skip to main content
article

Architectural implications of quantum computing technologies

Published:01 January 2006Publication History
Skip Abstract Section

Abstract

In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering trade-offs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, storage capacity, and interconnection network topology influence algorithmic efficiency, while quantum error correction and necessary quantum state measurement are the ultimate drivers of logical clock speed. We discuss several proposed technologies. Finally, we use our taxonomy to explore architectural implications for common arithmetic circuits, examine the implementation of quantum error correction, and discuss cluster-state quantum computation.

References

  1. Aharonov, D. and Ben-Or, M. 1999. Fault-tolerant quantum computation with constant error rate. http://arXiv.org/quant-ph/9906129. (Extended version of STOC 1997 paper.) Google ScholarGoogle Scholar
  2. Aho, A. V. and Svore, K. M. 2003. Compiling quantum circuits using the palindrome transform. http://arXiv.org/quant-ph/0311008.Google ScholarGoogle Scholar
  3. Amdahl, G. 1967. Validity of the single processor approach to achieving large-scale computing capabilities. In AFIPS Conference Proceedings. 483--485.Google ScholarGoogle Scholar
  4. ARDA. 2004. A Quantum Information Science and Technology Roadmap, v2.0 ed. ARDA.Google ScholarGoogle Scholar
  5. Barenco, A., Bennett, C. H., Cleve, R., DiVincenzo, D. P., Margolus, N., Shor, P., Sleator, T., Smolin, J., and Weinfurter, H. 1995. Elementary gates for quantum computation. Phys. Rev. A 52, 3457.Google ScholarGoogle Scholar
  6. Barenco, A., Ekert, A., Suominen, K.-A., and Törma, P. 1996. Approximate quantum Fourier transform and decoherence. Phy. Rev. A 54, 139--146.Google ScholarGoogle Scholar
  7. Beckman, D., Chari, A. N., Devabhaktuni, S., and Preskill, J. 1996. Efficient networks for quantum factoring. Phys. Rev. A 54, 1034--1063. http://arXiv.org/quant-ph/9602016.Google ScholarGoogle Scholar
  8. Bennett, C. H. and Brassard, G. 1984. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing. IEEE. 175--179.Google ScholarGoogle Scholar
  9. Bennett, C. H., Brassard, G., Crépeau, C., Josza, R., Peres, A., and Wootters, W. 1993. Teleporting an unknown quantum state via dual classical and EPR channels. Phy. Rev. Lett. 70, 1895--1899.Google ScholarGoogle Scholar
  10. Boulant, N., Edmonds, K., Yang, J., Pravia, M. A., and Cory, D. G. 2003. Experimental demonstration of an entanglement swapping operation and improved control in NMR quantum-information processing. Phy. Rev. A 68, 032305.Google ScholarGoogle Scholar
  11. Brennen, G. K., Caves, C. M., Jessen, P. S., and Deutsch, I. H. 1999. Quantum logic gates in optical lattices. Phys. Rev. Lett. 82, 5 (Feb.), 1060--1063.Google ScholarGoogle Scholar
  12. Browne, D. E. and Rudolph, T. 2005. Resource-efficient linear optical quantum computation. Phys. Rev. Lett. 95, 010501.Google ScholarGoogle Scholar
  13. Burkard, G., Loss, D., DiVincenzo, D. P., and Smolin, J. A. 1999. Physical optimization of quantum error correction circuits. Phys. Rev. B 60, 16, 11404--11416.Google ScholarGoogle Scholar
  14. Calderbank, A. R. and Shor, P. W. 1996. Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098--1105.Google ScholarGoogle Scholar
