A New Way to Implement Quantum Computation

¹ University of Cassino, Cassino, Italy

Abstract

In this paper , I shall sketch a new way to consider a Lindenbaum-Tarski algebra as a 3D logical space in which any one (of the 256 statements ) occupies a well - defin ed position and it is identified by a numerical ID. This allows pure me chanical computation both for generating rules and inferences. It is shown that this abstract formalism can be geometri cally represented with logical spaces and subspaces allowing a vectorial representation. Finally, it show s the applica tion to quantum computing through the example of three coupled harmonic oscillators.

KeywordsLindenbaum-Tarski Algebra3D Logical SpaceMechanical ComputationInferenceQuantum Com-putingRaising OperatorsLowering Operators

G. Boole, “An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities,” New York, Dover, 1958.
A. Tarski, “On the Foundations of Boolean Algebra,” Vol. 10, 1935, pp. 320-341.
G. Auletta, “Mechanical Logic in three-Dimensional Space,” PanStanford Pub, Peking, 2014.
G. Auletta and S.-Y. Wang, “Quantum Mechanics for Thinkers,” Pan Stanford Pub, Peking, 2014.
G. Auletta, “Inferences with Information,” Universal Journal of Applied computer Science and Technology, Vol. 2, No. 2, 2012, pp. 216-221.
H.-K. Lo, S. Popescu and T. Spiller, “Introduction to Quantum Computation and Information,” World Scientific, Singapore, 1998.
M. A. Nielsen and I. L. Chuang, “Quantum Computation and Quantum Information,” University Press, Cambridge, 2011.
D. Bouwmeester, A. K. Ekert and A. Zeilinger, “The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation,” Springer, Berlin, 2000.
G. Auletta, M. Fortunato and G. Parisi, “Quantum Mechanics,” University Press, Cambridge, 2009.
A. Tarski, Logic, “Semantics, Meta-Mathematics,” University Press, Oxford, 1956.

Menu

A New Way to Implement Quantum Computation

Abstract

References (10)