vol 2: Synopsis
part IV: Divine dynamics
page 29: Quantum information theory
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Quantum information theory
Much of the physical theory that we have inherited from the past accepts implicitly that the world is dead and inert, needing to moved from outside by gods or angels. Modern quantum information theory suggests that the world itself is an intelligent mind, alive and self motivated at every point. Each organisms within the universe contributes to its overall glory and complexity.
A mathematical proof, executed by a Turing machine, is a deterministic process. It comprises a series of steps, each of which is bound to follow from the steps before, establishing a logical chain from hypothesis to conclusion. Eg, if Euclid's axioms of geometry are true, the square on the hypotenuse of a right angled triangle is equal to the sum of the squares on the other two sides.
The steps in a proof are represented by states of a physical system. In the classical pencil and paper approach to mathematics, these steps are represented by marks on paper. In an electronic computer theorem proving system, the states are represented by the presence or absence of electrons in different parts of the physical computer.
Now the question arises: can we represent the stages in a proof (or computation) by quantum states? The mathematical quantum theory represents these states as vectors in Hilbert spaces, and uses the rules of quantum theory to transform these vectors and predict the probabilities of various outcomes of a given initial state.
The answer to this question appears to be yes. Given that this is so, we will be able to turn the most delicate mechanisms in the world to the purpose of human computation. But if these things can be used for computation, perhaps computation is their natural role in the universe. We may then look at the quantum theory of many particles as descriptions of networks of communication and computation. This brings the physical nature of the universe a lot closer to human experience, since we are naturally information processing and communicating organisms.
Books
| Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. ... The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.' Amazon back |
| Lo, Hoi-Kwong, and Tim Spiller, Sandra Popescu, Introduction to Quantum Computation and Information, World Scientific 1998 Jacket: 'This book provides a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault tolerant quantum computation, as well as some experimental aspects of quantum computation and quantum cryptography. A knowledge of basic quantum mechanics is assumed.' Amazon back |
| Milburn, Gerard J, The Feynman Processor : Quantum Entanglement and the Computing Revolution , Perseus Jacket: 'Starting with a clear and concise description of the basic principles of quantum physics, Milburn goes on to introduce some of its most amazing, newly discovered (sic) phenomena, including quantum entanglement, the strangest property of what is already the strangest field of science. Quantum entanglement - which Einstein called "spooky action at a distance" - underlies the interdimensional connections that join seemingly unrelated events and objects. He shows how conventional computers cannot go on getting smaller and faster forever and how the unpredictability of matter at this level has enabled scientists to rethink the way that we could design, build and use the new "quantum computers". Finally Milburn takes us into the near future, when physicists and computer sceintists will build new and incredible devices that will deliver a world of lightning-fast computers, unbreakable codes, and even the beginning of Star-trek like matter teleportation.' Amazon back |
| Nielsen, Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and compuitation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002. Amazon back |
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