Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Consequences for practical aesthetics and for aesthetical theory of the insertion of principles from quantum theory in cellular automata.

Philip VAN LOOCKE

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

A cellular automaton that includes some principles from quantum theory is considered. The automaton generates forms of an aesthetic nature. At every time step, a form grows with a single cell. This cell is selected with a selection probability that is determined by an amplitude. If the algorithm is run with selection of the cell of maximal amplitude at every time step, a type of form results that is called'platonic'. Such forms typically have higher aesthetic complexity than their non-platonic counterparts. The case of selection probabilities determined by squares of amplitudes has a strong analogy with quantum theory. This analogy is elaborated by consideration of forms that have mutual correlations. These correlations can be of a classical nature, of a quantum mechanical type, or of a type that is termed'super-correlation'.

Related papers

Properties of Conscious Systems and Teleology: A Cellular Automaton Perspective

Philip VAN LOOCKE

The first part of this paper introduces a cellular automaton with properties that are often encountered in discussions on the relevance of quantum theory for consciousness.The automaton generates forms by a sequence of collapses of an amplitude function.The amplitudes can be complemented by a complex phase factor to generate effects of interference.The collapse of the amplitude function can be random, or it can be orchestrated in a number of different ways.How an interaction between the lowest cellular level and a higher level can take place is explained.Further, angular variables can be introduced that allow to visualize Bell-correlations and classical correlations between pairs of cells.How the present automaton can be adapted to generate a teleological dynamics is noted.The second part of the paper shows how the basic principles of the automaton, together with the teleological principle, can be adapted to result in a training method for connectionist systems that differs profoundly from the classical backpropagation algorithm.For the function estimation example that is considered, the results of the present teleological method are slightly better than the results obtained by backpropagation.

Journal of Intelligent Systems•Dec 1, 1999•3 citations

The emergence of quantum mechanics

Gerard ’t Hooft

It is pointed out that a mathematical relation exists between cellular automata and quantum field theories. Although the proofs are far from perfect, they do suggest a new look at the origin of quantum mechanics: quantum mechanics may be nothing but a natural way to handle the statistical correlations of a cellular automaton. An essential role for the gravitational force in these considerations is suspected.

AIP conference proceedings•Jan 1, 2012•9 citations

A decision procedure for well-formed linear quantum cellular automata

Christoph Dürr, Huong LêThanh, Miklós Sántha

In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is $O(n^2)$ in the algebraic model of computation if the input automaton has continuous neighborhood.

arXiv:cs/9906024•Jun 23, 1999•1 citation

QUANTUM FIELD THEORY FROM FIRST PRINCIPLES

Paolo Perinotti

The mathematical description of quantum systems univocally identies their nature. In other words we treat a system as quantum if we describe its behaviour adopting Hilbert spaces and structures thereof, as prescribed by the postulates of quantum theory. The choice of using quantum systems as the elementary systems of physics can be justied in terms of informational principles, thanks to results of the last decade. Such results come as the conclusion of a research program that lasted almost one century, with the aim of reformulating quantum theory in terms of operational principles. This achievement now poses a new challenge, that we face here. If the systems of quantum theory are thought of as elementary information carriers in the rst place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than space-time relations, then we need to nd the origin of mechanical concepts—that characterise quantum mechanics as a theory of physical systems. To this end,we will illustrate howphysical laws can be viewed as algorithms for the update of memory registers that make a physical system. Imposing the characteristic properties of physical laws to such an algorithm, i.e. homogeneity, reversibility and isotropy, we will show that the physical laws thus selected are particular algorithms known as cellular automata. Further assumptions regarding maximal simplicity of the algorithm lead to two cellular automata only, that in a suitable regime can be described by Weyl’s dierential equations, lying at the basis of the dynamics of relativistic quantum elds. We will nally discuss how the same cellular automaton can give rise to both Fermionic eld dynamics and to Maxwell’s equations, that rule the dynamics of the electromagnetic eld. We will conclude reviewing the discussion of the relativity principle, that must be suitably adapted to the scenario where space-time is not an elementary notion, through the denition of a change of inertial reference frame, and whose formulation leads to the recovery of the symmetry of Minkowski space-time, identied with Poincar´e’s group. Space-time thus emerges as one of the manifestations of physical laws, rather than the background where they occur, and its features are determined by the dynamics of systems, necessarily equipped with dierential equations that express it. In brief, there is no space-time unless an evolution rule requires it.

arXiv:2011.09881•Istituto Lombardo - Accademia di Scienze e Lettere - Rendiconti di Scienze•May 11, 2020•2 citations

Quantum features of natural cellular automata

Hans-Thomas Elze

Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schrödinger equation. This includes corresponding conservation laws. The class of "natural" Hamiltonian cellular automata is based exclusively on integer-valued variables and couplings and their dynamics derives from an Action Principle. They can be mapped reversibly to continuum models by applying Sampling Theory. Thus, "deformed" quantum mechanical models with a finite discreteness scale l are obtained, which for l → 0 reproduce familiar continuum results. We have recently demonstrated that such automata can form "multipartite" systems consistently with the tensor product structures of nonrelativistic many-body quantum mechanics, while interacting and maintaining the linear evolution. Consequently, the Superposition Principle fully applies for such primitive discrete deterministic automata and their composites and can produce the essential quantum effects of interference and entanglement.

