Skip to main content
SpringerLink
Log in
Book cover

Endohedral Fullerenes: Electron Transfer and Spin pp 297–324Cite as

Spin Quantum Computing with Endohedral Fullerenes

  • Chapter
  • First Online:

Part of the book series: Nanostructure Science and Technology ((NST))

Abstract

This chapter reviews the present state of the art in using the endohedral fullerenes N@C60 and P@C60 as qubits in a spin quantum computer. After a brief introduction to spin quantum computing (Sect. 14.1), we first discuss (Sect. 14.2) the rich spin structure of these endohedral fullerenes and specific theoretical proposals for architectures and operation models leading to a scalable quantum computer. We then briefly discuss (Sect. 14.3) those aspects of materials science that are needed to realize the proposed architectures. The central part of this chapter (Sect. 14.4) is a review of quantum operations and entanglement realized with endohedral fullerenes. Finally, we review (Sect. 14.5) efforts to realize single spin detection of endohedral fullerenes and conclude (Sect. 14.6) with a brief outlook on outstanding problems to be solved for obtaining a scalable quantum register.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Feynman RP (1982) Simulating physics with computers. Int J Theor Phys 21:467–488

    Article  Google Scholar 

  2. Deutsch D (1985) Quantum theory, the church-turing principle and the universal quantum computer. Proc R Soc A Math Phys Eng Sci 400:97–117

    Article  Google Scholar 

  3. Ladd TD et al (2010) Quantum computers. Nature 464:45–53

    Article  Google Scholar 

  4. Popov AA, Yang S, Dunsch L (2013) Endohedral fullerenes. Chem Rev 113:5989–6113

    Article  Google Scholar 

  5. Paech M, Stoesser R (2000) In: Auner N, Weis J (eds) Organosilicon Chemistry IV: From Molecules to Materials. Wiley-VCH Verlag GmbH, Germany, pp 521–525. doi:10.1002/9783527619917.ch87

  6. Jones MAG, Morton JJL, Taylor RA, Ardavan A, Briggs GAD (2006) PL, magneto-PL and PLE of the trimetallic nitride template fullerene Er3N@C80. Phys status solidi 243:3037–3041

    Article  Google Scholar 

  7. Brown RM et al (2010) Electron spin coherence in metallofullerenes: Y, Sc, and La@C82. Phys Rev B 82:33410

    Google Scholar 

  8. Schoenfeld RS, Harneit W, Paech M (2006) Pulsed and cw EPR studies on hydrogen atoms encaged in octasilsesquioxane molecules. Phys status solidi 243:3008–3012

    Article  Google Scholar 

  9. Mitrikas G, Efthimiadou EK, Kordas G (2014) Extending the electron spin coherence time of atomic hydrogen by dynamical decoupling. Phys Chem Chem Phys 16:2378–2383

    Article  Google Scholar 

  10. Cory DG et al (2000) NMR based quantum information processing: achievements and prospects. Fortschritte der Phys 48:875–907

    Article  Google Scholar 

  11. Vandersypen LMK et al (2001) Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414:883–887

    Article  Google Scholar 

  12. Lu D et al (2015) In: Takui T, Hanson G, Berliner L (eds) Electron Spin Resonance (ESR) Based Quantum Computing. Springer, New York at http://arxiv.org/abs/1501.01353, http://link.springer.com/chapter/10.1007/978-1-4939-3658-8_7

  13. Jones JA (2000) NMR quantum computation: a critical evaluation. Fortschritte der Phys 48:909–924

    Article  Google Scholar 

  14. Kane BE (1998) A silicon-based nuclear spin quantum computer. Nature 393:133–137

    Article  Google Scholar 

  15. Ladd TD et al (2002) All-silicon quantum computer. Phys Rev Lett 89:17901

    Article  Google Scholar 

  16. Laucht A et al (2015) Electrically controlling single-spin qubits in a continuous microwave field. Sci Adv 1:e1500022–e1500022

