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Controlled-NOT gate sequences for mixed spin qubit architectures in a noisy environment

  • E. Ferraro
  • M. Fanciulli
  • M. De Michielis
Article

Abstract

Explicit controlled-NOT gate sequences between two qubits of different types are presented in view of applications for large-scale quantum computation. Here, the building blocks for such composite systems are qubits based on the electrostatically confined electronic spin in semiconductor quantum dots. For each system the effective Hamiltonian models expressed by only exchange interactions between pair of electrons are exploited in two different geometrical configurations. A numerical genetic algorithm that takes into account the realistic physical parameters involved is adopted. Gate operations are addressed by modulating the tunneling barriers and the energy offsets between different couple of quantum dots. Gate infidelities are calculated considering limitations due to unideal control of gate sequence pulses, hyperfine interaction and charge noise.

Keywords

Quantum computation architectures and implementations Quantum dots Noise Quantum gate sequences 

Notes

Acknowledgements

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No. 688539.

References

  1. 1.
    Medford, J., Beil, J., Taylor, J.M., Bartlett, S.D., Doherty, A.C., Rashba, E.I., DiVincenzo, D.P., Lu, H., Gossard, A.C., Marcus, C.M.: Self-consistent measurement and state tomography of an exchange-only spin qubit. Nat. Nanotechnol. 8, 654 (2013)ADSCrossRefGoogle Scholar
  2. 2.
    Koppens, F.H.L., Buizert, C., Tielrooij, K.J., Vink, I.T., Nowack, K.C., Meunier, T., Kouwenhoven, L.P., Vandersypen, L.M.K.: Driven coherent oscillations of a single electron spin in a quantum dot. Nature (London) 442, 766 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    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 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    Veldhorst, M., Hwang, J.C.C., Yang, C.H., Leenstra, A.W., de Ronde, B., Dehollain, J.P., Muhonen, J.T., Hudson, F.E., Itoh, K.M., Morello, A., Dzurak, A.S.: An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nanotechnol. 9, 981 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    Kawakami, E., Scarlino, P., Ward, D.R., Braakman, F.R., Savage, D.E., Lagally, M.G., Friesen, M., Coppersmith, S.N., Eriksson, M.A., Vandersypen, L.M.K.: Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. Nat. Nanotechnol. 9, 666 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    Maune, B.M., Borselli, M.G., Huang, B., Ladd, T.D., Deelman, P.W., Holabird, K.S., Kiselev, A.A., Alvarado-Rodriguez, I., Ross, R.S., Schmitz, A.E., Sokolich, M., Watson, C.A., Gyure, M.F., Hunter, A.T.: Coherent singlet-triplet oscillations in a silicon-based double quantum dot. Nature 481, 344 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    Morton, J.J.L., McCamey, D.R., Eriksson, M.A., Lyon, S.A.: Embracing the quantum limit in silicon computing. Nature 479, 345 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    Levy, J.: Universal quantum computation with spin-1/2 pairs and Heisenberg exchange. Phys. Rev. Lett. 89, 147902 (2002)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Shi, Z., Simmons, C.B., Prance, J.R., Gamble, J.K., Koh, T.S., Shim, Y.P., Hu, X., Savage, D.E., Lagally, M.G., Eriksson, M.A., Friesen, M., Coppersmith, S.N.: Fast hybrid silicon double-quantum-dot qubit. Phys. Rev. Lett. 108, 140503 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120 (1998)ADSCrossRefGoogle Scholar
  11. 11.
    DiVincenzo, D.P., Bacon, D., Kempe, J., Burkard, G., Whaley, K.B.: Universal quantum computation with the exchange interaction. Nature (London) 408, 339 (2000)ADSCrossRefGoogle Scholar
  12. 12.
    Mehl, S., Bluhm, H., DiVincenzo, D.P.: Two-qubit couplings of singlet-triplet qubits mediated by one quantum state. Phys. Rev. B 90, 045404 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Doherty, A.C., Wardrop, M.P.: Two-qubit gates for resonant exchange qubits. Phys. Rev. Lett. 111, 050503 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    Veldhorst, M., Yang, C.H., Hwang, J.C.C., Huang, W., Dehollain, J.P., Muhonen, J.T., Simmons, S., Laucht, A., Hudson, F.E., Itoh, K.M., Morello, A., Dzurak, A.S., Two, A.: Qubit logic gate in silicon. Nature (London) 526, 410 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    Mehl, S., DiVincenzo, D.P.: Simple operation sequences to couple and interchange quantum information between spin qubits of different kinds. Phys. Rev. B 92, 115448 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    Nakajima, T., Delbecq, M.R., Otsuka, T., Amaha, S., Yoneda, J., Noiri, A., Takeda, K., Allison, G., Ludwig, A., Wieck, A.D., Tarucha, S.: Phase control of local and non-local entanglement in a triple spin qubit. arXiv:1604.02232 (2016)
  17. 17.
