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Entanglement generation of two quantum dots with Majorana fermions via optimal control

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Abstract

We propose schemes to entangle two quantum dots (QDs) with the aid of Majorana fermions via optimal control. Two paradigmatic cases, the teleportation and the intradot spin flip processes, are considered, respectively, in the charge and spin degrees of QDs. We demonstrate that optimal control techniques can be effectively used to prepare entanglement between two QDs through manipulating their chemical potentials. Significantly, our optimal control generation of entangled states has a prominent advantage: The runtime is much shorter than in adiabatic passage, providing a shortcut to adiabatic entanglement preparation.

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  1. http://qlib.info.

References

  1. Kitaev, A.Y.: Unpaired majorana fermions in quantum wires. Phys. Uspekhi 44, 131 (2001). http://stacks.iop.org/1063-7869/44/i=10S/a=S29

    Article  ADS  Google Scholar 

  2. Read, N., Green, D.: Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum hall effect. Phys. Rev. B 61, 10267–10297 (2000). https://doi.org/10.1103/PhysRevB.61.10267

    Article  ADS  Google Scholar 

  3. Ivanov, D.A.: Non-Abelian statistics of half-quantum vortices in \(\mathit{p}\)-wave superconductors. Phys. Rev. Lett. 86, 268–271 (2001). https://doi.org/10.1103/PhysRevLett.86.268

    Article  ADS  Google Scholar 

  4. Fu, L., Kane, C.L.: Superconducting proximity effect and majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008). https://doi.org/10.1103/PhysRevLett.100.096407

    Article  ADS  Google Scholar 

  5. Sau, J.D., Lutchyn, R.M., Tewari, S., Das Sarma, S.: Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, 040502 (2010). https://doi.org/10.1103/PhysRevLett.104.040502

    Article  ADS  Google Scholar 

  6. Lutchyn, R.M., Sau, J.D., Das Sarma, S.: Majorana fermions and a topological phase transition in semiconductor–superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010). https://doi.org/10.1103/PhysRevLett.105.077001

    Article  ADS  Google Scholar 

  7. Oreg, Y., Refael, G., von Oppen, F.: Helical liquids and majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010). https://doi.org/10.1103/PhysRevLett.105.177002

    Article  ADS  Google Scholar 

  8. Qi, X.-L., Zhang, S.-C.: Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011). https://doi.org/10.1103/RevModPhys.83.1057

    Article  ADS  Google Scholar 

  9. Alicea, J.: New directions in the pursuit of majorana fermions in solid state systems. Rep. Progr. Phys. 75, 076501 (2012). http://stacks.iop.org/0034-4885/75/i=7/a=076501

    Article  ADS  Google Scholar 

  10. Kitaev, A.: Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003). https://doi.org/10.1016/S0003-4916(02)00018-0

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Nayak, C., Simon, S.H., Stern, A., Freedman, M., Das Sarma, S.: Non-abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008). https://doi.org/10.1103/RevModPhys.80.1083

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Jiang, L., Kane, C.L., Preskill, J.: Interface between topological and superconducting qubits. Phys. Rev. Lett. 106, 130504 (2011). https://doi.org/10.1103/PhysRevLett.106.130504

    Article  ADS  Google Scholar 

  13. Bonderson, P., Lutchyn, R.M.: Topological quantum buses: coherent quantum information transfer between topological and conventional qubits. Phys. Rev. Lett. 106, 130505 (2011). https://doi.org/10.1103/PhysRevLett.106.130505

    Article  ADS  Google Scholar 

  14. Hassler, F., Akhmerov, A.R., Hou, C.-Y., Beenakker, C.W.J.: Anyonic interferometry without anyons: how a flux qubit can read out a topological qubit. New J. Phys. 12(12), 125002 (2010). http://stacks.iop.org/1367-2630/12/i=12/a=125002

    Article  ADS  Google Scholar 

  15. Sau, J.D., Tewari, S., Das Sarma, S.: Universal quantum computation in a semiconductor quantum wire network. Phys. Rev. A 82, 052322 (2010). https://doi.org/10.1103/PhysRevA.82.052322

