Quantum Theoretic Machines

Making Sense of Inner Sense 'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's greatest challenge is to answer the fundamental question: what precisely does a cognitive state amount to in physical terms? Albert Einstein insisted that the fundamental ideas of science are essentially simple and can be expressed in a language comprehensible to everyone. When one thinks about the complexities which present themselves in modern physics and even more so in the physics of life, one may wonder whether Einstein really meant what he said. Are we to consider the fundamental problem of the mind, whose understanding seems to lie outside the limits of the mind, to be essentially simple too? Knowledge is neither automatic nor universally deductive. Great new ideas are typically counterintuitive and outrageous, and connecting them by simple logical steps to existing knowledge is often a hard undertaking. The notion of a tensor was needed to provide the general theory of relativity; the notion of entropy had to be developed before we could get full insight into the laws of thermodynamics; the notice of information bit is crucial for communication theory, just as the concept of a Turing machine is instrumental in the deep understanding of a computer. To understand something, consciousness must reach an adequate intellectual level, even more so in order to understand itself. Reality is full of unending mysteries, the true explanation of which requires very technical knowledge, often involving notions not given directly to intuition. Even though the entire content and the results of this study are contained in the eight pages of the mathematical abstract, it would be unrealistic and impractical to suggest that anyone can gain full insight into the theory that presented here after just reading abstract. In our quest for knowledge we are exploring the remotest areas of the macrocosm and probing the invisible particles of the microcosm, from tiny neutrinos and strange quarks to black holes and the Big Bang. But the greatest mystery is very close to home: the greatest mystery is human consciousness. The question before us is whether the logical brain has evolved to a conceptual level where it is able to understand itself.

In his foreword to Schrödinger's Machines, Paul Davies writes, "The nineteenth century was known as the machine age, the twentieth century will go down in history as the information age. I believe the twenty-first century will be the quantum age." Perhaps the most successful scientific theory in history, quantum mechanics has already ushered in the information age with inventions like the transistor and the laser. In Schrödinger's Machines, renowned quantum physicist Gerard Milburn explores how our ever-increasing ability to manipulate atomic and subatomic processes is turning purely hypothetical situations and concepts (of a truly weird nature) into concrete, practical devices-- resulting in a complete transformation of our world view. Imagine the creation of machines the size of molecules, detectors sensitive enough to pick up the sound of a pin dropping on the other side of the earth, the fabrication of new and exotic materials, and extraordinarily powerful computers that can process information in many alternative realities simultaneously, creating a whole new type of mathematics. This isn't science fiction, but just some of the breathtaking possibilities offered by quantum technology over the next fifty years. Leaving the common sense of Newtonian machines far behind, Schrödinger's Machines is an advance preview of the strange new world ahead. Clearly presented, and with an acute awareness of recent advances in the field, it's indispensable reading for anyone interested in the future.

From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum physics First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to The Theoretical Minimum, Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics’ weirdness, Quantum Mechanics embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like The Theoretical Minimum, this volume runs parallel to Susskind’s eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.

"Unabridged republication of the second edition of the work, originally published in the Pure and applied physics series by Academic Press, Inc., New York, in 1972"--Title page verso.

'A gripping new drama in science ... if you want to understand how the concept of life is changing, read this' Professor Andrew Briggs, University of Oxford When Darwin set out to explain the origin of species, he made no attempt to answer the deeper question: what is life? For generations, scientists have struggled to make sense of this fundamental question. Life really does look like magic: even a humble bacterium accomplishes things so dazzling that no human engineer can match it. And yet, huge advances in molecular biology over the past few decades have served only to deepen the mystery. So can life be explained by known physics and chemistry, or do we need something fundamentally new? In this penetrating and wide-ranging new analysis, world-renowned physicist and science communicator Paul Davies searches for answers in a field so new and fast-moving that it lacks a name, a domain where computing, chemistry, quantum physics and nanotechnology intersect. At the heart of these diverse fields, Davies explains, is the concept of information: a quantity with the power to unify biology with physics, transform technology and medicine, and even to illuminate the age-old question of whether we are alone in the universe. From life's murky origins to the microscopic engines that run the cells of our bodies, The Demon in the Machine is a breath-taking journey across the landscape of physics, biology, logic and computing. Weaving together cancer and consciousness, two-headed worms and bird navigation, Davies reveals how biological organisms garner and process information to conjure order out of chaos, opening a window on the secret of life itself.

Quantum Machine Learning bridges the gap between abstract developments in quantum computing and the applied research on machine learning. Paring down the complexity of the disciplines involved, it focuses on providing a synthesis that explains the most important machine learning algorithms in a quantum framework. Theoretical advances in quantum computing are hard to follow for computer scientists, and sometimes even for researchers involved in the field. The lack of a step-by-step guide hampers the broader understanding of this emergent interdisciplinary body of research. Quantum Machine Learning sets the scene for a deeper understanding of the subject for readers of different backgrounds. The author has carefully constructed a clear comparison of classical learning algorithms and their quantum counterparts, thus making differences in computational complexity and learning performance apparent. This book synthesizes of a broad array of research into a manageable and concise presentation, with practical examples and applications. Bridges the gap between abstract developments in quantum computing with the applied research on machine learning Provides the theoretical minimum of machine learning, quantum mechanics, and quantum computing Gives step-by-step guidance to a broader understanding of this emergent interdisciplinary body of research

A complete overview of quantum mechanics, covering essential concepts and results, theoretical foundations, and applications. This undergraduate textbook offers a comprehensive overview of quantum mechanics, beginning with essential concepts and results, proceeding through the theoretical foundations that provide the field’s conceptual framework, and concluding with the tools and applications students will need for advanced studies and for research. Drawn from lectures created for MIT undergraduates and for the popular MITx online course, “Mastering Quantum Mechanics,” the text presents the material in a modern and approachable manner while still including the traditional topics necessary for a well-rounded understanding of the subject. As the book progresses, the treatment gradually increases in difficulty, matching students’ increasingly sophisticated understanding of the material. • Part 1 covers states and probability amplitudes, the Schrödinger equation, energy eigenstates of particles in potentials, the hydrogen atom, and spin one-half particles • Part 2 covers mathematical tools, the pictures of quantum mechanics and the axioms of quantum mechanics, entanglement and tensor products, angular momentum, and identical particles. • Part 3 introduces tools and techniques that help students master the theoretical concepts with a focus on approximation methods. • 236 exercises and 286 end-of-chapter problems • 248 figures

In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.

This book represents a simple idea with profound implications for science and philosophy. It develops a new foundation at both a popular and technological level of current fundamental theories.