    Koh, T.S., Gamble, J.K., Friesen, M., Eriksson, M.A., Coppersmith, S.N.: Pulse-gated quantum-dot hybrid qubit. Phys. Rev. Lett. 109, 250503 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Kim, D., Shi, Z., Simmons, C.B., Ward, D.R., Prance, J.R., Koh, T.S., Gamble, J.K., Savage, D.E., Lagally, M.G., Friesen, M., Coppersmith, S.N., Eriksson, M.A.: Quantum control and process tomography of a semiconductor quantum dot hybrid qubit. Nature 511, 70 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    Kim, D., Ward, D.R., Simmons, C.B., Savage, D.E., Lagally, M.G., Friesen, M., Coppersmith, S.N., Eriksson, M.A.: High-fidelity resonant gating of a silicon-based quantum dot hybrid qubit. Npj Quantum Inf. 1, 15004 (2015)ADSCrossRefGoogle Scholar
  20. 20.
    Wu, X., Ward, D.R., Prance, J.R., Kim, D., Gamble, J.K., Mohr, R.T., Shi, Z., Savage, D.E., Lagally, M.G., Friesen, M., Coppersmith, S.N., Eriksson, M.A.: Two-axis control of a singlettriplet qubit with an integrated micromagnet. PNAS 111, 11938–11942 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    Barnes, E., Rudner, M.S., Martins, F., Malinowski, F.K., Marcus, C.M., Kuemmeth, F.: Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits. Phys. Rev. B 93, 121407(R) (2016)ADSCrossRefGoogle Scholar
  22. 22.
    Pioro-Ladrière, M., Obata, T., Tokura, Y., Shin, Y.S., Kubo, T., Yoshida, K., Taniyama, T., Tarucha, S.: Electrically driven single-electron spin resonance in a slanting Zeeman field. Nat. Phys. 4, 776 (2008)CrossRefGoogle Scholar
  23. 23.
    Gonzalez-Zalba, M., Barraud, S., Ferguson, A., Betz, A.: Probing the limits of gate-based charge sensing. Nat. Commun. 6, 6084 (2014)CrossRefGoogle Scholar
  24. 24.
    Ferraro, E., De Michielis, M., Mazzeo, G., Fanciulli, M., Prati, E.: Effective Hamiltonian for the hybrid double quantum dot qubit. Quantum Inf. Process. 13, 1155 (2014)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Ferraro, E., De Michielis, M., Fanciulli, M., Prati, E.: Effective Hamiltonian for two interacting double-dot exchange-only qubits and their controlled-NOT operations. Quantum Inf. Process. 14, 47 (2015)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    De Michielis, M., Ferraro, E., Fanciulli, M., Prati, E.: Universal set of quantum gates for double-dot exchange-only spin qubits with intradot coupling. J. Phys. A Math. Theor. 48, 065304 (2015)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Ferraro, E., De Michielis, M., Fanciulli, M., Prati, E.: Coherent tunneling by adiabatic passage of an exchange-only spin qubit in a double quantum dot chain. Phys. Rev. B 91, 075435 (2015)ADSCrossRefzbMATHGoogle Scholar
  28. 28.
    Rotta, D., De Michielis, M., Ferraro, E., Fanciulli, M., Prati, E.: Maximum density of quantum information in a scalable CMOS implementation of the hybrid qubit architecture. Quantum Inf. Process. Top. Collection 15, 2253 (2016)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Fong, B.H., Wandzura, S.M.: Universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem. Quantum Inf. Comput. 11, 1003 (2011)zbMATHMathSciNetGoogle Scholar
  30. 30.
    Yuan, H., Khaneja, N.: Time optimal control of coupled qubits under nonstationary interactions. Phys. Rev. A 72, 040301 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    Khaneja, N., Brockett, R., Glaser, S.J.: Time optimal control of coupled qubits under nonstationary interactions. Phys. Rev. A 63, 032308 (2001)ADSCrossRefGoogle Scholar
  32. 32.
    Yoneda, J., Otsuka, T., Nakajima, T., Takakura, T., Obata, T., Pioro-Ladrire, M., Lu, H., Palmstrm, C.J., Gossard, A.C., Tarucha, S.: Fast electrical control of single electron spins in quantum dots with vanishing influence from nuclear spins. Phys. Rev. Lett. 113, 267601 (2014)ADSCrossRefGoogle Scholar
  33. 33.
    Neumann, R., Schreiber, L.R.: Simulation of micro-magnet stray-field dynamics for spin qubit manipulation. J. Appl. Phys. 117, 193903 (2015)ADSCrossRefGoogle Scholar
  34. 34.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  35. 35.
    Marinescu, D.C., Marinescu, G.M.: Classical and Quantum Information. Elsevier, Amsterdam (2012)zbMATHGoogle Scholar
  36. 36.
    Mehl, S.: Two-qubit pulse gate for the three-electron double quantum dot qubit. Phys. Rev. B 91, 035430 (2015)ADSCrossRefGoogle Scholar
  37. 37.
    Taylor, J.M., Petta, J.R., Johnson, A.C., Yacoby, A., Marcus, C.M., Lukin, M.D.: Relaxation, dephasing, and quantum control of electron spins in double quantum dots. Phys. Rev. B 76, 035315 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    Assali, L.V.C., Petrilli, H.M., Capaz, R.B., Koiller, B., Hu, X., Das Sarma, S.: Hyperfine interactions in silicon quantum dots. Phys. Rev. B 83, 165301 (2011)ADSCrossRefGoogle Scholar
  39. 39.
    Testolin, M.J., Cole, J.H., Hollenberg, L.C.L.: Modeling two-spin dynamics in a noisy environment. Phys. Rev. A 80, 042326 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    Möttönen, M., de Sousa, R., Zhang, J., Whaley, K.B.: High-fidelity one-qubit operations under random telegraph noise. Phys. Rev. A 73, 022332 (2006)ADSCrossRefGoogle Scholar
  41. 41.
    Arbitrary Waveform Generators: AWG70000A Series Datasheet. http://www.tek.com/datasheet/awg70000a-arbitrary-waveform-generator-datasheet
  42. 42.
    Schrieffer, J.R., Wolff, P.A.: Relation between the Anderson and Kondo Hamiltonians. Phys. Rev. 149, 491 (1966)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.CNR-IMM, Agrate UnitAgrate Brianza (MB)Italy
  2. 2.Dipartimento di Scienza dei MaterialiUniversity of Milano BicoccaMilanoItaly

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