    Article  ADS  Google Scholar 

  16. Leijnse, M., Flensberg, K.: Hybrid topological-spin qubit systems for two-qubit-spin gates. Phys. Rev. B 86, 104511 (2012). https://doi.org/10.1103/PhysRevB.86.104511

    Article  ADS  Google Scholar 

  17. Hyart, T., van Heck, B., Fulga, I.C., Burrello, M., Akhmerov, A.R., Beenakker, C.W.J.: Flux-controlled quantum computation with majorana fermions. Phys. Rev. B 88, 035121 (2013). https://doi.org/10.1103/PhysRevB.88.035121

    Article  ADS  Google Scholar 

  18. Kovalev, A.A., De, A., Shtengel, K.: Spin transfer of quantum information between majorana modes and a resonator. Phys. Rev. Lett. 112, 106402 (2014). https://doi.org/10.1103/PhysRevLett.112.106402

    Article  ADS  Google Scholar 

  19. Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998). https://doi.org/10.1103/PhysRevA.57.120

    Article  ADS  Google Scholar 

  20. 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). https://doi.org/10.1126/science.1116955. http://science.sciencemag.org/content/309/5744/2180

    Article  ADS  Google Scholar 

  21. Koppens, F.H.L., Folk, J.A., Elzerman, J.M., Hanson, R., van Beveren, L.H.W., Vink, I.T., Tranitz, H.P., Wegscheider, W., Kouwenhoven, L.P., Vandersypen, L.M.K.: Control and detection of singlet-triplet mixing in a random nuclear field. Science 309, 1346–1350 (2005). https://doi.org/10.1126/science.1113719. http://science.sciencemag.org/content/309/5739/1346

    Article  ADS  Google Scholar 

  22. Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T., Glaser, S.: Optimal control of coupled spin dynamics: design of nmr pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172, 296–305 (2005). https://doi.org/10.1016/j.jmr.2004.11.004. http://www.sciencedirect.com/science/article/pii/S1090780704003696

    Article  ADS  Google Scholar 

  23. Shi, Z.C., Wang, W., Yi, X.X.: Entangled states of two quantum dots mediated by Majorana fermions. New J. Phys. 18(2), 023005 (2016). http://stacks.iop.org/1367-2630/18/i=2/a=023005

    Article  ADS  Google Scholar 

  24. Machnes, S., Sander, U., Glaser, S.J., de Fouquières, P., Gruslys, A., Schirmer, S., Schulte-Herbrüggen, T.: Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework. Phys. Rev. A 84, 022305 (2011). https://doi.org/10.1103/PhysRevA.84.022305

    Article  ADS  Google Scholar 

  25. Fu, L.: Electron teleportation via majorana bound states in a mesoscopic superconductor. Phys. Rev. Lett. 104, 056402 (2010). https://doi.org/10.1103/PhysRevLett.104.056402

    Article  ADS  Google Scholar 

  26. Zazunov, A., Yeyati, A.L., Egger, R.: Coulomb blockade of majorana-fermion-induced transport. Phys. Rev. B 84, 165440 (2011). https://doi.org/10.1103/PhysRevB.84.165440

    Article  ADS  Google Scholar 

  27. Hützen, R., Zazunov, A., Braunecker, B., Yeyati, A.L., Egger, R.: Majorana single-charge transistor. Phys. Rev. Lett. 109, 166403 (2012). https://doi.org/10.1103/PhysRevLett.109.166403

    Article  ADS  Google Scholar 

  28. Plugge, S., Zazunov, A., Sodano, P., Egger, R.: Majorana entanglement bridge. Phys. Rev. B 91, 214507 (2015). https://doi.org/10.1103/PhysRevB.91.214507

    Article  ADS  Google Scholar 

  29. Flensberg, K.: Non-Abelian operations on majorana fermions via single-charge control. Phys. Rev. Lett. 106, 090503 (2011). https://doi.org/10.1103/PhysRevLett.106.090503

