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Abstract

After a very brief survey of the key milestones and open problems in quantum computation and information, the research effort at IST-UTL is outlined, namely, the goals, ongoing tasks and results of the QuantLog project. In order to illustrate some key issues in quantum computation, the problem of minimizing the number of qubits in quantum automata is presented in detail at a level appropriate for non-specialists.

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References

  1. Abadi M, Gordon AD. “A calculus for cryptographic protocols: The Spi Calculus”, Information and Computation, vol. 148 no. 1, pp. 1–70, 1999. Full version available as SRC Research Report 149, January 1998.

    Article  MATH  MathSciNet  Google Scholar 

  2. Adão P, Bana G, Herzog J, Scedrov A. “Soundness and completeness of formal encryption: The cases of key-cycles and partial information leakage”, Preprint, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2005. Submitted for publication.

    Google Scholar 

  3. Adão P, Bana G, Herzog J, Scedrov A. “Soundness of formal encryption in the presence of key-cycles”, S. D. C. di Vimercati, P. Syverson, and D. Gollmann (eds.), Proceedings of the 10th European Symposium on Research in Computer Security (ESORICS), vol. 3679 of Lecture Notes in Computer Science, Springer-Verlag, 2005, pp. 374–396.

    Google Scholar 

  4. Adão P, Bana G, Scedrov A. “Computational and information-theoretic soundness and completeness of formal encryption”, Proceedings of the 18th IEEE Computer Security Foundations Workshop (CSFW), IEEE Computer Society Press, 2005, pp. 170–184.

    Google Scholar 

  5. Adão P, Fournet C. “Cryptographically sound implementations for communicating processes”, Preprint, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2006. Submitted for publication.

    Google Scholar 

  6. Adão P, Mateus P. “A process algebra for reasoning about quantum security”, Electronic Notes in Theoretical Computer Science, to appear. Preliminary version presented at 3rd International Workshop on Quantum Programming Languages, June 30–July 1, 2005, Chicago, Affiliated Workshop of LICS 2005.

    Google Scholar 

  7. Adão P, Mateus P, Reis T, Viganò L. “Towards a quantitave analysis of security protocols”, Preprint, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2006. Submitted for publication.

    Google Scholar 

  8. Agrawal M, Kayal N, Saxena N. “PRIMES is in P”, Annals of Mathematics, vol. 160 no. 2, pp. 781–793, 2004.

    MATH  MathSciNet  Google Scholar 

  9. Aharonov D, van Dam W, Kempe J, Landau Z, Lloyd S, Regev O. “Adiabatic quantum computation is equivalent to standard quantum computation”, FOCS’ 04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS’04), IEEE Computer Society, 2004, pp. 42–51.

    Google Scholar 

  10. Aspect A, Grangier P, Roger G. “Experimental tests of realistic local theories via Bell’s theorem”, Physical Review Letters, vol. 47, pp. 460, 1981.

    Article  Google Scholar 

  11. Bell JS. “On the Einstein-Podolsky-Rosen paradox”, Physics, vol. 1, pp.195, 1964.

    Google Scholar 

  12. Benioff P. “The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines”, Journal of Statistical Physics, vol. 22, pp.563–591, 1980.

    Article  MathSciNet  Google Scholar 

  13. Benioff P. “Quantum mechanical models of Turing machines that dissipate no energy”, Physical Review Letters, vol. 48, pp.1581–1585, 1982.

    Article  MathSciNet  Google Scholar 

  14. Bennett CH, Brassard G. “Quantum cryptography: Public key distribution and coin tossing”, Proceedings of IEEE international Conference on Computers, Systems and Signal Processing, IEEE Press, 1984, pp.175–179.

    Google Scholar 

  15. Bennett CH, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W. “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels”, Physical Review Letters, vol. 70 no. 13, pp.1895–1899, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  16. Bennett CH, Wiesner SJ. “Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states”, Physical Review Letters, vol. 69 no. 20, pp.2881–2884, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  17. Birkhoff G, von Neumann J. “The logic of quantum mechanics”, Annals of Mathematics, vol. 37 no. 4, pp.823–843, 1936.

    Article  MathSciNet  Google Scholar 

  18. Boyer M, Brassard G, Høyer P, Tapp A. “Tight bounds on quantum searching”, Fortschritte der Physik, vol. 46 no. 1–5, pp.493–505, 1998.

    Article  Google Scholar 

  19. Caleiro C, Mateus P, Sernadas A, Sernadas C. “Quantum institutions”, Preprint, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2005. Submitted for publication.

    Google Scholar 

  20. Caleiro C, Viganò L, Basin D. “Deconstructing Alice and Bob”, Electronic Notes in Theoretical Computer Science, vol. 135 no. 1, pp.3–22, 2005. Preliminary version presented at ICALP’05 ARSPA Workshop.

    Article  Google Scholar 

  21. Caleiro C, Viganò L, Basin D. “Metareasoning about security protocols using distributed temporal logic”, Electronic Notes in Theoretical Computer Science, vol. 125 no. 1, pp.67–89, 2005. Preliminary version presented at IJCAR’04 ARSPA Workshop.

    Article  Google Scholar 

  22. Caleiro C, Viganò L, Basin D. “On the expresiveness of a message sequence formalism for security protocols”, Preprint, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2005. Submitted for publication.

    Google Scholar 

  23. Caleiro C, Viganò L, Basin D. “Relating strand spaces and distributed temporal logic for security protocol analysis”, Logic Journal of the IGPL, vol. 13 no. 6, pp.637–664, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  24. Canetti R. “Universally composable security: A new paradigm for cryptographic protocols”, 42nd IEEE Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society Press, 2001, pp.136–145. Full version available at IACR ePrint Archive, Report 2000/067.

    Google Scholar 

  25. Chadha R, Mateus P, Sernadas A. “Reasoning about states of probabilistic sequential programs”, Preprint, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2006. Submitted for publication.

    Google Scholar 

  26. Chadha R, Mateus P, Sernadas A, Sernadas C. “Extending classical logic for reasoning about quantum systems”, Preprint, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2005. Submitted for publication.

    Google Scholar 

  27. Chiara MLD, Giuntini R, Greechie R. Reasoning in Quantum Theory, Dordrecht, The Netherlands, Kluwer Academic Publishers, 2004.

    MATH  Google Scholar 

  28. Childs AM, Cleve R, Deotto E, Farhi E, Gutmann S, Spielman DA. “Exponential algorithmic speedup by a quantum walk”, STOC’03: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, ACM Press, 2003, pp.59–68.

    Google Scholar 

  29. Cook SA. “The complexity of theorem-proving procedures”, STOC’71: Proceedings of the 3rd Annual ACM Symposium on Theory of Computing, ACM Press, 1971, pp.151–158.

    Google Scholar 

  30. Cook SA, Reckhow RA. “Time bounded random access machines”, Journal of Computer and System Sciences, vol. 7 no. 4, pp.354–375, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  31. Costa Jr AT, Bose S, Omar Y. “Entanglement of two impurities through electron scattering”, Preprint, CFP, Department of Physics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2005. Submitted for publication.

    Google Scholar 

  32. Deutsch D. “Quantum theory, the Church-Turing principle and the universal quantum computer”, Proceedings of the Royal Society of London A, vol. 400, pp.97–117, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  33. Devetak I. “The private classical capacity and quantum capacity of a quantum channel”, IEEE Transactions on Information Theory, vol. 51, pp.44–55, 2005.

    Article  MathSciNet  Google Scholar 

  34. DiVincenzo DP. “Two-bit gates are universal for quantum computation”, Physical Review A, vol. 51, pp.1015–1022, 1995.

    Article  Google Scholar 

  35. Ekert AK. “Quantum cryptography based on Bell’s theorem”, Physical Review Letters, vol. 67 no. 6, pp.661–663, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  36. Farhi E, Goldstone J, Gutmann S, Sipser M. “Quantum computation by adiabatic evolution”, Technical Report quant-ph/0001106, ArXiv, USA, 2000.

    Google Scholar 

  37. Feynman RP. “Simulating Physics with computers”, International Journal of Theoretical Physics, vol. 21, pp.467, 1982.

    Article  MathSciNet  Google Scholar 

  38. Foulis DJ. “A half-century of quantum logic. What have we learned?”, Quantum Structures and the Nature of Reality, vol. 7 of Einstein Meets Magritte, Kluwer Acad. Publ., 1999, pp.1–36.

