The Quantum Speed up as Advanced Cognition of the Solution

  • Giuseppe Castagnoli


Solving a problem requires a problem solving step (deriving, from the formulation of the problem, the solution algorithm) and a computation step (running the algorithm). The latter step is generally oblivious of the former. We unify the two steps into a single physical interaction: a many body interaction in an idealized classical framework, a measurement interaction in the quantum framework. The many body interaction is a useful conceptual reference. The coordinates of the moving parts of a perfect machine are submitted to a relation representing problem-solution interdependence. Moving an “input” part nondeterministically produces a solution through a many body interaction. The kinematics and the statistics of this problem solving mechanism apply to quantum computation—once the physical representation is extended to the oracle that produces the problem. Configuration space is replaced by phase space. The relation between the coordinates of the machine parts now applies to a set of variables representing the populations of the qubits of a quantum register during reduction. The many body interaction is replaced by the measurement interaction, which changes the population variables from the values before to the values after measurement (and the forward evolution into the backward evolution, the same unitary transformation but ending with the state after measurement). Quantum computation is reduction on the solution of the problem under the problem-solution interdependence relation.

The speed up is explained by a simple consideration of time-symmetry, it is the gain of information about the solution due to backdating, to before running the algorithm, a time-symmetric part of the reduction on the solution. This advanced cognition of the solution reduces the solution space to be explored by the algorithm. The quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of the information acquired by reading the solution (i.e. by measuring the content of the computer register at the end of the quantum algorithm).

From another standpoint, the notion that a computation process is condensed into a single physical interaction explains the fact that we perceive many things at the same time in the introspective “present” (the instant of the interaction in the classical case, the time interval spanned by backdated reduction in the quantum case).


Quantum computation Quantum speed up Quantum measurement Many body Quantum consciousness 


  1. 1.
    Abbagnano, N.: Storia della Filosofia, vol. I, p. 87. U.T.E.T., Turin (1958) Google Scholar
  2. 2.
    Castagnoli, G.: Quantum computation based on retarded and advanced propagation. quant-ph/9706019 (1997)
  3. 3.
    Castagnoli, G.: Quantum problem solving as simultaneous computation. arXiv:0710.1744 (2007)
  4. 4.
    Castagnoli, G.: On a fundamental problem solving mechanism explaining the wholeness of perception. In: Hameroff, S.R., Kaszniak, A.W., Scott, A.C. (eds.) Toward a Science of Consciousness 2008—Tucson Discussions and Debates, p. 456. MIT Press, Cambridge (2008) Google Scholar
  5. 5.
    Castagnoli, G.: The mechanism of quantum computation. Int. J. Theor. Phys. (2008). Special issue “Quantum Computation 2008”. UV Google Scholar
  6. 6.
    Castagnoli, G., Finkelstein, D.: Theory of the quantum speed up. Proc. R. Soc. Lond. A 457, 1799 (2001). quant-ph/0010081 MATHADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Castagnoli, G., Monti, D., Sergienko, A.: Performing quantum measurement in suitably entangled states originates the quantum computation speed up. quant-ph/9908015 (1999)
  8. 8.
    Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proc. R. Soc. Lond. A 454(1969), 339–354 (1996). quant-ph/9708016 MathSciNetADSGoogle Scholar
  9. 9.
    Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97 (1985) MATHADSMathSciNetGoogle Scholar
  10. 10.
    Finkelstein, D.R.: Space-time structure in high energy interactions. In: Gudehus, T., Kaiser, G., Perlmutter, A. (eds.) Coral Gables Conference on Fundamental Interactions at High Energy. Center of Theoretical Studies, January 22–24, 1969. University of Miami, pp. 324–343. Gordon & Breach, New York (1969) Google Scholar
  11. 11.
    Finkelstein, D.R.: Generational Quantum Theory. Preprint (2008) Google Scholar
  12. 12.
    Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theor. Phys. 21, 219 (1982) MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proc. 28th Ann. ACM Symp. Theory of Computing (1996) Google Scholar
  14. 14.
    Grover, L.K.: From Schrodinger equation to quantum search algorithm. quant-ph/0109116 (2001)
  15. 15.
    Hameroff, S.R., Penrose, R.: Orchestrated reduction of quantum coherence in brain microtubules: a model for consciousness? In: Hameroff, S.R., Kaszniak, A.W., Scott, A.C. (eds.) Toward a Science of Consciousness—the First Tucson Discussions and Debates, pp. 507–540. MIT Press, Cambridge (1996) Google Scholar
  16. 16.
    Kaye, P., Laflamme, R., Mosca, M.: An Introduction to Quantum Computing. Oxford University Press, New York (2007) MATHGoogle Scholar
  17. 17.
    Mosca, M., Ekert, A.: The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer. Lecture Notes in Computer Science, vol. 1509. Springer, Berlin (1999) Google Scholar
  18. 18.
    Mulligan, K., Smith, B.: Mach and Ehrenfels: The foundations of gestalt theory. In: Smith, B. (ed.) Foundations of Gestalt Theory, Munich and Vienna. Philosophia, vol. 124 (1988).
  19. 19.
    Penrose, R.: Shadows of the Mind—a Search for the Missing Science of Consciousness. Oxford University Press, London (1994) Google Scholar
  20. 20.
    Sheehan, D.: Consciousness and the physics of time. In: Consciousness Research Abstracts, Proceedings of the Toward a Science of Consciousness Meeting, April 8–12, 2008, Tucson, Arizona Google Scholar
  21. 21.
    Simon, D.: On the power of quantum computation. In: Proc. 35th Ann. Symp. on Foundations of Comp. Sci., pp. 116–123 (1994) Google Scholar
  22. 22.
    Stapp, H.P.: Mind, Matter, and Quantum Mechanics. Springer, Heidelberg (1993) MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Pieve LigureItaly

Personalised recommendations