    Article  ADS  Google Scholar 

  30. Wang, Z., Hu, X.-Y., Liang, Q.-F., Hu, X.: Detecting majorana fermions by nonlocal entanglement between quantum dots. Phys. Rev. B 87, 214513 (2013). https://doi.org/10.1103/PhysRevB.87.214513

    Article  ADS  Google Scholar 

  31. Walter, S., Budich, J.C.: Teleportation-induced entanglement of two nanomechanical oscillators coupled to a topological superconductor. Phys. Rev. B 89, 155431 (2014). https://doi.org/10.1103/PhysRevB.89.155431

    Article  ADS  Google Scholar 

  32. Nazarov, Y.V., Blanter, Y.M.: Quantum Transport: Introduction to Nanoscience. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  33. Arenz, C., Gualdi, G., Burgarth, D.: Control of open quantum systems: case study of the central spin model. New J. Phys. 16(6), 065023 (2014). http://stacks.iop.org/1367-2630/16/i=6/a=065023

    Article  ADS  Google Scholar 

  34. Tewari, S., Zhang, C., Das Sarma, S., Nayak, C., Lee, D.-H.: Testable signatures of quantum nonlocality in a two-dimensional chiral \(p\)-wave superconductor. Phys. Rev. Lett. 100, 027001 (2008). https://doi.org/10.1103/PhysRevLett.100.027001

    Article  ADS  Google Scholar 

  35. Leijnse, M., Flensberg, K.: Quantum information transfer between topological and spin qubit systems. Phys. Rev. Lett. 107, 210502 (2011). https://doi.org/10.1103/PhysRevLett.107.210502

    Article  ADS  Google Scholar 

  36. Ke, S.-S., Lü, H.-F., Yang, H.-J., Guo, Y., Zhang, H.-W.: Nonlocal entanglement and noise between spin qubits induced by Majorana bound states. Phys. Lett. A 379, 170–174 (2015). https://doi.org/10.1016/j.physleta.2014.08.015. http://www.sciencedirect.com/science/article/pii/S0375960114008287

    Article  ADS  Google Scholar 

  37. Khaetskii, A.V., Nazarov, Y.V.: Spin relaxation in semiconductor quantum dots. Phys. Rev. B 61, 12639–12642 (2000). https://doi.org/10.1103/PhysRevB.61.12639

    Article  ADS  Google Scholar 

  38. Mourik, V., Zuo, K., Frolov, S.M., Plissard, S.R., Bakkers, E.P.A.M., Kouwenhoven, L.P.: Signatures of Majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012). https://doi.org/10.1126/science.1222360. http://science.sciencemag.org/content/336/6084/1003

    Article  ADS  Google Scholar 

  39. Rokhinson, L.P., Liu, X., Furdyna, J.K.: The fractional ac josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles. Nat. Phys. 8, 795–799 (2012). https://doi.org/10.1038/nphys2429. http://www.nature.com/nphys/journal/v8/n11/abs/nphys2429.html#supplementary-information

    Article  ADS  Google Scholar 

  40. van Woerkom, D.J., Geresdi, A., Kouwenhoven, L.P.: One minute parity lifetime of a nbtin cooper-pair transistor. Nat. Phys. 11, 547–550 (2015). https://doi.org/10.1038/nphys3342. http://www.nature.com/nphys/journal/v11/n7/abs/nphys3342.html#supplementary-information

    Article  ADS  Google Scholar 

  41. Higginbotham, A., Albrecht, S., Kiršanskas, G., Chang, W., Kuemmeth, F., Krogstrup, P., Jespersen, T., Nygård, J., Flensberg, K., Marcus, C.: Parity lifetime of bound states in a proximitized semiconductor nanowire. Nat. Phys. 11, 1017–1021 (2015). https://doi.org/10.1038/nphys3461. http://www.nature.com/nphys/journal/v11/n12/abs/nphys3461.html#supplementary-information

    Article  ADS  Google Scholar 

  42. Das, A., Ronen, Y., Most, Y., Oreg, Y., Heiblum, M., Shtrikman, H.: Zero-bias peaks and splitting in an al-inas nanowire topological superconductor as a signature of Majorana fermions. Nat. Phys. 8, 887–895 (2012). https://doi.org/10.1038/nphys2479. http://www.nature.com/nphys/journal/v8/n12/abs/nphys2479.html#supplementary-information

