Spin Quantum Computing

Living reference work entry

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.

Keywords

Hyperfine Interaction Quantum Gate Gate Operation CNOT Gate Quantum Error Correction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of 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. 1.
    Struck PR (2013) Spin coherence in carbon-based nanodevices. Chapter 2, PhD thesis, University of KonstanzGoogle Scholar
  2. 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 124Google Scholar
  3. 3.
    DiVincenzo DP (2000) The physical implementation of quantum computation. Fortschr Phys 48:771; quant-ph/0002077CrossRefMATHGoogle Scholar
  4. 4.
    Nielsen MA, Chuang IL (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge, UKMATHGoogle Scholar
  5. 5.
    Preskill J (1998) Reliable quantum computers. Proc Roy Soc Lond A 454:385MathSciNetCrossRefADSMATHGoogle Scholar
  6. 6.
    Mermin ND (2007) Quantum computer science: an introduction. Cambridge University Press, Cambridge, UKCrossRefGoogle Scholar
  7. 7.
    Knill E (2005) Quantum computing with realistically noisy devices. Nature 434:39CrossRefADSGoogle Scholar
  8. 8.
    Fowler AG, Mariantoni M, Martinis JM, Cleland AN (2012) Surface codes: Towards practical large-scale quantum computation. Phys Rev A 86:032324CrossRefADSGoogle Scholar
  9. 9.
    DiVincenzo DP (1995) Two-qubit gates are universal for quantum computation. Phys Rev A 51:1015CrossRefADSGoogle Scholar
  10. 10.
    Barenco A et al (1995) Elementary gates for quantum computation. Phys Rev A 52:3457CrossRefADSGoogle Scholar
  11. 11.
    Loss D, DiVincenzo DP (1998) Quantum computation with quantum dots. Phys Rev B 57:120CrossRefADSGoogle Scholar
  12. 12.
    Cirac JI, Zoller P (2012) Goals and opportunities in quantum simulation. Nat Phys 8:264CrossRefGoogle Scholar
  13. 13.
    Deutsch D (1985) Quantum theory, the Church-Turing principle and the universal quantum computer. Proc Roy Soc Lond A 400:97MathSciNetCrossRefADSMATHGoogle Scholar
  14. 14.
    Kane BE (1998) A silicon-based nuclear spin quantum computer. Nature 393:6681CrossRefGoogle Scholar
  15. 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 62:012306CrossRefADSGoogle Scholar
  16. 16.
    Barnes CHW, Shilton JM, Robinson AM (2000) Quantum computation using electrons trapped by surface acoustic waves. Phys Rev B 62:8410CrossRefADSGoogle Scholar
  17. 17.
    Kloeffel C, Loss D (2013) Prospects for Spin-based quantum computing. Annu Rev Condens Matter Phys 4:51; arXiv:1204.5917CrossRefADSGoogle Scholar
  18. 18.
    Hanson R, Kouwenhoven LP, Petta JR, Tarucha JR, Vandersypen LMK (2007) Spins in few-electron quantum dots. Rev Mod Phys 79:1217CrossRefADSGoogle Scholar
  19. 19.
    Burkard G, Loss D, DiVincenzo D (1999) Coupled quantum dots as quantum gates. Phys Rev A 59:2070ADSGoogle Scholar
  20. 20.
    Petta JR et al (2005) Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots. Science 309:2180CrossRefADSGoogle Scholar
  21. 21.
    Kavokin KV (2001) Anisotropic exchange interaction of localized conduction-band electrons in semiconductors. Phys Rev B 64:075305CrossRefADSGoogle Scholar
  22. 22.
    Bonesteel NE, Stepanenko D, DiVincenzo DP (2001) Anisotropic spin exchange in pulsed quantum gates. Phys Rev Lett 87:207901CrossRefADSGoogle Scholar
  23. 23.
    Koppens FHL et al (2006) Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442:766CrossRefADSGoogle Scholar
  24. 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 107:146801CrossRefADSGoogle Scholar
  25. 25.
    DiVincenzo DP, Bacon D, Kempe J, Burkard G, Whaley KB (2000) Universal quantum computation with the exchange interaction. Nature 408:339CrossRefADSGoogle Scholar
  26. 26.
    Kawano Y et al (2005) Existence of the exact CNOT on a quantum computer with the exchange interaction. Quantum Inf Process 4:65MathSciNetCrossRefGoogle Scholar
  27. 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/0411013MathSciNetMATHGoogle Scholar
  28. 28.
    Zeuch D (2011) Quantum computation with restricted spin interactions. Diploma thesis, University of KonstanzGoogle Scholar
  29. 29.
    Medford J et al (2013) Quantum-dot-based resonant exchange qubit. Phys Rev Lett 111:050501CrossRefADSGoogle Scholar
  30. 30.
    Taylor JM, Srinivasa V, Medford J (2013) Electrically protected resonant exchange qubits in triple quantum dots. Phys Rev Lett 111:050502CrossRefADSGoogle Scholar
  31. 31.
    Doherty AC, Wardrop MP (2013) Two-qubit gates for resonant exchange qubits. Phys Rev Lett 111:050503CrossRefADSGoogle Scholar
  32. 32.
    Levy J (2002) Universal quantum computation with spin-1/2 pairs and Heisenberg exchange. Phys Rev Lett 89:147902MathSciNetCrossRefADSGoogle Scholar
  33. 33.
    Kempe J, Whaley KB (2002) Exact gate sequences for universal quantum computation using the XY interaction alone. Phys Rev A 65:052330CrossRefADSGoogle Scholar
  34. 34.
    Vala J, Whaley KB (2002) Encoded universality for generalized anisotropic exchange hamiltonians. Phys Rev A 66:022304MathSciNetCrossRefADSGoogle Scholar
  35. 35.
    Burkard G, Loss D, DiVincenzo DP, Smolin JA (1999) Physical optimization of quantum error correction circuits. Phys Rev B 60:11404CrossRefADSGoogle Scholar
  36. 36.
    Khaetskii AV, Nazarov YV (2001) Spin-flip transitions between zeeman sublevels in semiconductor quantum dots. Phys Rev B 64:125316CrossRefADSGoogle Scholar
  37. 37.
    Dyakonov MI, Yu V (1986) Spin relaxation of two-dimensional electrons in noncentrosymmetric semiconductors. Kachorovskii Fiz Tech Poluprovodn 20:178; Sov Phys Semicond 20:110Google Scholar
  38. 38.
    van Vleck J (1940) Paramagnetic relaxation times for titanium and chrome alum. Phys Rev 57:426CrossRefADSGoogle Scholar
  39. 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 100:46803CrossRefADSGoogle Scholar
  40. 40.
    Bulaev DV, Loss D (2005) Spin relaxation and decoherence of holes in quantum dots. Phys Rev Lett 95:076805CrossRefADSGoogle Scholar
  41. 41.
    Heiss D et al (2007) Observation of extremely slow hole spin relaxation in self-assembled quantum dots. Phys Rev B 76:241306CrossRefADSGoogle Scholar
  42. 42.
    Gerardot BD et al (2008) Optical pumping of a single hole spin in a quantum dot. Nature 451:441CrossRefADSGoogle Scholar
  43. 43.
    Golovach VN, Khaetskii AV, Loss D (2004) Phonon-induced decay of the electron spin in quantum dots. Phys Rev Lett 93:016601CrossRefADSGoogle Scholar
  44. 44.
    Coish WA (2006) Spins in quantum dots: Hyperfine interaction, transport, and coherent control. PhD thesis, University of BaselGoogle Scholar
  45. 45.
    Coish WA, Baugh J (2009) Nuclear spins in nanostructures. Phys Status Solidi B 246:2203CrossRefADSGoogle Scholar
  46. 46.
    Urbaszek B et al (2013) Nuclear spin physics in quantum dots: An optical investigation. Rev Mod Phys 85:79CrossRefADSGoogle Scholar
  47. 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 73:205302CrossRefADSGoogle Scholar
  48. 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 78:155329CrossRefADSGoogle Scholar
  49. 49.
    Coish WA, Loss D (2004) Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics. Phys Rev B 70:195340CrossRefADSGoogle Scholar
  50. 50.
    Chekhovich EA et al (2010) Pumping of nuclear spins by optical excitation of spin-forbidden transitions in a quantum dot. Phys Rev Lett 104:066804CrossRefADSGoogle Scholar
  51. 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 5:903CrossRefGoogle Scholar
  52. 52.
    Ribeiro H, Burkard G (2009) Nuclear state preparation via landau-zener-stückelberg transitions in double quantum dots. Phys Rev Lett 102:216802CrossRefADSGoogle Scholar
  53. 53.
    Stepanenko D, Burkard G, Giedke G, Imamoglu A (2006) Enhancement of electron spin coherence by optical preparation of nuclear spins. Phys Rev Lett 96:136401CrossRefADSGoogle Scholar
  54. 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 478:497501CrossRefGoogle Scholar
  55. 55.
    Taylor JM et al (2005) Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins. Nat Phys 1:177CrossRefGoogle Scholar
  56. 56.
    Hanson R, Burkard G (2007) Universal set of quantum gates for double-dot spin qubits with fixed interdot coupling. Phys Rev Lett 98:050502CrossRefADSGoogle Scholar
  57. 57.
    Trauzettel B, Bulaev DV, Loss D, Burkard G (2007) Spin qubits in graphene quantum dots. Nat Phys 3:192CrossRefGoogle Scholar
  58. 58.
    Diez M, Burkard G (2012) Bias-dependent D’yakonov-Perel’spin relaxation in bilayer graphene. Phys Rev B 85:195412CrossRefADSGoogle Scholar
  59. 59.
    Kormanyos A et al (2013) Intrinsic and substrate induced spin-orbit interaction in chirally stacked trilayer graphene. Phys Rev B 88:045416CrossRefADSGoogle Scholar
  60. 60.
    Klinovaja J, Loss D (2013) Spintronics in MoS2 monolayer quantum wires. Phys Rev B 88:075404CrossRefADSGoogle Scholar
  61. 61.
    Rohling N, Burkard G (2012) Universal quantum computing with spin and valley states. New J Phys 14:083008CrossRefGoogle Scholar
  62. 62.
    Katsnelson MI (2012) Graphene: Carbon in Two Dimensions. Graphene. Cambridge University PressGoogle Scholar
  63. 63.
    Brey L, Fertig HA (2006) Electronic states of graphene nanoribbons studied with the Dirac equation. Phys Rev B 73:235411CrossRefADSGoogle Scholar
  64. 64.
    Tworzydło J, Trauzettel B, Titov M, Rycerz A, Beenakker CWJ (2006) Sub-poissonian shot noise in graphene. Phys Rev Lett 96:246802CrossRefADSGoogle Scholar
  65. 65.
    Liu XL, Hug D, Vandersypen LMK (2010) Gate-defined graphene double quantum dot and excited state spectroscopy. Nano Lett 10:1623CrossRefADSGoogle Scholar
  66. 66.
    Braun M, Struck PR, Burkard G (2011) Spin exchange interaction with tunable range between graphene quantum dots. Phys Rev B 84:115445CrossRefADSGoogle Scholar
  67. 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 76:073103CrossRefADSGoogle Scholar
  68. 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 79:85407CrossRefADSGoogle Scholar
  69. 69.
    Goossens ASM et al (2012) Gate-defined confinement in bilayer graphene-hexagonal boron nitride hybrid devices. Nano Lett 12:4656CrossRefADSGoogle Scholar
  70. 70.
    Struck PR, Burkard G (2010) Effective time-reversal symmetry breaking in the spin relaxation in a graphene quantum dot. Phys Rev B 82:125401CrossRefADSGoogle Scholar
  71. 71.
    Fischer J, Trauzettel B, Loss D (2009) Hyperfine interaction and electron-spin decoherence in graphene and carbon nanotube quantum dots. Phys Rev B 80:155401CrossRefADSGoogle Scholar
  72. 72.
    Palyi A, Burkard G (2009) Hyperfine-induced valley mixing and the spin-valley blockade in carbon-based. Phys Rev B 80:201404(R)CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of KonstanzKonstanzGermany

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