Layered Architectures for Quantum Computers and Quantum Repeaters

Part of the Lecture Notes in Physics book series (LNP, volume 911)

Abstract

This chapter examines how to organize quantum computers and repeaters using a systematic framework known as layered architecture, where machine control is organized in layers associated with specialized tasks. The framework is flexible and could be used for analysis and comparison of quantum information systems. To demonstrate the design principles in practice, we develop architectures for quantum computers and quantum repeaters based on optically controlled quantum dots, showing how a myriad of technologies must operate synchronously to achieve fault-tolerance. Optical control makes information processing in this system very fast, scalable to large problem sizes, and extendable to quantum communication.

Keywords

Quantum computer Quantum dot Quantum repeater 

Notes

Acknowledgements

This work was supported by the National Science Foundation CCF-0829694, the Univ. of Tokyo Special Coordination Funds for Promoting Science and Technology, NICT, and the Japan Society for the Promotion of Science (JSPS) through its “Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program).”

References

  1. 1.
    T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J.L. O’Brien, Quantum computers. Nature 464, 45–53 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    S.M. Clark, K.-M.C. Fu, T.D. Ladd, Y. Yamamoto, Quantum computers based on electron spins controlled by ultrafast off-resonant single optical pulses. Phys. Rev. Lett. 99, 040501 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    D. Press, T.D. Ladd, B. Zhang, Y. Yamamoto, Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature 456, 218–221 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    J. Berezovsky, M.H. Mikkelsen, N.G. Stoltz, L.A. Coldren, D.D. Awschalom, Picosecond coherent optical manipulation of a single electron spin in a quantum dot. Science 320(5874), 349–352 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    D.P. DiVincenzo, The physical implementation of quantum computation. Fortschritte der Physik 48(9–11), 771–783 (2000)ADSCrossRefMATHGoogle Scholar
  6. 6.
    A.M. Steane, Quantum computer architecture for fast entropy extraction. Quantum Inf. Comput. 2, 297 (2002)MATHGoogle Scholar
  7. 7.
    A.M. Steane, How to build a 300 bit, 1 Giga-operation quantum computer. Quantum Inf. Comput. 7, 171 (2007)MathSciNetMATHGoogle Scholar
  8. 8.
    T.P. Spiller, W.J. Munro, S.D. Barrett, P. Kok, An introduction to quantum information processing: applications and realizations. Contemp. Phys. 46(6), 407–436 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    R. Van Meter, M. Oskin, Architectural implications of quantum computing technologies. ACM J. Emerg. Technol. Comput. Syst. 2(1), 31–63 (2006)CrossRefGoogle Scholar
  10. 10.
    D. Kielpinski, C. Monroe, D. Wineland, Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002)ADSCrossRefGoogle Scholar
  11. 11.
    D. Copsey, M. Oskin, T. Metodiev, F.T. Chong, I. Chuang, J. Kubiatowicz, The effect of communication costs in solid-state quantum computing architectures, in Proceedings of the Fifteenth Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA’03) (ACM, New York, 2003), pp. 65–74Google Scholar
  12. 12.
    K.M. Svore, A.V. Aho, A.W. Cross, I. Chuang, I.L. Markov, A layered software architecture for quantum computing design tools. Computer 39(1), 74–83 (2006)CrossRefGoogle Scholar
