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The Existence Of Quantum Computer

Petr Pushkarev

Published Jul 6, 2016• 0 citations
Publisher

Abstract

We extend an empirically grounded theory of the existence of quantum computer. The main question that we are considering is a question about the quantum computer’s possibility of existence and creation. As empirical evidence, we use logic, which we show in cognitive perspective. For a definition of the computer, we use a formal definition of Turing machine. By formulating many definitions abstractly and phenomenologically we go around the areas of quantum physics, quantum computing and other quantum-related fields of science which could give an unambiguous answer to our question about the essence of quantum computer and which is developed so they can’t. In many ways, it makes this theory about the existence of quantum computer universal for these areas, although less applied for them. We consider some corollary of the essences of quantum computer, including the possibility of quantum computer for the human. References to research of cognitive nature of logic suggest empirical basis which we follow in our theory.

DOI
10.5281/zenodo.822077

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We extend an empirically grounded theory of the existence of quantum computer. The main question that we are considering is a question about the quantum computer’s possibility of existence and creation. As empirical evidence, we use logic, which we show in cognitive perspective. For a definition of the computer, we use a formal definition of Turing machine. By formulating many definitions abstractly and phenomenologically we go around the areas of quantum physics, quantum computing and other quantum-related fields of science which could give an unambiguous answer to our question about the essence of quantum computer and which is developed so they can’t. In many ways, it makes this theory about the existence of quantum computer universal for these areas, although less applied for them. We consider some corollary of the essences of quantum computer, including the possibility of quantum computer for the human. References to research of cognitive nature of logic suggest empirical basis which we follow in our theory.
. 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.
Abstract Quantum logics are non-classical logics defined from the mathematical formalism of quantum mechanics. While they are conventionally used to model inferential processes in physics, their scope of application is potentially much broader. We argue that quantum logics can serve as a framework to model human cognition, as their semantics seem able to capture not only how people make inferences about quantum mechanics, but also how they reason in general. We begin by defining quantum logics from an algebraic perspective in a classical first-order setting. Next, we present findings from cognitive science that suggest these logics are apt to characterize human reasoning. We then consider how such a connection between quantum logics and cognition contributes to longstanding philosophical debates about the epistemological status of logic and the problem of adoption. Finally, we discuss how cognitive applications of quantum logics could advance our understanding of human psychology and even quantum foundations.
Cognitive Science is the study of the mind and how it relates to human behaviour. As a field, it is highly interdisciplinary, bringing together theories from Psychology, Neuroscience, Biology, and others. The field of cognitive science operates at a number of levels. On the one hand, some aspects of cognitive science look at the behaviour of neurons, whereas other aspects look to explain human behaviour at a more abstract level, seeking to explain human decision making or reasoning. A key area of research in cognitive science is how to formalise human behaviours around judgements of similarity, categorization, and decision making. In the field of Physics, Quantum Mechanics has fundamentally altered our understanding of the way in which particles behave. Quantum mechanics has a number of unintuitive phenomena, some of which can be used model unusual aspects of human behaviour. The application of quantum theory to model human behaviour is wide-ranging. In this chapter we will look at three main areas in which it has been applied. One key area is in how similarity judgements can be modelled. There are a number of phenomena around similarity judgements that are not well modelled using a view of concepts that does not take the state of the observer into account. These include the asymmetry of similarity judgements and the fact that similarity can change depending on other exemplars that are present. Another key area is in judgement and decision-making. Again, puzzling phenomena have been observed regarding the fact that judgements do not follow classical probability theory, known as the conjunction fallacy, can depend crucially on the order in which questions are presented or on the amount of knowledge about the world. Finally, approaches to modelling cognitive phenomena at the neural level will also be discussed within a quantum-theoretic framework.
Any computer can create a model of reality. The hypothesis that quantum computer can generate such a model designated as quantum, which coincides with the modeled reality, is discussed. Its reasons are the theorems about the absence of “hidden variables” in quantum mechanics. The quantum modeling requires the axiom of choice. The following conclusions are deduced from the hypothesis. A quantum model unlike a classical model can coincide with reality. Reality can be interpreted as a quantum computer. The physical processes represent computations of the quantum computer. Quantum information is the real fundament of the world. The conception of quantum computer unifies physics and mathematics and thus the material and the ideal world. Quantum computer is a non-Turing machine in principle. Any quantum computing can be interpreted as an infinite classical computational process of a Turing machine. Quantum computer introduces the notion of “actually infinite computational process”. The discussed hypothesis is consistent with all quantum mechanics. The conclusions address a form of neo-Pythagoreanism: Unifying the mathematical and physical, quantum computer is situated in an intermediate domain of their mutual transformation.