    Article  Google Scholar 

  17. Pla JJ et al (2012) A single-atom electron spin qubit in silicon. Nature 489:541–545

    Article  Google Scholar 

  18. Pla JJ et al (2013) High-fidelity readout and control of a nuclear spin qubit in silicon. Nature 496:334–338

    Article  Google Scholar 

  19. Gruber A et al (1997) Scanning confocal optical microscopy and magnetic resonance on single defect centers. Science 276:2012–2014

    Google Scholar 

  20. Jelezko F et al (2004) Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys Rev Lett 93:130501

    Article  Google Scholar 

  21. Childress L, Hanson R (2013) Diamond NV centers for quantum computing and quantum networks. MRS Bull 38:134–138

    Article  Google Scholar 

  22. Orwa JO et al (2010) Fabrication of single optical centres in diamond—a review. J Lumin 130:1646–1654

    Article  Google Scholar 

  23. Grinolds MS et al (2014) Subnanometre resolution in three-dimensional magnetic resonance imaging of individual dark spins. Nat Nanotechnol 9:279–284

    Article  Google Scholar 

  24. Bhallamudi VP, Hammel PC (2015) Nitrogen–vacancy centres: nanoscale MRI. Nat Nanotechnol 10:104–106

    Article  Google Scholar 

  25. Harneit W (2002) Fullerene-based electron-spin quantum computer. Phys Rev A 65:32322

    Article  Google Scholar 

  26. Ardavan A et al (2003) Nanoscale solid-state quantum computing. Philos Trans R Soc A 361:1473–1485

    Article  Google Scholar 

  27. Meyer C, Harneit W, Weidinger A, Lips K (2002) Experimental steps towards the realisation of a fullerene quantum computer. Phys status solidi 233:462–466

    Article  Google Scholar 

  28. Vinit, Sujith SV, Ramachandran CN (2016) Spin-spin coupling in nitrogen atom encapsulated C60, C59 N, and their respective dimers. J Phys Chem A 120:6990–6997

    Google Scholar 

  29. Almeida Murphy T et al (1996) Observation of atom like nitrogen in nitrogen-implanted solid C60. Phys Rev Lett 77:1075–1078

    Article  Google Scholar 

  30. Greer JC (2000) The atomic nature of endohedrally encapsulated nitrogen N@C60 studied by density functional and Hartree-Fock methods. Chem Phys Lett 326:567–572

    Article  Google Scholar 

  31. Knapp C et al (1998) Electron paramagnetic resonance study of atomic phosphorus encapsulated in [60]fullerene. Mol Phys 95:999–1004

    Article  Google Scholar 

  32. Larsson JA, Greer JC, Harneit W, Weidinger A (2002) Phosphorous trapped within buckminsterfullerene. J Chem Phys 116:7849

    Article  Google Scholar 

  33. Gün A, Gençten A (2011) Three-qubit quantum entanglement for SI (S = 3/2, I = 1/2) spin system. Int J Quantum Inf 9:1635–1642

    Article  Google Scholar 

  34. Gün A, Çakmak S, Gençten A (2013) Construction of four-qubit quantum entanglement for SI (S = 3/2, I = 3/2) spin system. Quantum Inf Process 12:205–215

    Article  Google Scholar 

  35. Twamley J (2003) Quantum-cellular-automata quantum computing with endohedral fullerenes. Phys Rev A 67:52318

    Article  Google Scholar 

  36. Teles J et al (2012) Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei. Philos Trans R Soc A 370:4770–4793

    Article  Google Scholar 

  37. Gedik Z et al (2015) Computational speed-up with a single qudit. Sci Rep 5:14671

    Article  Google Scholar 

  38. Harneit W, Huebener K, Naydenov B, Schaefer S, Scheloske M (2007) N@C60 quantum bit engineering. Phys status solidi 244:3879–3884

    Article  Google Scholar 

  39. Suter D, Lim K (2002) Scalable architecture for spin-based quantum computers with a single type of gate. Phys Rev A 65:52309

    Article  Google Scholar 

  40. Ju C, Suter D, Du J (2007) Two-qubit gates between noninteracting qubits in endohedral-fullerene-based quantum computation. Phys Rev A 75:12318