    MathSciNet  Google Scholar 

  39. Gobby C, Yuan ZL, Shields AJ. “Quantum key distribution over 122 km of standard telecom fiber”, Applied Physics Letters, vol. 84 no. 19, pp.3762–3764, 2004.

    Article  Google Scholar 

  40. Grover LK. “A fast quantum mechanical algorithm for database search”, STOC’96: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, ACM Press, 1996, pp.212–219.

    Google Scholar 

  41. Grover LK. “Quantum mechanics helps in searching for a needle in a haystack”, Physical Review Letters, vol. 79 no. 2, pp.325–328, 1997.

    Article  Google Scholar 

  42. Häffner H, Hänsel W, Roos CF, Benhelm J, Chekalkar D, Chwalla M, Körber T, Rapol UD, Riebe M, Schmidt PO, Becher C, Gühne O, Dür W, Blatt R. “Scalable multiparticle entanglement of trapped ions”, Nature, vol. 438, pp.643–646, 2005.

    Article  Google Scholar 

  43. Hallgren S. “Polynomial-time quantum algorithms for Pell’s equation and the principal ideal problem”, STOC’02: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, ACM Press, 2002, pp.653–658.

    Google Scholar 

  44. Halpern JY. “An analysis of first-order logics of probability”, Artificial Intelligence, vol. 46, pp.311–350, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  45. Hansson H, Jonsson B. “A logic for reasoning about time and reliability”, Formal Aspects of Computing, vol. 6, pp.512–535, 1995.

    Article  Google Scholar 

  46. Holevo AS. “The capacity of quantum channel with general signal states”, IEEE Transactions on Information Theory, vol. 44, pp.269, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  47. Knill E. “Conventions for quantum pseudocode”, Technical Report LAUR-96-2724, Los Alamos National Laboratory, Los Alamos, USA, 1996.

    Google Scholar 

  48. Mateus P, Mitchell J, Scedrov A. “Composition of cryptographic protocols in a probabilistic polynomial-time process calculus”, R. Amadio and D. Lugiez (eds.), CONCUR 2003 — Concurrency Theory, vol. 2761 of Lecture Notes in Computer Science, Springer, 2003, pp.327–349.

    Google Scholar 

  49. Mateus P, Omar Y. “Quantum pattern matching”, Preprint, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2005. ArXiv quantph/0508237. Full version of [50].

    Google Scholar 

  50. Mateus P, Omar Y. “A quantum algorithm for closest pattern matching”, D. Angelakis and M. Christandl (eds.), Proceedings of NATO ASI Quantum Computation and Information, IOS Press, in print. Short version of [49].

    Google Scholar 

  51. Mateus P, Sernadas A. “Exogenous quantum logic”, W. A. Carnielli, F. M. Dionísio, and P. Mateus (eds.), Proceedings of CombLog’04, Workshop on Combination of Logics: Theory and Applications, Departamento de Matemática, Instituto Superior Técnico, Lisboa, 2004, pp.141–149. Extended abstract.

    Google Scholar 

  52. Mateus P, Sernadas A. “Reasoning about quantum systems”, J. Alferes and J. Leite (eds.), Logics in Artificial Intelligence, Ninth European Conference, JELIA’04, vol. 3229 of Lecture Notes in Artificial Intelligence, Springer-Verlag, 2004, pp.239–251.

    Google Scholar 

  53. Mateus P, Sernadas A. “Complete exogenous quantum propositional logic”, Technical report, CLC, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2005. Extended abstract. Short presentation at LICS 2005, Chicago, USA, June 26–29.

    Google Scholar 

  54. Mateus P, Sernadas A. “Weakly complete axiomatization of exogenous quantum propositional logic”, Information and Computation, in print. ArXiv math.LO/0503453.

    Google Scholar 

  55. Mateus P, Sernadas A, Sernadas C. “Exogenous semantics approach to enriching logics”, G. Sica (ed.), Essays on the Foundations of Mathematics and Logic, vol. 1 of Advanced Studies in Mathematics and Logic, Polimetrica, 2005, pp.165–194.

    Google Scholar 

  56. Mitchell J, Ramanathan A, Scedrov A, Teague V. “A probabilistic polynomial-time calculus for analysis of cryptographic protocols (Preliminary Report)”, Electronic Notes in Theoretical Computer Science, vol. 45, pp.1–31, 2001.

    Article  Google Scholar 

  57. Moore C, Crutchfield JP. “Quantum automata and quantum grammars”, Theoretical Computer Science, vol. 237 no. 1–2, pp.275–306, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  58. Navarro G. “A guided tour to approximate string matching”, ACM Computing Surveys, vol. 33 no. 1, pp.31–88, 2001.

    Article  Google Scholar 

  59. Nielsen MA, Chuang IL. Quantum Computation and Quantum Information, Cambridge, UK, Cambridge University Press, 2000.

    MATH  Google Scholar 

  60. Omar Y. “Indistinguishable particles in quantum mechanics: An introduction”, Contemporary Physics, vol. 46, pp.437–448, 2005.

    Article  Google Scholar 

  61. Omar Y. “Particle statistics in quantum information processing”, International Journal of Quantum Information, vol. 3 no. 1, pp.201–205, 2005.

    Article  Google Scholar 

  62. Omar Y, Paunkovic N, Sheridan L, Bose S. “Quantum walk on a line with two entangled particles”, Preprint, CFP, Department of Physics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2004. Submitted for publication.

    Google Scholar 

  63. Raussendorf R, Briegel HJ. “A one-way quantum computer”, Physical Review Letters, vol. 86 no. 22, pp.5188–5191, 2001.

    Article  Google Scholar 

  64. Schrödinger E. “Die gegenwartige Situation in der Quantenmechanik”, Naturwissenschaften, vol. 23, pp.807–812, 823–823, 844–849, 1935. English translation: John D Trimmer, Proceedings of the American Philosophical Society, 124, 323–38 (1980), Reprinted in Quantum Theory and Measurement, p. 152 (1983).

    Article  Google Scholar 

  65. Schumacher B. “Quantum coding”, Physical Review A, vol. 51, pp.2738–2747, 1995.

    Article  MathSciNet  Google Scholar 

  66. Schumacher B, Westmoreland M. “Sending classical information via noisy quantum channels”, Physical Review A, vol. 56, pp.131–138, 1997.

    Article  Google Scholar 

  67. Schwartz JT. “Fast probabilistic algorithms for verification of polynomial identities”, Journal of the ACM, vol. 27 no. 4, pp.701–717, 1980.

    Article  MATH  Google Scholar 

  68. Shannon CE. “A mathematical theory of communication”, Bell System Technical Journal, vol. 27, pp.379, 623, 1948.

    MathSciNet  MATH  Google Scholar 

  69. Shor PW. “Algorithms for quantum computation: Discrete logarithms and factoring”, S. Goldwasser (ed.), Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, IEEE Computer Society, 1994, pp.124–134.

    Google Scholar 

  70. Shor PW. “Scheme for reducing decoherence in quantum computer memory”, Physical Review A, vol. 52, pp.R2493, 1995.

    Article  Google Scholar 

  71. Shor PW. “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer”, SIAM Journal on Computing, vol. 26 no. 5, pp.1484–1509, 1997. Presented at FOCS’94.

    Article  MATH  MathSciNet  Google Scholar 

  72. Steane AM. “Error correcting codes in quantum theory”, Physical Review Letters, vol. 77 no. 5, pp.793–797, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  73. Vandersypen LMK, Steffen M, Breyta G, Yannoni CS, Sherwood MH, Chuang IL. “Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance”, Nature, vol. 414, pp.883–887, 2001.

    Article  Google Scholar 

  74. Wiesner S. “Conjugate coding”, SIGACT News, vol. 15 no. 1, pp.78–88, 1983. Original manuscript written circa 1970.

    Article  Google Scholar 

  75. Yao AC. “Theory and applications of trapdoor functions”, 23rd IEEE Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society, 1982, pp.80–91.

    Google Scholar 

  76. Zippel R. “Probabilistic algorithms for sparse polynomials”, EUROSAM’ 79: Proceedings of the International Symposiumon on Symbolic and Algebraic Computation, Springer-Verlag, 1979, pp.216–226.

    Google Scholar 

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Sernadas, A., Mateus, P., Omar, Y. (2007). Quantum Computation and Information. In: Pereira, M.S. (eds) A Portrait of State-of-the-Art Research at the Technical University of Lisbon. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5690-1_3

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