  13. 13.
    M. Oskin, F.T. Chong, I.L. Chuang, J. Kubiatowicz, Building quantum wires: the long and the short of it, in 30th International Symposium on Computer Architecture, 2003 (ISCA’03), San Diego (2003), pp. 374–385Google Scholar
  14. 14.
    L.-M. Duan, C. Monroe, Colloquium: quantum networks with trapped ions. Rev. Mod. Phys. 82(2), 1209–1224 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    J. Kim, C. Kim, Integrated optical approach to trapped ion quantum computation. Quantum Inf. Comput. 9, 181–202 (2009)ADSGoogle Scholar
  16. 16.
    A.G. Fowler, W.F. Thompson, Z. Yan, A.M. Stephens, B.L.T. Plourde, F.K. Wilhelm, Long-range coupling and scalable architecture for superconducting flux qubits. Phys. Rev. B 76(17), 174507 (2007)Google Scholar
  17. 17.
    M. Whitney, N. Isailovic, Y. Patel, J. Kubiatowicz, Automated generation of layout and control for quantum circuits, in Proceedings of the 4th International Conference on Computing Frontiers, Ischia (2007), pp. 83–94Google Scholar
  18. 18.
    M.G. Whitney, N. Isailovic, Y. Patel, J. Kubiatowicz, A fault tolerant, area efficient architecture for shor’s factoring algorithm, in 36th International Symposium on Computer Architecture, 2009 (ISCA’09), Austin (2009)Google Scholar
  19. 19.
    N. Isailovic, Y. Patel, M. Whitney, J. Kubiatowicz, Interconnection networks for scalable quantum computers, in 33rd International Symposium on Computer Architecture, 2006 (ISCA’06), Boston (2006), pp. 366–377Google Scholar
  20. 20.
    N. Isailovic, M. Whitney, Y. Patel, J. Kubiatowicz, Running a quantum circuit at the speed of data, in 35th International Symposium on Computer Architecture, 2008 (ISCA’08), Beijing (2008)Google Scholar
  21. 21.
    R. Stock, D.F.V. James, Scalable, high-speed measurement-based quantum computer using trapped ions. Phys. Rev. Lett. 102(17), 170501 (2009)Google Scholar
  22. 22.
    S.J. Devitt, A.G. Fowler, T. Tilma, W.J. Munro, K. Nemoto, Classical processing requirements for a topological quantum computing system. Int. J. Quantum Inf. 8(1–2), 121–147 (2010)CrossRefGoogle Scholar
  23. 23.
    N. Cody Jones, R. Van Meter, A.G. Fowler, P.L. McMahon, J. Kim, T.D. Ladd, Y. Yamamoto, Layered architecture for quantum computing. Phys. Rev. X 2, 031007 (2012)Google Scholar
  24. 24.
    A.G. Fowler, M. Mariantoni, J.M. Martinis, A.N. Cleland, Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    M.D. Reed, L. DiCarlo, S.E. Nigg, L. Sun, L. Frunzio, S.M. Girvin, R.J. Schoelkopf, Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 382 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T.C. White, J. Mutus, A.G. Fowler, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, C. Neill, P. O‘Malley, P. Roushan, A. Vainsencher, J. Wenner, A.N. Korotkov, A.N. Cleland, J.M. Martinis, Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500 (2014)Google Scholar
  27. 27.
    D. Nigg, M. Mueller, E.A. Martinez, P. Schindler, M. Hennrich, T. Monz, M.A. Martin-Delgado, R. Blatt, Quantum computations on a topologically encoded qubit. Science 345, 302 (2014)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    W. Dür, H.-J. Briegel, J.I. Cirac, P. Zoller, Quantum repeaters based on entanglement purification. Phys. Rev. A 59(1), 169–181 (1999)ADSCrossRefGoogle Scholar
  29. 29.
    R. Van Meter, T.D. Ladd, A.G. Fowler, Y. Yamamoto, Distributed quantum computation architecture using semiconductor nanophotonics. Int. J. Quantum Inf. 8, 295–323 (2010) Preprint available as arXiv:quant-ph/0906.2686v2Google Scholar
  30. 30.
    A.G. Fowler, D.S. Wang, C.D. Hill, T.D. Ladd, R. Van Meter, L.C.L. Hollenberg, Surface code quantum communication. Phys. Rev. Lett. 104(18), 180503 (2010)Google Scholar
  31. 31.
    G. Björk, S. Pau, J. Jacobson, Y. Yamamoto, Wannier exciton superradiance in a quantum-well microcavity. Phys. Rev. B 50(23), 17336–17348 (1994)ADSCrossRefGoogle Scholar
  32. 32.
    A. Imamoglu, D.D. Awschalom, G. Burkard, D.P. DiVincenzo, D. Loss, M. Sherwin, A. Small, Quantum information processing using quantum dot spins and cavity qed. Phys. Rev. Lett. 83(20), 4204–4207 (1999)ADSCrossRefGoogle Scholar
  33. 33.
    N.H. Bonadeo, G. Chen, D. Gammon, D.G. Steel, Single quantum dot nonlinear optical spectroscopy. Physica Status Solidi B 221(1), 5–18 (2000)ADSCrossRefGoogle Scholar
  34. 34.
    J.R. Guest, T.H. Stievater, X. Li, J. Cheng, D.G. Steel, D. Gammon, D.S. Katzer, D. Park, C. Ell, A. Thränhardt, G. Khitrova, H.M. Gibbs, Measurement of optical absorption by a single quantum dot exciton. Phys. Rev. B 65(24), 241310 (2002)Google Scholar
  35. 35.
    J. Hours, P. Senellart, E. Peter, A. Cavanna, J. Bloch, Exciton radiative lifetime controlled by the lateral confinement energy in a single quantum dot. Phys. Rev. B 71(16), 161306 (2005)Google Scholar
  36. 36.
    Y. Yamamoto, T.D. Ladd, D. Press, S. Clark, K. Sanaka, C. Santori, D. Fattal, K.M. Fu, S. Höfling, S. Reitzenstein, A. Forchel, Optically controlled semiconductor spin qubits for quantum information processing. Physica Scripta 2009(T137), 014010 (2009)Google Scholar
  37. 37.
    M. Bayer, G. Ortner, O. Stern, A. Kuther, A.A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T.L. Reinecke, S.N. Walck, J.P. Reithmaier, F. Klopf, F. Schäfer, Fine structure of neutral and charged excitons in self-assembled in(ga)as/(al)gaas quantum dots. Phys. Rev. B 65(19), 195315 (2002)Google Scholar
  38. 38.
    C. Kim, C. Knoernschild, B. Liu, J. Kim, Design and characterization of mems micromirrors for ion-trap quantum computation. IEEE J. Sel. Top. Quantum Electron. 13(2), 322–329 (2007)CrossRefGoogle Scholar
  39. 39.
    C. Knoernschild, C. Kim, B. Liu, F.P. Lu, J. Kim, Mems-based optical beam steering system for quantum information processing in two-dimensional atomic systems. Opt. Lett. 33(3), 273–275 (2008)ADSCrossRefGoogle Scholar
  40. 40.
    T.D. Ladd, Y. Yamamoto, Simple quantum logic gate with quantum dot cavity QED systems. Phys. Rev. B 84, 235307 (2011)ADSCrossRefGoogle Scholar
  41. 41.
    D. Loss, D.P. DiVincenzo, Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)ADSCrossRefGoogle Scholar
  42. 42.
    R. Hanson, L.P. Kouwenhoven, J.R. Petta, S. Tarucha, L.M.K. Vandersypen, Spins in few-electron quantum dots. Rev. Mod. Phys. 79(4), 1217–1265 (2007)ADSCrossRefGoogle Scholar
  43. 43.
    M. Kuwahara, T. Kutsuwa, K. Ono, H. Kosaka, Single charge detection of an electron created by a photon in a g-factor engineered quantum dot. Appl. Phys. Lett. 96(16), 163107 (2010)Google Scholar
  44. 44.
    D. Kim, S.G. Carter, A. Greilich, A.S. Backer, D. Gammon, Ultrafast optical control of entanglement between two quantum dot spins. arXiv:quant-ph/1007.3733 (2010, preprint)Google Scholar
  45. 45.
    C. Piermarocchi, P. Chen, L.J. Sham, D.G. Steel, Optical rkky interaction between charged semiconductor quantum dots. Phys. Rev. Lett. 89, 167402 (2002)ADSCrossRefGoogle Scholar
  46. 46.
    G.F. Quinteiro, J. Fernandez-Rossier, C. Piermarocchi, Long-range spin-qubit interaction mediated by microcavity polaritons. Phys. Rev. Lett. 97(9), 097401–097404 (2006)ADSCrossRefGoogle Scholar
  47. 47.
    A. Imamoḡlu, D.D. Awschalom, G. Burkard, D.P. DiVincenzo, D. Loss, M. Shermin, A. Small, Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett. 83, 4204 (1999)ADSCrossRefGoogle Scholar
  48. 48.
    T. Szkopek, P.O. Boykin, H. Fan, V.P. Roychowdhury, E. Yablonovitch, G. Simms, M. Gyure, B. Fong, Threshold error penalty for fault-tolerant quantum computation with nearest neighbor communication. IEEE Trans. Nanotechnol. 5(1), 42–49 (2006)ADSCrossRefGoogle Scholar
  49. 49.
    T.D. Ladd et al., High-speed quantum computer with semiconductor spins, in Semiconductor Quantum Bits, eds. F. Henneberger, O. Benson, vol. 453 (Pan Stanford Publishing, Singapore, 2009)Google Scholar
  50. 50.
    J. Berezovsky, M.H. Mikkelsen, O. Gywat, N.G. Stoltz, L.A. Coldren, D.D. Awschalom, Nondestructive optical measurements of a single electron spin in a quantum dot. Science 314(5807), 1916–1920 (2006)ADSCrossRefGoogle Scholar
  51. 51.
    M. Atatüre, J. Dreiser, A. Badolato, A. Imamoglu, Observation of faraday rotation from a single confined spin. Nat. Phys. 3, 101–106 (2007)CrossRefGoogle Scholar
  52. 52.
    I. Fushman, D. Englund, A. Faraon, N. Stoltz, P. Petroff, J. Vuckovic, Controlled phase shifts with a single quantum dot. Science 320(5877), 769–772 (2008)ADSCrossRefGoogle Scholar
  53. 53.
    R. Long, T. Steinmetz, P. Hommelhoff, W. Hänsel, T.W. Hänsch, J. Reichel, Magnetic microchip traps and single-atom detection. Philos. Trans.: Math. Phys. Eng. Sci. 361(1808), 1375–1389 (2003)Google Scholar
  54. 54.
    D. Press, K. De Greve, P.L. McMahon, T.D. Ladd, B. Friess, C. Schneider, M. Kamp, S. Höfling, A. Forchel, Y. Yamamoto, Ultrafast optical spin echo in a single quantum dot. Nat. Photonics 4, 367–370 (2010)ADSCrossRefGoogle Scholar
  55. 55.
    L. Viola, E. Knill, Robust dynamical decoupling of quantum systems with bounded controls. Phys. Rev. Lett. 90(3), 037901 (2003)Google Scholar
  56. 56.
    H.K. Ng, D.A. Lidar, J. Preskill, Combining dynamical decoupling with fault-tolerant quantum computation. Phys. Rev. A84, 012305 (2011)ADSCrossRefGoogle Scholar
  57. 57.
    R. Raussendorf, J. Harrington, K. Goyal, Topological fault-tolerance in cluster state quantum computation. New J. Phys. 9(6), 199 (2007)Google Scholar
  58. 58.
    K.R. Brown, A.W. Harrow, I.L. Chuang, Arbitrarily accurate composite pulse sequences. Phys. Rev. A 70, 052318 (2004)ADSCrossRefGoogle Scholar
  59. 59.
    Y. Tomita, J.T. Merrill, K.R. Brown, Multi-qubit compensation sequences. New J. Phys. 12(1), 015002 (2010)Google Scholar
  60. 60.
    P.W. Shor, Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52(4), R2493–R2496 (1995)ADSCrossRefGoogle Scholar
  61. 61.
    A.M. Steane, Error correcting codes in quantum theory. Phys. Rev. Lett. 77(5), 793–797 (1996)ADSMathSciNetCrossRefMATHGoogle Scholar
  62. 62.
    A.R. Calderbank, P.W. Shor, Good quantum error-correcting codes exist. Phys. Rev. A 54(2), 1098–1105 (1996)ADSCrossRefGoogle Scholar
  63. 63.
    D. Gottesman, Stabilizer codes and quantum error correction. PhD thesis, California Institute of Technology, Pasadena, 1997Google Scholar
  64. 64.
