-tolerant quantum computation on decoherence-free subspaces. Phys. Rev. Lett. 85, 1758–1761 (2000)

    Article  ADS  Google Scholar 

  71. Brion, E., Pedersen, L.H., Mømer, K., Chutia, S., Saffman, M.: Universal quantum computation in a neutral-atom decoherence-free subspace. Phys. Rev. A 75, 032328 (2007)

    Article  ADS  Google Scholar 

  72. Lidar, D.A.: Towards fault tolerant adiabatic quantum computation. Phys. Rev. Lett. 100, 160506 (2008)

    Article  ADS  Google Scholar 

  73. Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)

    Article  ADS  Google Scholar 

  74. Steane, A.M.: Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  75. Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493 (1995)

    Article  ADS  Google Scholar 

  76. Knill, E., Laflamme, R.: Theory of quantum error-correcting codes. Phys. Rev. A 55, 900–911 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  77. Kovalev, A.A., Pryadko, L.P.: Quantum Kronecker sum-product low-density parity-check codes with finite rate. Phys. Rev. A 88, 012311 (2013)

    Article  ADS  Google Scholar 

  78. De, A., Pryadko, L.P.: Universal set of scalable dynamically corrected gates for quantum error correction with always-on qubit couplings. Phys. Rev. Lett. 110, 070503 (2013)

    Article  ADS  Google Scholar 

  79. McDermott, R., Vavilov, M.G.: Accurate qubit control with single flux quantum pulses. Phys. Rev. Appl. 2, 014007 (2014)

    Article  ADS  Google Scholar 

  80. De, A.: Coupled-qubit Tavis-Cummings scheme for prolonging quantum coherence. Phys. Rev. A 91, 012317 (2015)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

I wish to thank Alexander Korotkov for his initial participation and for his helpful comments on this manuscript. I would also like to thank Leonid Pryadko for several very helpful discussions and for his support. AD has been supported by the US Army Research Office, Grant No. W911NF-11-1-0027 and W911NF-14-1-0272, and by the NSF, Grant No. 1018935.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, University of California, Riverside, CA, 92521, USA

    Amrit De

Authors
  1. Amrit De
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amrit De.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

De, A. Fast two-quadrature adiabatic quantum gates for weakly nonlinear qubits: a tight-binding approach. Quantum Inf Process 18, 165 (2019). https://doi.org/10.1007/s11128-019-2285-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2285-7

Keywords

Search

Navigation