arXiv:1604.06652•Journal of Physics Conference Series•Mar 1, 2016•6 citations

A decision procedure for well-formed linear quantum cellular automata

Christoph Dürr, Huong L�Thanh, Miklós Sántha

In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is O(n2) in the algebraic model of computation if the input automaton has continuous neighborhood. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11, 381–394 (1997)

Random Structures and Algorithms•Dec 1, 1997•19 citations
A cellular automaton that includes some principles from quantum theory is considered. The automaton generates forms of an aesthetic nature. At every time step, a form grows with a single cell. This cell is selected with a selection probability that is determined by an amplitude. If the algorithm is run with selection of the cell of maximal amplitude at every time step, a type of form results that is called'platonic'. Such forms typically have higher aesthetic complexity than their non-platonic counterparts. The case of selection probabilities determined by squares of amplitudes has a strong analogy with quantum theory. This analogy is elaborated by consideration of forms that have mutual correlations. These correlations can be of a classical nature, of a quantum mechanical type, or of a type that is termed'super-correlation'.
The first part of this paper introduces a cellular automaton with properties that are often encountered in discussions on the relevance of quantum theory for consciousness.The automaton generates forms by a sequence of collapses of an amplitude function.The amplitudes can be complemented by a complex phase factor to generate effects of interference.The collapse of the amplitude function can be random, or it can be orchestrated in a number of different ways.How an interaction between the lowest cellular level and a higher level can take place is explained.Further, angular variables can be introduced that allow to visualize Bell-correlations and classical correlations between pairs of cells.How the present automaton can be adapted to generate a teleological dynamics is noted.The second part of the paper shows how the basic principles of the automaton, together with the teleological principle, can be adapted to result in a training method for connectionist systems that differs profoundly from the classical backpropagation algorithm.For the function estimation example that is considered, the results of the present teleological method are slightly better than the results obtained by backpropagation.
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is O(n2)O(n^2)O(n2) in the algebraic model of computation if the input automaton has continuous neighborhood.
The mathematical description of quantum systems univocally identies their nature. In other words we treat a system as quantum if we describe its behaviour adopting Hilbert spaces and structures thereof, as prescribed by the postulates of quantum theory. The choice of using quantum systems as the elementary systems of physics can be justied in terms of informational principles, thanks to results of the last decade. Such results come as the conclusion of a research program that lasted almost one century, with the aim of reformulating quantum theory in terms of operational principles. This achievement now poses a new challenge, that we face here. If the systems of quantum theory are thought of as elementary information carriers in the rst place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than space-time relations, then we need to nd the origin of mechanical concepts—that characterise quantum mechanics as a theory of physical systems. To this end,we will illustrate howphysical laws can be viewed as algorithms for the update of memory registers that make a physical system. Imposing the characteristic properties of physical laws to such an algorithm, i.e. homogeneity, reversibility and isotropy, we will show that the physical laws thus selected are particular algorithms known as cellular automata. Further assumptions regarding maximal simplicity of the algorithm lead to two cellular automata only, that in a suitable regime can be described by Weyl’s dierential equations, lying at the basis of the dynamics of relativistic quantum elds. We will nally discuss how the same cellular automaton can give rise to both Fermionic eld dynamics and to Maxwell’s equations, that rule the dynamics of the electromagnetic eld. We will conclude reviewing the discussion of the relativity principle, that must be suitably adapted to the scenario where space-time is not an elementary notion, through the denition of a change of inertial reference frame, and whose formulation leads to the recovery of the symmetry of Minkowski space-time, identied with Poincar´e’s group. Space-time thus emerges as one of the manifestations of physical laws, rather than the background where they occur, and its features are determined by the dynamics of systems, necessarily equipped with dierential equations that express it. In brief, there is no space-time unless an evolution rule requires it.
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schrödinger equation. This includes corresponding conservation laws. The class of "natural" Hamiltonian cellular automata is based exclusively on integer-valued variables and couplings and their dynamics derives from an Action Principle. They can be mapped reversibly to continuum models by applying Sampling Theory. Thus, "deformed" quantum mechanical models with a finite discreteness scale l are obtained, which for l → 0 reproduce familiar continuum results. We have recently demonstrated that such automata can form "multipartite" systems consistently with the tensor product structures of nonrelativistic many-body quantum mechanics, while interacting and maintaining the linear evolution. Consequently, the Superposition Principle fully applies for such primitive discrete deterministic automata and their composites and can produce the essential quantum effects of interference and entanglement.
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is O(n2) in the algebraic model of computation if the input automaton has continuous neighborhood. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11, 381–394 (1997)