    Article  Google Scholar 

  41. Ju C, Suter D, Du J (2011) An endohedral fullerene-based nuclear spin quantum computer. Phys Lett A 375:1441–1444

    Article  Google Scholar 

  42. Waiblinger M et al (2000) Magnetic interaction in diluted N@C60. AIP Conference Proceedings 544:195–198(AIP)

    Google Scholar 

  43. Heiney PA et al (1991) Orientational ordering transition in solid C60. Phys Rev Lett 66:2911–2914

    Article  Google Scholar 

  44. Harneit W, Meyer C, Weidinger A, Suter D, Twamley J (2002) Architectures for a spin quantum computer based on endohedral fullerenes. Phys status solidi 233:453–461

    Article  Google Scholar 

  45. Yang WL, Xu ZY, Wei H, Feng M, Suter D (2010) Quantum-information-processing architecture with endohedral fullerenes in a carbon nanotube. Phys Rev A 81:32303

    Article  Google Scholar 

  46. Kamenev DI, Berman GP, Tsifrinovich VI (2006) Creation of entanglement in a scalable spin quantum computer with long-range dipole-dipole interaction between qubits. Phys Rev A 73:62336

    Article  Google Scholar 

  47. Feng M, Twamley J (2004) Selective pulse implementation of two-qubit gates for spin-3/2-based fullerene quantum-information processing. Phys Rev A 70:32318

    Article  Google Scholar 

  48. Morton JJL et al (2006) Bang–bang control of fullerene qubits using ultrafast phase gates. Nat Phys 2:40–43

    Article  Google Scholar 

  49. Hu YM, Yang WL, Feng M, Du JF (2009) Distributed quantum-information processing with fullerene-caged electron spins in distant nanotubes. Phys Rev A 80:22322

    Article  Google Scholar 

  50. Pietzak B, Weidinger A, Dinse K-P, Hirsch A (2002) In: Akasaka T, Nagase S (eds) Endofullerenes: a new family of carbon clusters. Springer, Netherlands, pp 13–65. doi:10.1007/978-94-015-9938-2_2

  51. Porfyrakis K (2016) In: Popov AA (ed) Endohedral fullerenes: electron transfer and spin. Springer, Verlag

    Google Scholar 

  52. Jakes P, Dinse K-P, Meyer C, Harneit W, Weidinger A (2003) Purification and optical spectroscopy of N@C60. Phys Chem Chem Phys 5:4080

    Article  Google Scholar 

  53. Zhang J et al (2006) The effects of a pyrrolidine functional group on the magnetic properties of N@C60. Chem Phys Lett 432:523–527

    Article  Google Scholar 

  54. Waiblinger M et al (2001) Corrected article: thermal stability of the endohedral fullerenes N@C60, N@C70, and P@C60. Phys Rev B 64:159901

    Article  Google Scholar 

  55. Tóth S et al (2008) Enhanced thermal stability and spin-lattice relaxation rate of N@C60 inside carbon nanotubes. Phys Rev B 77:214409

    Article  Google Scholar 

  56. Eckardt M, Wieczorek R, Harneit W (2015) Stability of C60 and N@C60 under thermal and optical exposure. Carbon N Y 95:601–607

    Article  Google Scholar 

  57. Zhou S, Rašović I, Briggs GAD, Porfyrakis K (2015) Synthesis of the first completely spin-compatible N@C60 cyclopropane derivatives by carefully tuning the DBU base catalyst. Chem Commun 51:7096–7099

    Article  Google Scholar 

  58. Pong W-T, Durkan C, Li H, Harneit W (2006) Strategies for the deposition of free radical organic molecules for scanning-probe microscopy experiments. J Scanning Probe Microsc 1:55–62

    Article  Google Scholar 

  59. Červenka J, Flipse CFJ (2010) Fullerene monolayer formation by spray coating. Nanotechnology 21:65302

    Article  Google Scholar 

  60. Simon F et al (2004) Low temperature fullerene encapsulation in single wall carbon nanotubes: synthesis of N@C60@SWCNT. Chem Phys Lett 383:362–367

    Article  Google Scholar 

  61. Khlobystov AN et al (2004) Low temperature assembly of fullerene arrays in single-walled carbon nanotubes using supercritical fluids. J Mater Chem 14:2852