    P. John, Fault-tolerant quantum computation, in Quantum information and computation, ed. by H.-K. Lo, T. Spiller, S. Popescu (World Scientific, Singapore, 1998)Google Scholar
  65. 65.
    A. Kitaev, Fault-tolerant quantum computation by anyons. arXiv:quant-ph/9707021 (1997, preprint)Google Scholar
  66. 66.
    S.B. Bravyi, A.Y. Kitaev, Quantum codes on a lattice with boundary. arXiv:quant-ph/9811052 (1998, preprint)Google Scholar
  67. 67.
    A.G. Fowler, A.M. Stephens, P. Groszkowski, High-threshold universal quantum computation on the surface code. Phys. Rev. A 80(5), 052312 (2009)Google Scholar
  68. 68.
    D. Aharonov, M. Ben-Or, Fault-tolerant quantum computation with constant error, in Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing (STOC’97) (ACM, New York, 1997), pp. 176–188Google Scholar
  69. 69.
    A. Aspuru-Guzik, A.D. Dutoi, P.J. Love, M. Head-Gordon, Simulated quantum computation of molecular energies. Science 309(5741), 1704–1707 (2005)ADSCrossRefGoogle Scholar
  70. 70.
    R. Raussendorf, J. Harrington, Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98(19), 190504 (2007)Google Scholar
  71. 71.
    A.G. Fowler, D.S. Wang, L.C.L. Hollenberg, Surface code quantum error correction incorporating accurate error propagation. Quantum Inf. Comput. 11, 8 (2011)MathSciNetMATHGoogle Scholar
  72. 72.
    D.S. Wang, A.G. Fowler, L.C.L. Hollenberg, Surface code quantum computing with error rates over 1%. Phys. Rev. A83, 020302(R) (2011)Google Scholar
  73. 73.
    S.J. Devitt, A.G. Fowler, A.M. Stephens, A.D. Greentree, L.C.L. Hollenberg, W.J. Munro, K. Nemoto, Architectural design for a topological cluster state quantum computer. New J. Phys. 11(8), 083032 (2009)Google Scholar
  74. 74.
    E. Knill, Quantum computing with realistically noisy devices. Nature 434, 39–44 (2005)ADSCrossRefGoogle Scholar
  75. 75.
    D.P. DiVincenzo, P. Aliferis, Effective fault-tolerant quantum computation with slow measurements. Phys. Rev. Lett. 98(2), 020501 (2007)Google Scholar
  76. 76.
    S. Anders, H.J. Briegel, Fast simulation of stabilizer circuits using a graph-state representation. Phys. Rev. A 73(2), 022334 (2006)Google Scholar
  77. 77.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, 1 edn. (Cambridge University Press, Cambridge/New York, 2000)MATHGoogle Scholar
  78. 78.
    N.C. Jones, J.D. Whitfield, P.L. McMahon, M.-H. Yung, R. Van Meter, A. Aspuru-Guzik, Y. Yamamoto, Faster quantum chemistry simulation on fault-tolerant quantum computers. New J. Phys. 14(11), 115023 (2012)Google Scholar
  79. 79.
    S. Bravyi, A. Kitaev, Universal quantum computation with ideal clifford gates and noisy ancillas. Phys. Rev. A 71(2), 022316 (2005)Google Scholar
  80. 80.
    C.M. Dawson, M.A. Nielsen, The solovay-kitaev algorithm. Quantum Inf. Comput. 6, 81 (2006)MathSciNetMATHGoogle Scholar
  81. 81.
    K. De Greve, L. Yu, P.L. McMahon, J.S. Pelc, C.M. Natarajan, N. Young Kim, E. Abe, S. Maier, C. Schneider, M. Kamp, S. Höfling, R.H. Hadfield, A. Forchel, M.M. Fejer, Y. Yamamoto, Quantum-dot spin–photon entanglement via frequency downconversion to telecom wavelength. Nature 491, 421 (2012)ADSCrossRefGoogle Scholar
  82. 82.
    D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, A. Sanpera, Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818–2821 (1996)ADSCrossRefGoogle Scholar

Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.Edward L. Ginzton LaboratoryStanford UniversityStanfordUSA

Personalised recommendations