Half Day Tutorial on Using Quantum Probability Theory to Model Cognition Emmanuel M. Pothos (Emmanuel.pothos.1@city.ac.uk) Department of Psychology, City University London, London, EC1R 0JD, UK Zheng Wang (wang.1243@osu.edu) School of Communication, Derby Hall, The Ohio State University, Columbus, OH 43210 USA. Keywords: probability theory, Bayesian probability, quantum theory, decision making, probabilistic models. General Purpose This tutorial introduces why and how to build cognitive models using quantum probability (QP) theory. In the tutorial, we will show that QP is inherently consistent with deeply rooted psychological conceptions and intuitions. It offers a fresh conceptual framework for explaining some puzzling empirical findings of cognition, and provides a rich new source of alternative formal tools, compared to classical probability (CP) theory, for cognitive modeling. CP models, including Bayesian models, have had an enormous influence in cognitive science (e.g., Griffiths et al., 2010). Such formal models are appealing for many reasons. First, CP theory provides an integrated, coherent, self-consistent set of principles, which can be flexibly applied in any inductive inference situation. Second, such approaches are more falsifiable. Core principles of CP theory are inter-dependent, and identifying an empirical violation of one principle in a setting could invalidate the applicability of CP theory as a whole in that setting. Third, CP principles are intuitive. In the words of Laplace (1816, cited in Perfors et al., 2011), “probability theory is nothing but common sense reduced to calculation.” However, human cognition often goes against the description and prescription from CP theory. In one of the most influential empirical traditions in cognitive psychology, Kahneman, Tversky, and colleagues have reported persistent, clear violations of CP principles in decision making (e.g., Tversky & Kahneman, 1974). For example, consider the famous conjunction fallacy. Participants are told of a person, Linda, looking very much like a feminist and unlike a bank teller. Then, they are asked to judge probabilities of some events. Violating CP rules, people think the probability that Linda is a bank teller and a feminist is higher than the probability that she is just a bank teller. According to CP theory, it is a fallacy to think P(A and B)>P(A). Importantly, even when we become aware of our “fallacy,” we cannot shake off the impression that Linda is indeed more likely to be a bank teller and a feminist, than to be just a bank teller. Important findings like this have led to intense and extensive controversy about the mechanisms which guide human cognition and decision making. The inspiration for Jerome R. Busemeyer (jbusemey@indiana.edu) Psychological and Brain Sciences, Indiana University, Bloomington 47468 Indiana, USA. exploring QP theory in cognitive modeling partly arises as a way to resolve this controversy. The physical theory of quantum mechanics is a marriage between a framework for how to assign probabilities to events and assumptions regarding the nature of the physical world. We can call the former QP theory (or just quantum theory). Can it be applied outside of physics? The motivation for doing so is twofold. First, QP theory is a highly rigorous framework for probabilistic inference. It has been developed over several decades by some of the most brilliant scientists of all time (e.g., Bohr, Dirac, von Neumann, Planck) and has been intensely scrutinized ever since. Thus, the application of QP theory in cognitive modeling has exactly the same formal advantages as that of CP theory. Second, quantum theory allows us to consider the possible relevance in cognitive modeling of several novel concepts. For example, in quantum theory, a cognitive system can be in a superposition state. This means that relative to a question or measurement, the system is in an indefinite state, with all definite states having potential to be expressed. This provides an intrinsic formal representation of the conflict, ambiguity, or uncertainty that people experience in cognitive processes. For another example: states can be entangled, which means a change in one part of the system inexorably and instantaneously affects another part. Entanglement is a form of extreme association, which can be helpful for formalizing important cognitive processes, such as holism, cognitive dissonance, and social projection. Fundamental quantum conceptions, such as superposition, entanglement, interference, and complementarity, have no formal counterparts in cognitive theory. We are part of a growing group of researchers who have been intensely exploring their applicability in understanding human cognition. Quantum theory reveals alternative intuitions in probabilistic models of cognition. The quantum cognition research program aims to explore whether these alternative intuitions can explain paradoxical findings in decision, memory, and other areas of cognitive processing. The tutorial introduce the basic principles of quantum theory, in the context of well-known empirical findings in psychological literature. The basic elements of QP theory will require only some knowledge of linear algebra. No background in physics or quantum theory is assumed. The tutorial will be self-contained. It will show how probability
Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality.