This chapter explores how the logic of physical and biological processes may be employed in the design and programing of computers. Quantum processes do not follow Boolean logic; the development of quantum computers requires the formulation of an appropriate logic. While in Boolean logic, entities are static, opposites exclude each other, and change is not creative, natural processes involve action, opposition, and creativity. Creativity is detected by changes in pattern, diversification, and novelty. Causally-generated creative patterns (Bios) are found in numerous processes at all levels of organization: recordings of presumed gravitational waves, the distribution of galaxies and quasars, population dynamics, cardiac rhythms, economic data, and music. Quantum processes show biotic patterns. Bios is generated by mathematical equations that involve action, bipolar opposition, and continuous transformation. These features are present in physical and human processes. They are abstracted by lattice, algebras, and topology, the three mother structures of mathematics, which may then be considered as dynamic logic. Quantum processes as described by the Schrödinger’s equation involve action, coexisting and interacting opposites, and the causal creation of novelty, diversity, complexity and low entropy. In addition to ‘economic’ (not entropy producing) reversible gates (the current goal in the design of quantum gates), irreversible, entropy generating, gates may contribute to quantum computation, because quantum measurements, as well as creation and decay, are irreversible processes.
This chapter explores how the logic of physical and biological processes may be employed in the design and programing of computers. Quantum processes do not follow Boolean logic; the development of quantum computers requires the formulation of an appropriate logic. While in Boolean logic, entities are static, opposites exclude each other, and change is not creative, natural processes involve action, opposition, and creativity. Creativity is detected by changes in pattern, diversification, and novelty. Causally-generated creative patterns (Bios) are found in numerous processes at all levels of organization: recordings of presumed gravitational waves, the distribution of galaxies and quasars, population dynamics, cardiac rhythms, economic data, and music. Quantum processes show biotic patterns. Bios is generated by mathematical equations that involve action, bipolar opposition, and continuous transformation. These features are present in physical and human processes. They are abstracted by lattice, algebras, and topology, the three mother structures of mathematics, which may then be considered as dynamic logic. Quantum processes as described by the Schrödinger’s equation involve action, coexisting and interacting opposites, and the causal creation of novelty, diversity, complexity and low entropy. In addition to ‘economic’ (not entropy producing) reversible gates (the current goal in the design of quantum gates), irreversible, entropy generating, gates may contribute to quantum computation, because quantum measurements, as well as creation and decay, are irreversible processes.
This chapter explores how the logic of physical and biological processes may be employed in the design and programing of computers. Quantum processes do not follow Boolean logic; the development of quantum computers requires the formulation of an appropriate logic. While in Boolean logic, entities are static, opposites exclude each other, and change is not creative, natural processes involve action, opposition, and creativity. Creativity is detected by changes in pattern, diversification, and novelty. Causally-generated creative patterns (Bios) are found in numerous processes at all levels of organization: recordings of presumed gravitational waves, the distribution of galaxies and quasars, population dynamics, cardiac rhythms, economic data, and music. Quantum processes show biotic patterns. Bios is generated by mathematical equations that involve action, bipolar opposition, and continuous transformation. These features are present in physical and human processes. They are abstracted by lattice, algebras, and topology, the three mother structures of mathematics, which may then be considered as dynamic logic. Quantum processes as described by the Schrödinger’s equation involve action, coexisting and interacting opposites, and the causal creation of novelty, diversity, complexity and low entropy. In addition to ‘economic’ (not entropy producing) reversible gates (the current goal in the design of quantum gates), irreversible, entropy generating, gates may contribute to quantum computation, because quantum measurements, as well as creation and decay, are irreversible processes.
Quantum computing forces a reexamination of logic. We examine its historical roots in logos, the logic of nature, and it is manifested by the laws of physics. A new logic comes out of this inquiry and it is applied to quantum computing. The logical design of computers according to the logic of quantum physics will allow the full use of quantum processes for computation and also adapt our humanly conceived computer logic to the actual logic of nature. The basic principles of quantum physics are homologically repeated in fundamental processes at all levels of organization. Thus, the principles of action, opposition such as charge and spin, chromatic structure, and the creation of novelty, diversity, and complexity can guide logic. Explicit realizations of these ideas are provided.Request access from your librarian to read this chapter's full text.
This chapter makes us walk a few preliminary, but decisive, steps towards quantum information theory (QIT), which will be the focus of the rest of this book. Here, we shall remain in the classical world, yet getting a hint that it is possible to think of a different world where computations may be reversible, namely, without any loss of information. One key realization through this paradigm shift is that “information is physical.” As we shall see, such a nonintuitive and striking conclusion actually results from the age-long paradox of Maxwell's demon in thermodynamics, which eventually found an elegant conclusion in Landauer's principle. This principle states that the erasure of a single bit of information requires one to provide an energy that is proportional to log 2, which, as we know from Shannon's theory, is the measure of information and also the entropy of a two-level system with a uniformly distributed source. This consideration brings up the issue of irreversible computation. Logic gates, used at the heart of the CPU in modern computers, are based on such computation irreversibility. I shall then describe the computers' von Newman's architecture, the intimate workings of the ALU processing network, and the elementary logic gates on which the ALU is based. This will also provide some basics of Boolean logic, expanding on Chapter 1, which is the key to the following logic-gate concepts.
Every process of our universe is based on the fundamental elements of nature: information and computation.The basic motivation behind the study of quantum cellular automata (QCA) is the wish to analyze the processes of nature.QCA provide a natural framework within which to describe many classically undescribable and uncomputable physical phenomena, such as the properties of quantum physical systems and the complex background of quantum dynamics.Quantum cellular automata models are based on the working mechanism of classical cellular automata models and use the power of reversible quantum computation.Cellular automata can be used in many fields of science, such as parallel computation, artificial intelligence, image processing, biological systems, simulation of physics systems, hardware design, algorithm theory, and many more.In the first part of this chapter, we give a brief overview of the basic properties of quantum information processing and analyze the quantum versions of classical cellular automata models.We present all materials in a clear, perspicuous, and comprehensible manner, without using a complex mathematical background.After reviewing physical QCA implementations, we sketch future directions, and then conclude the first part.In the second part of the chapter, we examine one possible application of QCA, which uses quantum computing to realize real-life based, truly random network organization.This abstract machine is called a Quantum Cellular Machine (QCM), and we design it for controlling a truly random biologically-inspired network, and to integrate quantum learning algorithms and quantum searching into a controlled, self-organizing system.The selforganizing processes in classical systems cannot be truly random.Using our quantum probabilistic QCM unit, we can add truly random behavior to the self-organizing processes of biological networks.A quantum mechanical-based quantum cellular machine (QCM) controls the self-organizing processes of the network and uses a closed, non-classical quantum mechanical-based language inside the QCM.The proposed QCM solution has deep relevance in the evolution of truly random quantum probabilistic self-organizing network structures.The QCM controls the evolution of the system, changes its environment and creates plans without any human interaction, using truly random quantum probabilistic decisions.In a classical system, the classical circuits can only exhibit deterministic behavior.In a quantum probabilistic control system, the quantum circuits can follow both deterministic and quantum probabilistic quantum cellular machine control behaviors.The QCM has classical and quantum communication layers, it uses the classical layer to detect www.intechopen.comCellular Automata -Innovative Modelling for Science and Engineering 114 the network environment.The lower layer of the quantum cellular machine contains the non-deterministic quantum probabilistic decisions and interacts with the classical level.The quantum cellular machine model with the power of quantum computing can be used for the development of a real-life based network organism.We show, that a real, biologically inspired, non-deterministic, truly random network model can be achieved by the discussed QCM model.In the third part of this chapter, we show that a very efficient quantum searching algorithm can be integrated into the QCM, to find the best solution to a given network input command.We present a quantum searching based method specially designed for quantum probabilistic self-organizing networks, to reduce the complexity of the classical traditional search in the network.The proposed QCM can process both quantum and classical information, and accomplish both deterministic and quantum probabilistic tasks.The information unit is a quantum bit, which can lie in a coherent superposition state of logical states zero and one, and can thus simultaneously store zero and one.Using quantum bits, we can speed up the solutions of classical problems, and even solve some hard problems that classical computers can't solve.The key aspect behind the optimal decisions of a QCM is to design a high-efficiency searching algorithm.A QCM updates the probability amplitudes of its quantum register, according to a given reward value, derived from the network environment.The QCM repeatedly applies a unitary transformation to the quantum states, thus it can enhance, for example, the probability amplitude of the optimal path in the self-organizing network environment, while suppressing the amplitude of all other solutions.The QCM's quantum searching algorithm can help resolve many hard tasks, for example it could be applied to find an optimal logical path, using the effects of quantum mechanics.In the numerical analysis we will show that the quantum communication layer could improve the performance of classical systems.
§1. Introduction. Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently dramatically changed our life. A new layer of logic has been developing ever since the discovery of quantum mechanics. G. D. Birkhoff and von Neumann introduced quantum logic in a seminal paper in 1936 [1]. But the definition of quantum logic varies among authors (see [2]). How to capture the logic structure inherent in quantum mechanics is very interesting and challenging. Given the close connection between classical logic and theoretical computer science as exemplified by the coincidence of computable functions through Turing machines, recursive function theory, and λ-calculus, we are interested in how to gain some insights about quantum logic from quantum computing. In this note we make some observations about quantum logic as motivated by quantum computing (see [5]) and hope more people will explore this connection. The quantum logic as envisioned by Birkhoff and von Neumann is based on the lattice of closed subspaces of a Hilbert space, usually an infinite dimensional one. The quantum logic of a fixed Hilbert space ℍ in this note is the variety of all the true equations with finitely many variables using the connectives meet, join and negation. Quantum computing is theoretically based on quantum systems with finite dimensional Hilbert spaces, especially the states space of a qubit ℂ2. (Actually the qubit is merely a convenience.
While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term “equilibraton” is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence.