BRILL eBooks

ENTANGLING EFFECTIVE PROCEDURES: FROM LOGIC MACHINES TO QUANTUM AUTOMATA

Rossella Lupacchini

Published Jan 1, 2011• 0 citations

Abstract

Turing machines and Godel's incompleteness results take classical determinism to its limits by showing the extent to which symbolic knowledge can grow inside a nite state closed system. Those limits overlap with classical physics'. To master intelligence, machines must appear to behave as if they had "free will". Insofar as such a behaviour depends on randomness and interference, that appearance of free will can result from quantum physics. As it is bound to the changeable and unpredictable system-observer interaction, knowledge emerging out of quantum physics cannot be comprised in any closed system. However, it might be grasped through a hierarchy of measurements performable by a "quantum automaton".

DOI: 10.1163/9789401207157_012

Related papers

Quantum Collapse and Computation in an Everett Multiverse

Fabrizio Tamburini, Ignazio Francesco Licata

The mathematical representation of the universe consists of sequences of symbols, rules and operators containing Gödel's undecidable propositions: information and its manipulation, also with Turing Machines. Classical information theory and mathematics, ideally independent from the medium used, can be interpreted realistically and objectively from their correspondence with quantum information, which is physical. Each representation of the universe and its evolution are, in any case, physical subsets of the universe, structured sets of observers and their complements in the universe made with spacetime events generated by local quantum measurements. Their description becomes a semantically closed structure without a global object-environment loss of decoherence as a von Neumann's universal constructor with a semantical abstract whose structure cannot be decided deterministically a priori from an internal observer. In a semantically closed structure, the realization of a specific event that writes the semantical abstract of the constructor is a problem of finding "which way" for the evolution of the universe as a choice of the constructor's state in a metastructure, like the many-world Everett scenario, from a specific result of any quantum measurement, corresponding to a Gödel undecidable proposition for an internal observer.

arXiv:2401.13336EntropyDec 9, 20241 citation

Quantum Reality

Andreas Wichert

Information is a part of the physical universe as matter and energy. Today first small quantum computers begin to appear. A quantum computer represents information by qubits. In quantum computation there are two principles (algorithms) that speed up the computation, Fourier Transform and Grover's amplification algorithm. Quantum artificial intelligence is introduced by linear algebra-based quantum machine learning and symbolical quantum artificial intelligence. The initial motivation for relating quantum theory to consciousness was related to free free will in a deterministic world, since the quantum world is nondeterministic. The dualism of mind and matter involves the unresolved problem of how the mind and brain could interact. The relationship of union between the mind and the body of a person is resolved by quantum measurement. Sir Roger Penrose argues that elementary acts of consciousness cannot be described by a Turing machine. Such non-countable elementary acts of conscious ness are only present in the wave function collapse (measurement). Penrose assumes that the wave function collapse is not random, it represents an objective reduction.

Chapman & Hall/CRC eBooksAug 12, 20220 citations

Machines, Logic and Quantum Physics

David Deutsch, ARTUR K. EKERT, Rossella Lupacchini

Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.

arXiv:math/9911150Nov 19, 19994 citations

A uniform approach to test computational complementarity

Elena Calude, Bruce Mills, Lan Mills

Information about the initial state of a nite automaton may be obtained by interacting with it. Some automata display behaviour analogous to quantum complementarity: two pieces of information can be obtained separately, but not in conjunction. Studies of two computational complementarity properties in nite state interactive automata may shed light on the nature of both quantum and classical computation. But, it can be dicult to determine the statistics of its occurrence. This paper introduces the concept of an observation graph of an automaton. The observation graph can be used as the foundation of algorithms for testing in a uniform manner for a variety of complementarity properties. Implementations have been run in practical time on a standard desktop computer examining all 6-state, 2-symbol automata.

Acta CyberneticaAug 1, 20040 citations

Dusting Off the Turing Test

A. Hodges, Alan Mathison Turing

then inter- est theory and a problem about the observation of quantum systems (now as the quantum Zeno effect). With his death, train was lost, but the question computa- tion to fundamental physics has remained. Since the computing given a practical technological arena in which computation and quantum physics interact excitingly, it has not yet changed Tur- ing s picture of what is computable. There are also thought-experiment models that explore what it would mean beyond the ally require machine operate with speed or allow unlim- ited accuracy probe more the nature physical world. Perhaps the body of ideas is that of Roger Penrose ( 7). These draw strongly on the very thing motivated Tur- ing s early relationship operations to the imply that uncomputable physics abstract of how states are in the world. The problem remains: Does computation with discrete symbols a complete the world? If it does, how can make this connection manifest? If it does not, where does fail, and what would this tell us about fundamental science?

Jan 1, 20120 citations

Undecidable Problems in Physics: From Computation to Quantum Fields — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Undecidable problems extend from computation to quantum field theory and many-body physics, revealing fundamental limits on what can be known or computed about physical systems. | MATH: Halting problem: no Turing machine can decide if an arbitrary program halts (Turing 1936). Gödel incompleteness: any consistent formal system containing arithmetic has true but unprovable statements. Reducibility: problem A reduces to B if solving B solves A (A ≤ B). In QFT, spectral gap problem is undecidable (Cubitt, Perez-Garcia, Wolf 2015): no algorithm can determine if a quantum many-body system has a nonzero energy gap. | CONNECTION: Undecidability in physics often arises from encoding Turing machines into Hamiltonian lattice systems — this maps computational logic onto geometric lattice structures (e.g., 2D spin lattices with local interactions). The spectral gap problem's undecidability proof uses aperiodic tilings and translation-invariant Hamiltonians, linking to crystallographic symm Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Jul 25, 20260 citations