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.
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.
Quantum computing, which is the most famed topic in this era, a combination of quantum mechanics from the 1900s and the computing point of view, takes a huge place in the quantum realm. Starting from the foundation of abacus since 2700–2300 BC, we humans have always been trying to compute in different ways, and the most modern way of doing it comes with the binary system. Bit is the smallest unit of a binary system and can be in two states, either 0 or 1. On the contrary, quantum computing deals with the “quantum bit” or “qubit”; possible outcomes from the qubits are neither 0 nor 1. It will always be a combination of 0 and 1, which is based on the superposition principle from quantum physics. In this chapter, details of quantum logic gates are discussed for the circuit design perspective, which will be achievable for future realization of quantum computers. Architecture and corresponding formation of basic quantum circuits are discussed, along with the methods of quantum computing. How the technique differs from conventional approaches is also highlighted. The work may be directed toward future hardware realization of quantum information processing.
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.
§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.
. Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond those in the familiar classical world. To help in this thinking, we give a description of the foundational ideas that hold in all of our successful physical models, including quantum theory. Our emphasis will be on the proper interpretation of our theories, and not just their statements. Our tact will be to build on the concept of information, which lies central to the operation of not just computers, but the Universe. For application to quantum computing, the essence of quantum theory is given, together with special precautions and limitations. Introduction. Having a grasp on the ideas behind a theory helps to apply it correctly, to understand its limitations, and to generate new ideas. Getting a firm hold on quantum theory is not an easy task, because our experiences and even our genetic predispositions have been developed in a world in which quantum effects are largely washed out. Remarkably, our predilection for finding logic behind the behavior of what we observe, including that of electrons and atoms, has led us to quantum theory, a description of nature that is hard for us to conceptualize, but is logical, accurate, and explains a wide variety of phenomena with only a few statements and input. As background to quantum theory and quantum computing, an attempt is made here to give the primitive notions and essential observations that underlie current physical theories, so that foundational ideas are explicit, and a common language is established. In our description, information storage and transfer is made central. A short description of quantum theory follows, and then applied to quantum computing, focusing on what the theory says, and particularly does not say, in areas where conceptual difficulties have arisen. Physical theory and reality. A physical theory is a logical model capable of making predictions of what we observe. It is judged by its accuracy in matching measurements, and by its economy, i.e. whether the proposed theory has only a few relationships and input data needed for its ability to explain observations over a wide realm.
Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of primary importance for the realization of quantum computing machines. To this end, this chapter studies neural structures with weights that follow the model of the quantum harmonic oscillator. The proposed neural networks have stochastic weights which are calculated from the solution of Schrödingers equation under the assumption of a parabolic (harmonic) potential. These weights correspond to diffusing particles, which interact with each other as the theory of Brownian motion (Wiener process) predicts. The learning of the stochastic weights (convergence of the diffusing particles to an equilibrium) is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of patterns storage capacity (number of attractors). It is also shown that conventional neural networks and learning algorithms based on error gradient can be conceived as a subset of the proposed quantum neural structures. Thus, the complementarity between classical and quantum physics is also validated in the field of neural computation.Request access from your librarian to read this chapter's full text.