  15. Cavallar, S., Dodson, B., Lenstra, A. K., Lioen, W., Montgomery, P. L., Murphy, B., Te Riele, H., Aardal, K., Gilchrist, J., Guillerm, G., Leyland, P., Marchand, J., Morain, F., Muffett, A., Putnam, C., Putnam, C., and Zimmermann, P. 2000. Factorization of a 512-bit RSA modulus. In Advances in Cryptology---EUROCRYPT 2000: International Conference on the Theory and Application of Cryptographic Techniques. Lecture Notes in Computer Science, vol. 1807. 1. Springer-Verleg, New York, 2000. Google ScholarGoogle Scholar
  16. Chiaverini, J., Leibfried, D., Schaetz, T., Barrett, M. D., Blakestad, R. B., Britton, J., Itano, W. M., Jost, J. D., Knill, E., Langer, C., Ozeri, R., and Wineland, D. J. 2004. Realization of quantum error correction. Nature 432, 602--605.Google ScholarGoogle Scholar
  17. Childress, L., Taylor, J. M., Sørensen, A. S., and Lukin, M. 2005. Fault-tolerant quantum repeaters with minimal physical resources, and implementations based on single-photon emitters. http://arXiv.org/quant-ph/0502112.Google ScholarGoogle Scholar
  18. Chiorescu, I., Bertet, P., Semba, K., Nakamura, Y., Harmans, C. J. P. M., and Mooij, J. E. 2004. Coherent dynamics of a flux qubit coupled to a harmonic oscillator. Nature 431, 159--162.Google ScholarGoogle Scholar
  19. Cirac, J. I. and Zoller, P. 1995. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091--4094.Google ScholarGoogle Scholar
  20. Clark, R. G. et al. 2003. Progress in silicon-based quantum computing. Phil. Trans. R. Soc. London A 361, 1451--1471.Google ScholarGoogle Scholar
  21. Cleve, R. and Watrous, J. 2000. Fast parallel circuits for the quantum Fourier transform. In Proceedings of the 41st Annual Symposium on Foundations of Computer Science. ACM, New York, 526--536. Google ScholarGoogle Scholar
  22. Copsey, D., Oskin, M., Metodiev, T., Chong, F. T., Chuang, I., and Kubiatowicz, J. 2003. The effect of communication costs in solid-state quantum computing architectures. In Proceedings of the 15th Annual ACM Symposium on Parallel Algorithms and Architectures. 65--74. Google ScholarGoogle Scholar
  23. Cory, D. G. 2004. Private communication.Google ScholarGoogle Scholar
  24. Cuccaro, S. A., Draper, T. G., Kutin, S. A., and Moulton, D. P. 2004. A new quantum ripple-carry addition circuit. http://arXiv.org/quant-ph/0410184.Google ScholarGoogle Scholar
  25. Dawson, C. M., Haselgrove, H. L., and Nielsen, M. A. 2005. Noise thresholds for optical quantum computers. http://arXiv.org/quant-ph/0509060.Google ScholarGoogle Scholar
  26. Deutsch, D. and Jozsa, R. 1992. Rapid solution of problems by quantum computation. Proc. R. Soc. London Ser. A, 439, 553.Google ScholarGoogle Scholar
  27. Devitt, S. J., Fowler, A. G., and Hollenberg, L. C. 2004. Simulations of Shor's algorithm with implications to scaling and quantum error correction. http://arXiv.org/quant-ph/0408081.Google ScholarGoogle Scholar
  28. DiVincenzo, D. P. 1994. Two-bit gates are universal for quantum computation. Phys. Rev. A. http://arXiv.org/cond-mat/9407022.Google ScholarGoogle Scholar
  29. DiVincenzo, D. P. 1995. Quantum computation. Science 270, 5234, 255--261.Google ScholarGoogle Scholar
  30. DiVincenzo, D. P., Bacon, D., Kempe, J., Burkard, G., and Whaley, K. B. 2000. Universal quantum computation with the exchange interaction. Nature 408, 339--342.Google ScholarGoogle Scholar
  31. Draper, T. G. 2000. Addition on a quantum computer. http://arXiv.org/quant-ph/0008033. (First draft dated Sept. 1998.)Google ScholarGoogle Scholar
  32. Draper, T. G., Kutin, S. A., Rains, E. M., and Svore, K. M. 2004. A logarithmic-depth quantum carry-lookahead adder. http://arXiv.org/quant-ph/0406142. Google ScholarGoogle Scholar
  33. Elliott, C., Pearson, D., and Troxel, G. 2003. Quantum cryptography in practice. In Proceedings of the SIGCOMM 2003. ACM, New York. http://arXiv.org/quant-ph/0307049. Google ScholarGoogle Scholar
  34. Ercegovac, M. D. and Lang, T. 2004. Digital Arithmetic. Morgan Kaufmann, San Francisco, CA.Google ScholarGoogle Scholar
  35. ESIA, JEITIA, KSIA, TSIA, and SIA. 2003. International technology roadmap for semiconductors. Tech. Rep., ESIA and JEITIA and KSIA and TSIA and SIA. http://public.itrs.net/Files/2003ITRS/Home2003.htm.Google ScholarGoogle Scholar
  36. Fleischhauer, M. and Lukin, M. D. 2000. Dark-state polaritons in electromagnetically induced transparency. Phys. Rev. Lett. 84, 5094--5097.Google ScholarGoogle Scholar
  37. Folman, R., Krüger, P., Cassettari, D., Hessmo, B., Maier, T., and Schmiedmayer, J. 2000. Controlling cold atoms using nanofabricated surfaces: Atom chips. Phys. Rev. Lett. 84, 4749--4752.Google ScholarGoogle Scholar
  38. Fowler, A. G., Devitt, S. J., and Hollenberg, L. C. 2004. Implementation of Shor's algorithm on a linear nearest neighbor qubit array. Quantum Inf. Comput. 4, 4, 237. http://arXiv.org/quant-ph/ 0402196. Google ScholarGoogle Scholar
  39. Fowler, A. G., Hill, C. D., and Hollenberg, L. C. L. 2004. Quantum error correction on linear nearest neighbor qubit arrays. Phys. Rev. A 69, 042314.Google ScholarGoogle Scholar
  40. Fujisawa, T., Oosterkamp, T. H., van der Wiel, W. G., Broer, B. W., Aguado, R., Tarucha, S., and Kouwenhoven, L. P. 1998. Spontaneous emission spectrum in double quantum dot devices. Science 282, 932--935.Google ScholarGoogle Scholar
  41. Furusawa, A., Sørensen, J. L., Braunstein, S. L., Fuchs, C. A., Kimble, H. J., and Polzik, E. S. 1998. Unconditional quantum teleportation. Science 282, 5389, 706--709.Google ScholarGoogle Scholar
  42. Galindo, A. and Martin-Delgado, M. A. 2002. Information and computation: Classical and quantum aspects. Rev. Modern Phys. 74, 347--423.Google ScholarGoogle Scholar
  43. Gasparoni, S., Pan, J., Walther, P., Rudolph, T., and Zeilinger, A. 2004. Realization of a photonic controlled-NOT gate sufficient for quantum computation. Phys. Rev. Lett. 93, 020504.Google ScholarGoogle Scholar
  44. Gossett, P. 1998. Quantum carry-save arithmetic. http://arXiv.org/quant-ph/9808061.Google ScholarGoogle Scholar
  45. Gottesman, D. 1999. Fault tolerant quantum computation with local gates. http://arXiv.org/quant-ph/9903099. Google ScholarGoogle Scholar
  46. Gottesman, D. and Chuang, I. L. 1999. Quantum teleportation is a universal computational primitive. Nature 402, 390--393.Google ScholarGoogle Scholar
  47. Grover, L. 1996. A fast quantum-mechanical algorithm for database search. In Proceedings of the 28th Annual ACM Symposium on the Theory of Computation. 212--219. http://arXiv.org/quant-ph/9605043. Google ScholarGoogle Scholar
  48. Grover, L. K. 1997. Quantum telecomputation. http://arXiv.org/quant-ph/9704012.Google ScholarGoogle Scholar
  49. Hales, L. and Hallgren, S. 2000. An improved quantum Fourier transform algorithm and applications. In Proceedings of the 41st Annual Symposium on Foundations of Computer Science. ACM, New York. Google ScholarGoogle Scholar
  50. Harris, S. E. 1997. Electromagnetically induced transparency. Phys. Today 50, 7 (July), 36--42.Google ScholarGoogle Scholar
  51. Isailovic, N., Whitney, M., Patel, Y., Kubiatowicz, J., Copsey, D., Chong, F. T., Chuang, I. L., and Oskin, M. 2004. Datapath and control for quantum wires. ACM Trans. Architecture and Code Optimization 1, 1 (Mar.). Google ScholarGoogle Scholar
  52. James, D. F. V. and Kwiat, P. G. 2002. Atomic-vapor-based high efficiency optical detectors with photon number resolution. Phys. Rev. Lett. 89, 183601.Google ScholarGoogle Scholar
  53. Jelezko, F., Gaebel, T., Popa, I., Domhan, M., Gruber, A., and Wratchtrup, J. 2004. Observation of coherence oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys. Rev. Lett. 93, 130501.Google ScholarGoogle Scholar
  54. Kane, B. E. 1998. A silicon-based nuclear spin quantum computer. Nature 393, 133--137.Google ScholarGoogle Scholar
  55. Kawano, Y., Yamashita, S., and Kitagawa, M. 2005. Explicit implementation of quantum circuits on a unidirectional periodic structure. Phys. Rev. A 72, 012301.Google ScholarGoogle Scholar
  56. Kielpinski, D., Monroe, C., and Wineland, D. J. 2002. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709--711.Google ScholarGoogle Scholar
  57. Kim, J. et al. 2005. System design for large-scale ion trap quantum information processor. Quantum Inf. and Comput. 5, 7, 515--537. Google ScholarGoogle Scholar
  58. Knill, E. 2003. Bounds on the probability of success of postselected nonlinear sign shifts implemented with linear optics. Phys. Rev. A 68, 064303.Google ScholarGoogle Scholar
  59. Knill, E., Laflamme, R., and Milburn, G. J. 2000. Thresholds for linear optics quantum computation. http://arXiv.org/quant-ph/0006120.Google ScholarGoogle Scholar
  60. Knill, E., Laflamme, R., and Milburn, G. J. 2001. A scheme for efficient quantum computation with linear optics. Nature 409, 46--52.Google ScholarGoogle Scholar
  61. Knuth, D. E. 1998. The Art of Computer Programming, vol. 2 / Seminumerical Algorithms, 3rd ed. Addison-Wesley, Reading, MA. Google ScholarGoogle Scholar
  62. Kunihiro, N. 2005. Exact analyses of computational time for factoring in quantum computers. IEICE Trans. Fundamentals E88-A, 1, 105--111.Google ScholarGoogle Scholar
  63. Ladd, T. D., Goldman, J. R., Yamaguchi, F., Yamamoto, Y., Abe, E., and Itoh, K. M. 2002. All-silicon quantum computer. Phys. Rev. Lett. 89, 1 (July), 17901.Google ScholarGoogle Scholar
  64. Ladd, T. D., Maryenko, D., Yamamoto, Y., Abe, E., and Itoh, K. M. 2003. Coherence time of a solid-state nuclear qubit. http://arXiv.org/quant-ph/0309164.Google ScholarGoogle Scholar
  65. Lantz, J., Wallquist, M., Shumeiko, V. S., and Wendin, G. 2004. Josephson junction qubit network with current-controlled interaction. Phys. Rev. B 70, 140507.Google ScholarGoogle Scholar
  66. Lenstra, A., Tromer, E., Shamir, A., Kortsmit, W., Dodson, B., Hughes, J., and Leyland, P. 2003. Factoring estimates for a 1024-bit RSA modulus. In AsiaCrypt 2003. Lecture Notes in Computer Science. Springer-Verlag, New York.Google ScholarGoogle Scholar
  67. Leung, D. W., Chuang, I. L., Yamaguchi, F., and Yamamoto, Y. 2000. Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices. Phys. Rev. A 61. http://arXiv.org/quant-ph/9904100.Google ScholarGoogle Scholar
  68. Lidar, D. A., Chuang, I. L., and Whaley, K. B. 1998. Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 12 (Sept.), 2594--2597.Google ScholarGoogle Scholar
  69. Lidar, D. A. and Whaley, K. B. 2003. Irreversible Quantum Dynamics. Chapter Decoherence-Free Subspaces and Subsystems. Lecture Notes in Phys., vol. 622. Springer-Verlag, New York.Google ScholarGoogle Scholar
  70. Lim, Y. L., Barrett, S. D., Beige, A., Kok, P., and Kwek, L. C. 2005. Repeat-Until-Success quantum computing using stationary and flying qubits. http://arXiv.org/quant-ph/0508218.Google ScholarGoogle Scholar
  71. Lloyd, S. 1993. A potentially realizable quantum computer. Science 261, 1569--1571.Google ScholarGoogle Scholar
  72. Lloyd, S., Shahriar, M. S., and Hemmer, P. 2000. Teleportation and the quantum internet. http://arXiv.org/quant-ph/0003147.Google ScholarGoogle Scholar
  73. Loss, D. and DiVincenzo, D. P. 1998. Quantum computation with quantum dots. Phys. Rev. A 57, 120.Google ScholarGoogle Scholar
  74. Martinis, J. M., Nam, S., Aumentado, J., and Urbina, C. 2002. Rabi oscillations in a large Josephson-junction qubit. Phys. Rev. Lett. 89, 117901.Google ScholarGoogle Scholar
  75. Matsukevich, D. N. and Kuzmich, A. 2004. Quantum state transfer between matter and light. Science 306, 5696, 663--666.Google ScholarGoogle Scholar
  76. Mehring, M., Mende, J., and Scherer, W. 2003. Entanglement between an electron and a nuclear spin 1/2. Phys. Rev. Lett. 90, 153001.Google ScholarGoogle Scholar
  77. Metodiev, T., Cross, A., Thaker, D., Brown, K., Copsey, D., Chong, F. T., and Chuang, I. L. 2003. Preliminary results on simulating a scalable fault tolerant ion-trap system for quantum computation. In Proceedings of the 3rd Workshop on Non-Silicon Computation (NSC-3).Google ScholarGoogle Scholar
  78. Miller, A. J., Nam, S. W., Martinis, J. M., and Sergienko, A. V. 2003. Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination. Appl. Phys. Lett. 83, 791--793.Google ScholarGoogle Scholar
  79. Mooij, J. E., Orlando, T. P., Levitov, L., Tian, L., van der Wal, C. H., and Lloyd, S. 1999. Josephson persistent-current qubit. Science 285, 1036--1039.Google ScholarGoogle Scholar
  80. Moore, C. and Nilsson, M. 2001. Parallel quantum computation and quantum codes. SIAM J. Comput. 31, 3, 799--815. http://arxiv.org/abs/quant-ph/9808027. Google ScholarGoogle Scholar
  81. Moore, G. E. 1965. Cramming more components onto integrated circuits. Electronics 38, 8 (Apr.).Google ScholarGoogle Scholar
  82. Myrgren, E. S. and Whaley, K. B. 2003. Implementing a quantum algorithm with exchange-coupled quantum dots: A feasibility study. Quantum Inf. Proces. to appear: http://arXiv.org/quant-ph/0309051. Google ScholarGoogle Scholar
  83. Nakajima, Y., Kawano, Y., and Sekigawa, H. 2005. A new algorithm for producing quantum circuits using KAK decompositions. http://arXiv.org/quant-ph/0509196.Google ScholarGoogle Scholar
  84. Nakamura, Y., Pashkin, Y. A., and Tsai, J. S. 1999. Coherent control of macroscopic quantum states in a single-cooper-pair box. Nature 398, 786--788.Google ScholarGoogle Scholar
  85. Nielsen, M. A. 2004. Optical quantum computation using cluster states. Phys. Rev. Lett. 93, 040503.Google ScholarGoogle Scholar
  86. Nielsen, M. A. 2005. Cluster-state quantum computation. http://arxiv.org/abs/quant-ph/0504097.Google ScholarGoogle Scholar
  87. Nielsen, M. A. and Chuang, I. L. 2000. Quantum Computation and Quantum Information. Cambridge University Press. Google ScholarGoogle Scholar
  88. Nielsen, M. A. and Dawson, C. M. 2004. Fault-tolerant quantum computation with cluster states. http://arXiv.org/quant-ph/0405134.Google ScholarGoogle Scholar
  89. O'Brien, J. L., Pryde, G. J., White, A. G., Ralph, T. C., and Branning, D. 2003. Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264--267.Google ScholarGoogle Scholar
  90. Ömer, B. 2002. Classical concepts in quantum programming. In Proc. Quantum Structures.Google ScholarGoogle Scholar
  91. Oskin, M., Chong, F. T., Chuang, I. L., and Kubiatowicz, J. 2003. Building quantum wires: The long and short of it. In Computer Architecture News, Proceedings of the 30th Annual International Symposium on Computer Architecture. ACM, New York. Google ScholarGoogle Scholar