    Article  ADS  Google Scholar 

  43. Deng, M.T., Yu, C.L., Huang, G.Y., Larsson, M., Caroff, P., Xu, H.Q.: Anomalous zero-bias conductance peak in a nb-insb nanowire-nb hybrid device. Nano Lett. 12, 6414–6419 (2012). https://doi.org/10.1021/nl303758w

    Article  ADS  Google Scholar 

  44. Finck, A.D.K., Van Harlingen, D.J., Mohseni, P.K., Jung, K., Li, X.: Anomalous modulation of a zero-bias peak in a hybrid nanowire-superconductor device. Phys. Rev. Lett. 110, 126406 (2013). https://doi.org/10.1103/PhysRevLett.110.126406

    Article  ADS  Google Scholar 

  45. Fasth, C., Fuhrer, A., Samuelson, L., Golovach, V.N., Loss, D.: Direct measurement of the spin-orbit interaction in a two-electron inas nanowire quantum dot. Phys. Rev. Lett. 98, 266801 (2007). https://doi.org/10.1103/PhysRevLett.98.266801

    Article  ADS  Google Scholar 

  46. Nilsson, H., Caroff, P., Thelander, C., Larsson, M., Wagner, J., Wernersson, L.-E., Samuelson, L., Xu, H.: Giant, level-dependent g factors in insb nanowire quantum dots. Nano Lett. 9, 3151–3156 (2009). https://doi.org/10.1021/nl901333a

    Article  ADS  Google Scholar 

  47. Dolde, F., Bergholm, V., Wang, Y., Jakobi, I., Naydenov, B., Pezzagna, S., Meijer, J., Jelezko, F., Neumann, P., Schulte-Herbrüggen, T.: High-fidelity spin entanglement using optimal control. Nat. Commun. 5, 4371 (2014). https://doi.org/10.1038/ncomms4371

    Article  Google Scholar 

  48. Waldherr, G., Wang, Y., Zaiser, S., Jamali, M., Schulte-Herbrüggen, T., Abe, H., Ohshima, T., Isoya, J., Du, J., Neumann, P., et al.: Quantum error correction in a solid-state hybrid spin register. Nature 506, 204–207 (2014). https://doi.org/10.1038/nature12919

    Article  ADS  Google Scholar 

  49. Nadj-Perge, S., Frolov, S., Bakkers, E., Kouwenhoven, L.P.: Spin–orbit qubit in a semiconductor nanowire. Nature 468, 1084–1087 (2010). https://doi.org/10.1038/nature09682. http://www.nature.com/nature/journal/v468/n7327/abs/nature09682.html#supplementary-information

    Article  ADS  Google Scholar 

  50. Petta, J.R., Johnson, A.C., Marcus, C.M., Hanson, M.P., Gossard, A.C.: Manipulation of a single charge in a double quantum dot. Phys. Rev. Lett. 93, 186802 (2004). https://doi.org/10.1103/PhysRevLett.93.186802

    Article  ADS  Google Scholar 

  51. Petersson, K.D., Petta, J.R., Lu, H., Gossard, A.C.: Quantum coherence in a one-electron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010). https://doi.org/10.1103/PhysRevLett.105.246804

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the Doctoral Startup Fund of East China University of Technology and the National Natural Science Foundation of China (Grants Nos. 11375025, 11274043). We acknowledge the DYNAMO code [24].

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Authors and Affiliations

  1. School of Science, East China University of Technology, Nanchang, 330013, China

    Xiong-Peng Zhang

  2. School of Physics, Beijing Institute of Technology, Beijing, 100081, China

    Xiong-Peng Zhang, Bin Shao & Jian Zou

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Zhang, XP., Shao, B. & Zou, J. Entanglement generation of two quantum dots with Majorana fermions via optimal control. Quantum Inf Process 17, 272 (2018). https://doi.org/10.1007/s11128-018-2039-y

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