    Article  Google Scholar 

  62. Diaconescu B et al (2009) Molecular self-assembly of functionalized fullerenes on a metal surface. Phys Rev Lett 102:56102

    Article  Google Scholar 

  63. Deak DS, Silly F, Porfyrakis K, Castell MR (2006) Template ordered open-grid arrays of paired endohedral fullerenes. J Am Chem Soc 128:13976–13977

    Article  Google Scholar 

  64. Jakes P et al (2002) Electron paramagnetic resonance investigation of endohedral fullerenes N@C60 and N@C70 in a liquid crystal. J Magn Reson 156:303–308

    Article  Google Scholar 

  65. Meyer C et al (2002) Alignment of the endohedral fullerenes N@C60 and N@C70 in a liquid crystal matrix. Phys Rev A 65:61201

    Article  Google Scholar 

  66. Liu G et al (2013) Alignment of N@C60 derivatives in a liquid crystal matrix. J Phys Chem B 117:5925–5931

    Article  Google Scholar 

  67. Naydenov B et al (2006) Ordered inclusion of endohedral fullerenes N@C60 and P@C60 in a crystalline matrix. Chem Phys Lett 424:327–332

    Article  Google Scholar 

  68. Naydenov B, Mende J, Harneit W, Mehring M (2008) Entanglement in P@C60 encapsulated in a solid state matrix. Phys status solidi 245:2002–2005

    Article  Google Scholar 

  69. Rabl P et al (2010) A quantum spin transducer based on nanoelectromechanical resonator arrays. Nat Phys 6:602–608

    Article  Google Scholar 

  70. Borneman TW, Granade CE, Cory DG (2012) Parallel information transfer in a multinode quantum information processor. Phys Rev Lett 108:140502

    Article  Google Scholar 

  71. Dinse K-P, Käß H, Knapp C, Weiden N (2000) EPR investigation of atoms in chemical traps. Carbon N Y 38:1635–1640

    Article  Google Scholar 

  72. Meyer C, Harneit W, Naydenov B, Lips K, Weidinger A (2004) N@C60 and P@C60 as quantum bits. Appl Magn Reson 27:123–132

    Article  Google Scholar 

  73. Wakahara T, Kato T, Miyazawa K, Harneit W (2012) N@C60 as a structural probe for fullerene nanomaterials. Carbon N Y 50:1709–1712

    Article  Google Scholar 

  74. Dietel E et al (1999) Atomic nitrogen encapsulated in fullerenes: effects of cage variations. J Am Chem Soc 121:2432–2437

    Article  Google Scholar 

  75. Franco L et al (2006) Synthesis and magnetic properties of N@C60 derivatives. Chem Phys Lett 422:100–105

    Article  Google Scholar 

  76. Goedde B et al (2001) ‘Nitrogen doped’ C60 dimers (N@C60–C60). Chem Phys Lett 334:12–17

    Google Scholar 

  77. Plant SR et al (2013) A two-step approach to the synthesis of N@C60 fullerene dimers for molecular qubits. Chem. Sci. 4:2971

    Article  Google Scholar 

  78. Farrington BJ et al (2012) Chemistry at the nanoscale: synthesis of an N@C60-N@C60 endohedral fullerene dimer. Angew Chemie 124:3647–3650

    Article  Google Scholar 

  79. Yang J et al (2012) Probing the zero-field splitting in the ordered N@C60 in buckycatcher C60H28 studied by EPR spectroscopy. Phys Lett A 376:1748–1751

    Article  Google Scholar 

  80. Gil-Ramírez G et al (2010) A cyclic porphyrin trimer as a receptor for fullerenes. Org Lett 12:3544–3547

    Article  Google Scholar 

  81. Couderc G, Hulliger J (2010) Channel forming organic crystals: guest alignment and properties. Chem Soc Rev 39:1545

    Article  Google Scholar 

  82. Naydenov B et al (2006) N@C60 and N@C70 oriented in a single-crystalline matrix. Phys status solidi 243:2995–2998

    Article  Google Scholar 

  83. Morton JJL et al (2006) Electron spin relaxation of N@C60 in CS2. J Chem Phys 124:14508

    Article  Google Scholar 

  84. Brown RM et al (2011) Coherent state transfer between an electron and nuclear spin in 15N@C60. Phys Rev Lett 106:110504

    Article  Google Scholar 

  85. Morton JJL et al (2007) Environmental effects on electron spin relaxation in N@C60. Phys Rev B 76:85418

    Article  Google Scholar 

  86. Menéndez J, Page JB (2000) Light scattering in solids VIII. In: Cardona M, Güntherodt G (eds) Topics in applied physics, vol 76. Spinger, Berlin, Heidelberg, pp 27–95

    Google Scholar 

  87. Knorr SB (2002) ESR studies of the electronic properties of fullerenes and their compounds (in German). PhD thesis. Universitaet Stuttgart, Germany

    Google Scholar 

  88. Morton JJL et al (2005) A new mechanism for electron spin echo envelope modulation. J Chem Phys 122:174504

    Article  Google Scholar 

  89. Meyer C (2003) Endohedral fullerenes for quantum computing. PhD thesis. Freie Universitaet Berlin, Germany

    Google Scholar 

  90. Naydenov B (2006) Encapsulation of endohedral fullerenes for quantum computing. PhD thesis. Freie Universitaet, Berlin

    Google Scholar 

  91. Morley GW et al (2007) Efficient dynamic nuclear polarization at high magnetic fields. Phys Rev Lett 98:220501

    Article  Google Scholar 

  92. Morton JJL et al (2006) The N@C60 nuclear spin qubit: bang-bang decoupling and ultrafast phase gates. Phys status solidi 243:3028–3031

    Article  Google Scholar 

  93. Morton JJL et al (2005) Measuring errors in single-qubit rotations by pulsed electron paramagnetic resonance. Phys Rev A 71:12332

    Article  Google Scholar 

  94. Morton JJL et al (2005) High fidelity single qubit operations using pulsed electron paramagnetic resonance. Phys Rev Lett 95:200501

    Article  Google Scholar 

  95. Simmons S, Wu H, Morton JJL (2012) Controlling and exploiting phases in multi-spin systems using electron spin resonance and nuclear magnetic resonance. Philos Trans R Soc A Math Phys Eng Sci 370:4794–4809

    Article  Google Scholar 

  96. Zhang J, Souza AM, Brandao FD, Suter D (2014) Protected quantum computing: interleaving gate operations with dynamical decoupling sequences. Phys Rev Lett 112:50502

    Article  Google Scholar 

  97. Mehring M, Scherer W, Weidinger A (2004) Pseudoentanglement of spin states in the multilevel 15N@C60 System. Phys Rev Lett 93:206603

    Article  Google Scholar 

  98. Scherer W, Mehring M (2008) Entangled electron and nuclear spin states in 15N@C60: density matrix tomography. J Chem Phys 128:52305

    Article  Google Scholar 

  99. Auccaise R et al (2008) A study of the relaxation dynamics in a quadrupolar NMR system using quantum state tomography. J Magn Reson 192:17–26

    Article  Google Scholar 

  100. Blank A, Suhovoy E, Halevy R, Shtirberg L, Harneit W (2009) ESR imaging in solid phase down to sub-micron resolution: methodology and applications. Phys Chem Chem Phys 11:6689

    Article  Google Scholar 

  101. Blank A, Talmon Y, Shklyar M, Shtirberg L, Harneit W (2008) Direct measurement of diffusion in liquid phase by electron spin resonance. Chem Phys Lett 465:147–152

    Article  Google Scholar 

  102. Artzi Y, Twig Y, Blank A (2015) Induction-detection electron spin resonance with spin sensitivity of a few tens of spins. Appl Phys Lett 106:84104

    Article  Google Scholar 

  103. Bienfait A et al (2015) Reaching the quantum limit of sensitivity in electron spin resonance. Nat Nanotechnol 11:253–257

    Article  Google Scholar 

  104. Grose JE et al (2008) Tunnelling spectra of individual magnetic endofullerene molecules. Nat Mater 7:884–889

    Article  Google Scholar 

  105. Harneit W et al (2007) Room temperature electrical detection of spin coherence in C60. Phys Rev Lett 98:216601

    Article  Google Scholar 

  106. Eckardt M, Behrends J, Münter D, Harneit W (2015) Compact electrically detected magnetic resonance setup. AIP Adv 5:47139

    Article  Google Scholar 

  107. Roch N et al (2011) Cotunneling through a magnetic single-molecule transistor based on N@C60. Phys Rev B 83:81407

    Article  Google Scholar 

  108. Elzerman JM et al (2004) Single-shot read-out of an individual electron spin in a quantum dot. Nature 430:431–435

    Article  Google Scholar 

  109. Petta JR et al (2005) Coherent Manipulation of Coupled Electron spins in semiconductor quantum dots. Science 309:2180–2184

    Google Scholar 

  110. Feng M, Twamley J (2004) Readout scheme of the fullerene-based quantum computer by a single-electron transistor. Phys Rev A 70:30303

    Article  Google Scholar 

  111. McCamey DR, Van Tol J, Morley GW, Boehme C (2010) Electronic spin storage in an electrically readable nuclear spin memory with a lifetime >100 seconds. Science 330:1652–1656

    Google Scholar 

  112. McCamey DR et al (2006) Electrically detected magnetic resonance in ion-implanted Si: P nanostructures. Appl Phys Lett 89:182115

    Article  Google Scholar 

  113. Eckardt M (2016) Electrically detected magnetic resonance on fullerene-based organic semiconductor devices and microcrystals. PhD thesis. Johannes Gutenberg-Universitaet Mainz, Germany

    Google Scholar 

  114. Filidou V et al (2012) Ultrafast entangling gates between nuclear spins using photoexcited triplet states. Nat Phys 8:596–600

    Article  Google Scholar 

  115. Grotz B et al (2011) Sensing external spins with nitrogen-vacancy diamond. New J Phys 13:55004

    Article  Google Scholar 

  116. Gaebel T et al (2006) Room-temperature coherent coupling of single spins in diamond. Nat Phys 2:408–413

    Article  Google Scholar 

  117. Huebener K, Schoenfeld RS, Kniepert J, Oelmueller C, Harneit W (2008) ODMR of NV centers in nano-diamonds covered with N@C60. Phys status solidi 245:2013–2017

    Article  Google Scholar 

  118. Schoenfeld RS (2011) Optical readout of single spins for quantum computing and magnetic sensing. PhD thesis. Freie Universitaet, Berlin

    Google Scholar 

  119. Shi F et al (2010) Room-temperature implementation of the deutsch-jozsa algorithm with a single electronic spin in diamond. Phys Rev Lett 105:40504

    Article  Google Scholar 

  120. Schoenfeld RS, Harneit W (2011) Real time magnetic field sensing and imaging using a single spin in diamond. Phys Rev Lett 106:30802

    Article  Google Scholar 

  121. Romach Y et al (2015) Spectroscopy of surface-induced noise using shallow spins in diamond. Phys Rev Lett 114:17601

    Article  Google Scholar 

  122. Nimmrich M et al (2010) Atomic-resolution imaging of clean and hydrogen-terminated C(100) − (2 × 1) diamond surfaces using noncontact AFM. Phys Rev B 81:201403

    Article  Google Scholar 

  123. Dyachenko O et al (2015) A diamond (100) surface with perfect phase purity. Chem Phys Lett 640:72–76

    Article  Google Scholar 

  124. Morton JJL, Lovett BW (2011) Hybrid solid-state qubits: the powerful role of electron spins. Annu Rev Condens Matter Phys 2:189–212

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Physik, Universität Osnabrück, Osnabrück, Germany

    Wolfgang Harneit

Authors
  1. Wolfgang Harneit
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wolfgang Harneit .

Editor information

Editors and Affiliations

  1. Leibniz Institute for Solid State and Materials Research, Dresden, Germany

    Alexey A. Popov

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Harneit, W. (2017). Spin Quantum Computing with Endohedral Fullerenes. In: Popov, A. (eds) Endohedral Fullerenes: Electron Transfer and Spin. Nanostructure Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-47049-8_14

Download citation

Publish with us

Policies and ethics

Search

Navigation