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Spin Quantum Computing

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Handbook of Spintronics

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Abstract

This chapter describes the use of electron spins in semiconductor quantum dots as quantum bits for quantum information processing. Among the central themes of the chapter is the mechanism for a two-qubit operation based on the exchange interaction. Another important topic pertains to the mechanisms that lead to the loss of quantum coherence and are related to phonons or nuclear spins in the host semiconductor. The last part of this chapter is focused on the prospects for extending the ideas of spin-based quantum information to new materials such as graphene, where both nuclear-spin- and phonon-induced decoherence and relaxation are suppressed.

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Abbreviations

13C:

Carbon-13

2D:

Two dimensional

2DEG:

Two-dimensional electron gas

AlGaAs:

Aluminum gallium arsenide

As:

Arsenic

CNOT:

Controlled NOT (NOT is not acronym)

EPC:

Electron phonon coupling

Ga:

Gallium

GaAs:

Gallium arsenide

HF:

Hyperfine

InGaAs:

Indium gallium arsenide

MoS2 :

Molybdenum disulfide

QD:

Quantum dot

QPC:

Quantum point contact

RSA:

Rivest–Shamir–Adleman

SiGe:

Silicon–germanium

SO:

Spin orbit

SU(2):

Special unitary group in two dimensions

WS2 :

Tungsten disulfide

XOR:

Exclusive OR (OR is not an acronym)

References

  1. Struck PR (2013) Spin coherence in carbon-based nanodevices. Chapter 2, PhD thesis, University of Konstanz

    Google Scholar 

  2. Shor P (1994) Algorithms for quantum computation: discrete logarithms and factoring. Proceedings of the 35th annual symposium on the foundations of computer science. IEEE Press, Los Alamitos, p 124

    Google Scholar 

  3. DiVincenzo DP (2000) The physical implementation of quantum computation. Fortschr Phys 48:771; quant-ph/0002077

    Article  MATH  Google Scholar 

  4. Nielsen MA, Chuang IL (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge, UK

    MATH  Google Scholar 

  5. Preskill J (1998) Reliable quantum computers. Proc Roy Soc Lond A 454:385

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Mermin ND (2007) Quantum computer science: an introduction. Cambridge University Press, Cambridge, UK

    Book  Google Scholar 

  7. Knill E (2005) Quantum computing with realistically noisy devices. Nature 434:39

    Article  ADS  Google Scholar 

  8. Fowler AG, Mariantoni M, Martinis JM, Cleland AN (2012) Surface codes: Towards practical large-scale quantum computation. Phys Rev A 86:032324

    Article  ADS  Google Scholar 

  9. DiVincenzo DP (1995) Two-qubit gates are universal for quantum computation. Phys Rev A 51:1015

    Article  ADS  Google Scholar 

  10. Barenco A et al (1995) Elementary gates for quantum computation. Phys Rev A 52:3457

    Article  ADS  Google Scholar 

  11. Loss D, DiVincenzo DP (1998) Quantum computation with quantum dots. Phys Rev B 57:120

    Article  ADS  Google Scholar 

  12. Cirac JI, Zoller P (2012) Goals and opportunities in quantum simulation. Nat Phys 8:264

    Article  Google Scholar 

  13. Deutsch D (1985) Quantum theory, the Church-Turing principle and the universal quantum computer. Proc Roy Soc Lond A 400:97

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Kane BE (1998) A silicon-based nuclear spin quantum computer. Nature 393:6681

    Article  Google Scholar 

  15. Vrijen R, Yablonovitch E, Wang K, Jiang HW, Balandin A, Roychowdhury V, Mor T, DiVincenzo DP (2000) Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures. Phys Rev A 62:012306

    Article  ADS  Google Scholar 

  16. Barnes CHW, Shilton JM, Robinson AM (2000) Quantum computation using electrons trapped by surface acoustic waves. Phys Rev B 62:8410

    Article  ADS  Google Scholar 

  17. Kloeffel C, Loss D (2013) Prospects for Spin-based quantum computing. Annu Rev Condens Matter Phys 4:51; arXiv:1204.5917

    Article  ADS  Google Scholar 

  18. Hanson R, Kouwenhoven LP, Petta JR, Tarucha JR, Vandersypen LMK (2007) Spins in few-electron quantum dots. Rev Mod Phys 79:1217

    Article  ADS  Google Scholar 

  19. Burkard G, Loss D, DiVincenzo D (1999) Coupled quantum dots as quantum gates. Phys Rev A 59:2070

    ADS  Google Scholar 

  20. Petta JR et al (2005) Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots. Science 309:2180

    Article  ADS  Google Scholar 

  21. Kavokin KV (2001) Anisotropic exchange interaction of localized conduction-band electrons in semiconductors. Phys Rev B 64:075305

    Article  ADS  Google Scholar 

  22. Bonesteel NE, Stepanenko D, DiVincenzo DP (2001) Anisotropic spin exchange in pulsed quantum gates. Phys Rev Lett 87:207901

    Article  ADS  Google Scholar 

  23. Koppens FHL et al (2006) Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442:766

    Article  ADS  Google Scholar 

  24. Brunner R et al (2011) Two-qubit gate of combined single-spin rotation and interdot spin exchange in a double quantum dot. Phys Rev Lett 107:146801

    Article  ADS  Google Scholar 

  25. DiVincenzo DP, Bacon D, Kempe J, Burkard G, Whaley KB (2000) Universal quantum computation with the exchange interaction. Nature 408:339

    Article  ADS  Google Scholar 

  26. Kawano Y et al (2005) Existence of the exact CNOT on a quantum computer with the exchange interaction. Quantum Inf Process 4:65

    Article  MathSciNet  Google Scholar 

  27. Fong BH, Wandzura SM (2011) Universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem. J Quantum Inf Comput 11:1003; arXiv:quant-ph/0411013

    MathSciNet  MATH  Google Scholar 

  28. Zeuch D (2011) Quantum computation with restricted spin interactions. Diploma thesis, University of Konstanz

    Google Scholar 

  29. Medford J et al (2013) Quantum-dot-based resonant exchange qubit. Phys Rev Lett 111:050501

    Article  ADS  Google Scholar 

  30. Taylor JM, Srinivasa V, Medford J (2013) Electrically protected resonant exchange qubits in triple quantum dots. Phys Rev Lett 111:050502

    Article  ADS  Google Scholar 

  31. Doherty AC, Wardrop MP (2013) Two-qubit gates for resonant exchange qubits. Phys Rev Lett 111:050503

    Article  ADS  Google Scholar 

  32. Levy J (2002) Universal quantum computation with spin-1/2 pairs and Heisenberg exchange. Phys Rev Lett 89:147902

    Article  MathSciNet  ADS  Google Scholar 

  33. Kempe J, Whaley KB (2002) Exact gate sequences for universal quantum computation using the XY interaction alone. Phys Rev A 65:052330

    Article  ADS  Google Scholar 

  34. Vala J, Whaley KB (2002) Encoded universality for generalized anisotropic exchange hamiltonians. Phys Rev A 66:022304

    Article  MathSciNet  ADS  Google Scholar 

  35. Burkard G, Loss D, DiVincenzo DP, Smolin JA (1999) Physical optimization of quantum error correction circuits. Phys Rev B 60:11404

    Article  ADS  Google Scholar 

  36. Khaetskii AV, Nazarov YV (2001) Spin-flip transitions between zeeman sublevels in semiconductor quantum dots. Phys Rev B 64:125316

    Article  ADS  Google Scholar 

  37. Dyakonov MI, Yu V (1986) Spin relaxation of two-dimensional electrons in noncentrosymmetric semiconductors. Kachorovskii Fiz Tech Poluprovodn 20:178; Sov Phys Semicond 20:110

    Google Scholar 

  38. van Vleck J (1940) Paramagnetic relaxation times for titanium and chrome alum. Phys Rev 57:426

    Article  ADS  Google Scholar 

  39. Amasha S, MacLean K, Radu IP, Zumbühl DM, Kastner MA, Hanson MP, Gossard AC (2008) Electrical control of spin relaxation in a quantum dot. Phys Rev Lett 100:46803

    Article  ADS  Google Scholar 

  40. Bulaev DV, Loss D (2005) Spin relaxation and decoherence of holes in quantum dots. Phys Rev Lett 95:076805

    Article  ADS  Google Scholar 

  41. Heiss D et al (2007) Observation of extremely slow hole spin relaxation in self-assembled quantum dots. Phys Rev B 76:241306

    Article  ADS  Google Scholar 

  42. Gerardot BD et al (2008) Optical pumping of a single hole spin in a quantum dot. Nature 451:441

    Article  ADS  Google Scholar 

  43. Golovach VN, Khaetskii AV, Loss D (2004) Phonon-induced decay of the electron spin in quantum dots. Phys Rev Lett 93:016601

    Article  ADS  Google Scholar 

  44. Coish WA (2006) Spins in quantum dots: Hyperfine interaction, transport, and coherent control. PhD thesis, University of Basel

    Google Scholar 

  45. Coish WA, Baugh J (2009) Nuclear spins in nanostructures. Phys Status Solidi B 246:2203

    Article  ADS  Google Scholar 

  46. Urbaszek B et al (2013) Nuclear spin physics in quantum dots: An optical investigation. Rev Mod Phys 85:79

    Article  ADS  Google Scholar 

  47. Klauser D, Coish WA, Loss D (2006) Nuclear spin state narrowing via gate-controlled Rabi oscillations in a double quantum dot. Phys Rev B 73:205302

    Article  ADS  Google Scholar 

  48. Fischer J, Coish W, Bulaev D, Loss D (2008) Spin decoherence of a heavy hole coupled to nuclear spins in a quantum dot. Phys Rev B 78:155329

    Article  ADS  Google Scholar 

  49. Coish WA, Loss D (2004) Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics. Phys Rev B 70:195340

    Article  ADS  Google Scholar 

  50. Chekhovich EA et al (2010) Pumping of nuclear spins by optical excitation of spin-forbidden transitions in a quantum dot. Phys Rev Lett 104:066804

    Article  ADS  Google Scholar 

  51. Foletti S, Bluhm H, Mahalu D, Umansky V, Yacoby A (2009) Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization. Nat Phys 5:903

    Article  Google Scholar 

  52. Ribeiro H, Burkard G (2009) Nuclear state preparation via landau-zener-stückelberg transitions in double quantum dots. Phys Rev Lett 102:216802

    Article  ADS  Google Scholar 

  53. Stepanenko D, Burkard G, Giedke G, Imamoglu A (2006) Enhancement of electron spin coherence by optical preparation of nuclear spins. Phys Rev Lett 96:136401

    Article  ADS  Google Scholar 

  54. Togan E, Chu Y, Imamoglu A, Lukin MD (2011) Laser cooling and real-time measurement of the nuclear spin environment of a solid-state qubit. Nature 478:497501

    Article  Google Scholar 

  55. Taylor JM et al (2005) Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins. Nat Phys 1:177

    Article  Google Scholar 

  56. Hanson R, Burkard G (2007) Universal set of quantum gates for double-dot spin qubits with fixed interdot coupling. Phys Rev Lett 98:050502

    Article  ADS  Google Scholar 

  57. Trauzettel B, Bulaev DV, Loss D, Burkard G (2007) Spin qubits in graphene quantum dots. Nat Phys 3:192

    Article  Google Scholar 

  58. Diez M, Burkard G (2012) Bias-dependent D’yakonov-Perel’spin relaxation in bilayer graphene. Phys Rev B 85:195412

    Article  ADS  Google Scholar 

  59. Kormanyos A et al (2013) Intrinsic and substrate induced spin-orbit interaction in chirally stacked trilayer graphene. Phys Rev B 88:045416

    Article  ADS  Google Scholar 

  60. Klinovaja J, Loss D (2013) Spintronics in MoS2 monolayer quantum wires. Phys Rev B 88:075404

    Article  ADS  Google Scholar 

  61. Rohling N, Burkard G (2012) Universal quantum computing with spin and valley states. New J Phys 14:083008

    Article  Google Scholar 

  62. Katsnelson MI (2012) Graphene: Carbon in Two Dimensions. Graphene. Cambridge University Press

    Google Scholar 

  63. Brey L, Fertig HA (2006) Electronic states of graphene nanoribbons studied with the Dirac equation. Phys Rev B 73:235411

    Article  ADS  Google Scholar 

  64. Tworzydło J, Trauzettel B, Titov M, Rycerz A, Beenakker CWJ (2006) Sub-poissonian shot noise in graphene. Phys Rev Lett 96:246802

    Article  ADS  Google Scholar 

  65. Liu XL, Hug D, Vandersypen LMK (2010) Gate-defined graphene double quantum dot and excited state spectroscopy. Nano Lett 10:1623

    Article  ADS  Google Scholar 

  66. Braun M, Struck PR, Burkard G (2011) Spin exchange interaction with tunable range between graphene quantum dots. Phys Rev B 84:115445

    Article  ADS  Google Scholar 

  67. Giovannetti G, Khomyakov PA, Brocks G, Kelly PJ, van den Brink J (2007) Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations. Phys Rev B 76:073103

    Article  ADS  Google Scholar 

  68. Recher P, Nilsson J, Burkard G, Trauzettel B (2009) Bound states and magnetic field induced valley splitting in gate-tunable graphene quantum dots. Phys Rev B 79:85407

    Article  ADS  Google Scholar 

  69. Goossens ASM et al (2012) Gate-defined confinement in bilayer graphene-hexagonal boron nitride hybrid devices. Nano Lett 12:4656

    Article  ADS  Google Scholar 

  70. Struck PR, Burkard G (2010) Effective time-reversal symmetry breaking in the spin relaxation in a graphene quantum dot. Phys Rev B 82:125401

    Article  ADS  Google Scholar 

  71. Fischer J, Trauzettel B, Loss D (2009) Hyperfine interaction and electron-spin decoherence in graphene and carbon nanotube quantum dots. Phys Rev B 80:155401

    Article  ADS  Google Scholar 

  72. Palyi A, Burkard G (2009) Hyperfine-induced valley mixing and the spin-valley blockade in carbon-based. Phys Rev B 80:201404(R)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Konstanz, Konstanz, D-78457, Germany

    Philipp R. Struck & Guido Burkard

Authors
  1. Philipp R. Struck
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  2. Guido Burkard
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Corresponding author

Correspondence to Philipp R. Struck .

Editor information

Editors and Affiliations

  1. Department of Electronics, The University of York, York, United Kingdom

    Yongbing Xu

  2. Dept. Physics, University of California, Santa Barbara College of Letters & Science, Santa Barbara, California, USA

    David D. Awschalom

  3. Graduate School of Engineering, Tohoku University, Aoba-ku, Sendai, Japan

    Junsaku Nitta

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Struck, P.R., Burkard, G. (2015). Spin Quantum Computing. In: Xu, Y., Awschalom, D., Nitta, J. (eds) Handbook of Spintronics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7604-3_5-1

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  • DOI: https://doi.org/10.1007/978-94-007-7604-3_5-1

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  • Online ISBN: 978-94-007-7604-3

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