  92. Pashkin, Y. A., Yamamoto, T., Astafiev, O., Nakamura, Y., Averin, D. V., and Tsai, J. S. 2003. Quantum oscillations in two coupled charge qubits. Nature 421, 823--826.Google ScholarGoogle Scholar
  93. Paterson, K. G., Piper, F., and Schack, R. 2004. Why quantum cryptography? http://arxiv.org/quant-ph/0406147.Google ScholarGoogle Scholar
  94. Patterson, D. A., Gibson, G., and Katz, R. H. 1988. A case for redundant arrays of inexpensive disks (RAID). In Proceedings of the 1998 ACM SIGMOD Conference. ACM, New York, 109--116. Google ScholarGoogle Scholar
  95. Pellizzari, T., Gardiner, S. A., Cirac, J. I., and Zoller, P. 1995. Decoherence, continuous observation, and quantum computing: A cavity QED model. Phys. Rev. Lett. 75, 3788--3791.Google ScholarGoogle Scholar
  96. Petta, J. R., Johnson, A. C., Taylor, J. M., Laird, E. A., Yacoby, A., Lukin, M. D., Marcus, C. M., Hanson, M. P., and Gossard, A. C. 2005. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180--2184.Google ScholarGoogle Scholar
  97. Pittman, T., Jacobs, B., and Franson, J. 2005. Demonstration of quantum error correction using linear optics. Phys. Rev. A, 052332.Google ScholarGoogle Scholar
  98. Pittman, T. B., Fitch, M. J., Jacobs, B. C., and Franson, J. D. 2003. Experimental controlled-NOT logic gate for single photons in the coincidence basis. Phys. Rev. A 68, 032316.Google ScholarGoogle Scholar
  99. Pittman, T. B., Jacobs, B. C., and Franson, J. D. 2002. Demonstration of nondeterministic quantum logic operations using linear optical elements. Phys. Rev. Lett. 88, 257902.Google ScholarGoogle Scholar
  100. Preskill, J. 1998a. Lectures notes on quantum computation. http://www.theory.caltech.edu/~preskill/ph219/index.html.Google ScholarGoogle Scholar
  101. Preskill, J. 1998b. Reliable quantum computers. Proc. Roy. Soc. Lond. A 454, 385--410.Google ScholarGoogle Scholar
  102. Ralph, T. C., Hayes, A. J. F., and Gilchrist, A. 2005. Loss-tolerant optical qubits. Phys. Rev. Lett. 95, 100501.Google ScholarGoogle Scholar
  103. Raussendorf, R., Browne, D. E., and Briegel, H. J. 2003. Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 022312.Google ScholarGoogle Scholar
  104. Roos, C. F., Riebe, M., Häffner, H., Hänsel, W., Benhelm, J., Lancaster, G. P., Becher, C., Schmidt-Kaler, F., and Blatt, R. 2004. Control and measurement of three-qubit entangled states. Science 304, 1478--1480.Google ScholarGoogle Scholar
  105. RSA Security Inc. 2004. web page. http://www.rsasecurity.com/rsalabs/node.asp?id=2096.Google ScholarGoogle Scholar
  106. Sanaka, K., Jennewein, T., Pan, J., Resch, K., and Zeilinger, A. 2004. Experimental nonlinear sign shift for linear optics quantum computation. Phys. Rev. Lett. 92, 017902.Google ScholarGoogle Scholar
  107. Santori, C., Fattal, D., Vuckovic, J., Solomon, G. S., and Yamamoto, Y. 2002. Indistinguishable photons from a single-photon device. Nature 419, 594--597.Google ScholarGoogle Scholar
  108. Scheel, S., Nemoto, K., Munro, W. J., and Knight, P. L. 2003. Measurement-induced nonlinearity in linear optics. Phys. Rev. A 68, 032310.Google ScholarGoogle Scholar
  109. Schmidt-Kaler, F., Haffner, H., Riebe, M., Gulde, S., Lancaster, G. P. T., Deuschle, T., Becher, C., Roos, C. F., Eschner, J., and Blatt, R. 2003. Realization of the Cirac-Zoller controlled-NOT quantum gate. Nature 422, 408.Google ScholarGoogle Scholar
  110. Schulman, L. J. and Vazirani, U. V. 1999. Molecular scale heat engines and scalable quantum computers. In Proceedings of the 31st ACM Symposium on the Theory of Computing. ACM, New York, p. 322. Google ScholarGoogle Scholar
  111. Shahriar, M. S., Hemmer, P. R., Lloyd, S., Bhatia, P. S., and Craig, A. E. 2002. Solid-state quantum computing using spectral holes. Phys. Rev. A 66, 032301.Google ScholarGoogle Scholar
  112. Shnirman, A., Schön, G., and Hermon, Z. 1997. Quantum manipulations of small Josephson junctions. Phys. Rev. Lett. 79, 2371--2374.Google ScholarGoogle Scholar
  113. Shor, P. W. 1994. Algorithms for quantum computation: Discrete logarithms and factoring. In Proceedings of the 35th Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 124--134.Google ScholarGoogle Scholar
  114. Shor, P. W. 1996. Fault-tolerant quantum computation. In Proceedings of the 37th Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 56--65. Google ScholarGoogle Scholar
  115. Shor, P. W. 1997. Polynomial time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Compt. 26, 5, 1484--1509. http://arXiv.org/quant-ph/9508027. Google ScholarGoogle Scholar
  116. Skinner, A. J., Davenport, M. E., and Kane, B. E. 2003. Hydrogenic spin quantum computing in silicon: A digital approach. Phys. Rev. Lett. 90, 087901. http://arXiv.org/quant-ph/0206159.Google ScholarGoogle Scholar
  117. Sørensen, A. and Mølmer, K. 2000. Entanglement and quantum computation with ions in thermal motion. Phys. Rev. A 62.Google ScholarGoogle Scholar
  118. Spiller, T. P., Munro, W. J., Barrett, S. D., and Kok, P. 2005. An introduction to quantum information processing: Applications and realisations. Tech. Rep. HPL-2005-192. Oct.Google ScholarGoogle Scholar
  119. Steane, A. 1996. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793--797.Google ScholarGoogle Scholar
  120. Steane, A. 1997. The ion trap quantum information processor. Appl. Phys. B 64, 623--642.Google ScholarGoogle Scholar
  121. Steane, A. et al. 2000. Speed of ion trap quantum information processors. Phys. Rev. A 62. http://arXiv.org/quant-ph/0003087.Google ScholarGoogle Scholar
  122. Steane, A. M. 2002. Quantum computer architecture for fast entropy extraction. Quantum Inf. Comput. 2, 4, 297--306. http://arxiv.org/quant-ph/0203047. Google ScholarGoogle Scholar
  123. Steane, A. M. 2003. Overhead and noise threshold of fault-tolerant quantum error correction. Phys. Rev. A 68, 042322. http://arXiv.org/quant-ph/0207119.Google ScholarGoogle Scholar
  124. Steane, A. M. and Ibinson, B. 2003. Fault-tolerant logical gate networks for CSS codes. http://arXiv.org/quant-ph/0311014.Google ScholarGoogle Scholar
  125. Steane, A. M. and Lucas, D. M. 2000. Quantum computing with trapped ions, atoms, and light. Fortschritte der Physik. http://arXiv.org/quant-ph/0004053.Google ScholarGoogle Scholar
  126. Svore, K. M., Terhal, B. M., and DiVincenzo, D. P. 2005. Local fault-tolerant quantum computation. Phys. Rev. A 72, 022317.Google ScholarGoogle Scholar
  127. Szkopek, T., Boykin, P., Fan, H., Roychowdhury, V., Yablonovitch, E., Simms, G., Gyure, M., and Fong, B. 2004. Threshold error penalty for fault tolerant computation with nearest neighbour communication. http://arxiv.org/abs/quant-ph/0411111. Google ScholarGoogle Scholar
  128. Van Meter, R. 2005. http://www.tera.ics.keio.ac.jp/person/rdv/quantum/arithmetic.html.Google ScholarGoogle Scholar
  129. Van Meter, R. and Itoh, K. M. 2005. Fast quantum modular exponentiation. Phys. Rev. A 71, 5 (May), 052320. http://arXiv.org/quant-ph/0408006.Google ScholarGoogle Scholar
  130. Van Meter, R., Itoh, K. M., and Ladd, T. D. 2005. Architecture-dependent execution time of Shor's algorithm. http://arXiv.org/quant-ph/0507023.Google ScholarGoogle Scholar
  131. Vandersypen, L. M. and Chuang, I. 2004. NMR techniques for quantum computation and control. Rev. Modern Phys. 76, 1037.Google ScholarGoogle Scholar
  132. Vandersypen, L. M. K., Steffen, M., Breyta, G., Yannoni, C. S., Sherwood, M. H., and Chuang, I. L. 2001. Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883--887.Google ScholarGoogle Scholar
  133. Varnava, M., Browne, D. E., and Rudolph, T. 2005. Loss tolerant one-way quantum computation---a horticultural approach.Google ScholarGoogle Scholar
  134. Vartiainen, J. J., Niskanen, A. O., Nakahara, M., and Salomaa, M. M. 2004. Implementing Shor's algorithm on Josephson charge qubits. Phys. Rev. A 70, 012319.Google ScholarGoogle Scholar
  135. Vedral, V., Barenco, A., and Ekert, A. 1996. Quantum networks for elementary arithmetic operations. Phys. Rev. A 54, 147--153. http://arXiv.org/quant-ph/9511018.Google ScholarGoogle Scholar
  136. Waks, E., Inoue, K., Oliver, W., Diamanti, E., and Yamamoto, Y. 2003. High-efficiency photon-number detection for quantum information processing. IEEE J. Selected Topics Quantum Electronics 9, 1502--1511.Google ScholarGoogle Scholar
  137. Wallraff, A., Schuster, D. I., Blais, A., Frunzio, L., Huang, R.-S., Majer, J., Kumar, S., Girvin, S. M., and Schoelkopf, R. J. 2004. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162--167.Google ScholarGoogle Scholar
  138. Walther, P., Resch, K. J., Rudolph, T., Schenck, E., Weinfurter, H., Vedral, V., Aspelmeyer, M., and Zeilinger, A. 2005. Experimental one-way quantum computing. Nature 434, 169--176.Google ScholarGoogle Scholar
  139. Williams, C. P. and Clearwater, S. H. 1999. Ultimate Zero and One: Computing at the Quantum Frontier. Copernicus Books.Google ScholarGoogle Scholar
  140. Wineland, D. J. et al. 2005. Quantum control, quantum information processing, and quantum-limited metrology with trapped ions. In Proceedings of the International Conference on Laser Spectroscopy (ICOLS). http://arxiv.org/quant-ph/0508025.Google ScholarGoogle Scholar
  141. Yao, A. 1993. Quantum circuit complexity. In Proceedings of the 34th Annual Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, CA, 352--361.Google ScholarGoogle Scholar
  142. Yimsiriwattana, A. and Lomonaco Jr., S. J. 2004. Distributed quantum computing: A distributed Shor algorithm. http://arxiv.org/quant-ph/0403146.Google ScholarGoogle Scholar
  143. Yoran, N. and Reznik, B. 2003. Deterministic linear optics quantum computation with single photon qubits. Phys. Rev. Lett. 91, 037903.Google ScholarGoogle Scholar
  144. You, J. Q., Tsai, J. S., and Nori, F. 2002. Scalable quantum computing with Josephson charge qubits. Phys. Rev. Lett. 89. http://arXiv.org/cond-mat/0306209.Google ScholarGoogle Scholar
  145. You, J. Q., Tsai, J. S., and Nori, F. 2003. Quantum computing with many superconducting qubits. http://arXiv.org/cond-mat/0306208.Google ScholarGoogle Scholar
  146. Yu, Y., Han, S., Chu, X., Chu, S.-I., and Wang, Z. 2002. Coherent temporal oscillations of macroscopic quantum states in a Josephson junction. Science 296, 5569, 889--892.Google ScholarGoogle Scholar
  147. Zalka, C. 1998. Fast versions of Shor's quantum factoring algorithm. http://arXiv.org/quant-ph/9806084.Google ScholarGoogle Scholar

Index Terms

  1. Architectural implications of quantum computing technologies

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader