This paper examines physical, algorithmic and hardware fundamentals of quantum information processing which includes computing, coding, communication, data storage and other tasks. Practical processing by microscopic (atomic and molecular) systems can be accomplished only by using measurable real-valued physical variables (quantities). These variables should be quantum-mechanically achivable, algorithmically processable and hardware realizable. The theoretical results of quantum mechanics must be experimentally substantiated by observing controlled quantum state transitions, transductions and evolutions in dynamic microscopic systems. The microscopic devices form processing fabrics. We examine the premise of quantum processing by: (1) Unifying and enabling theoretical computer science, quantum information science and computer engineering; (2) Examining the first principles of quantum information processing at the device and system levels; (3) Developing algorithmic and design paradigms with consistent processing calculus and arithmetics; (4) Fostering consistent and practical microscopic hardware solutions.
This paper examines physical, algorithmic and hardware fundamentals of quantum information processing which includes computing, coding, communication, data storage and other tasks. Practical processing by microscopic (atomic and molecular) systems can be accomplished only by using measurable real-valued physical variables (quantities). These variables should be quantum-mechanically achivable, algorithmically processable and hardware realizable. The theoretical results of quantum mechanics must be experimentally substantiated by observing controlled quantum state transitions, transductions and evolutions in dynamic microscopic systems. The microscopic devices form processing fabrics. We examine the premise of quantum processing by: (1) Unifying and enabling theoretical computer science, quantum information science and computer engineering; (2) Examining the first principles of quantum information processing at the device and system levels; (3) Developing algorithmic and design paradigms with consistent processing calculus and arithmetics; (4) Fostering consistent and practical microscopic hardware solutions.
This paper studies fundamentals of quantum processing on measurable processable compatible observables in microscopic systems which undergo quantum state transitions. The aforementioned microscopic devices (processing primitives) form processing fabrics. We examine the premise of quantum processing by: (1) Unifying and enabling theoretical concepts of theoretical computer science, computer engineering and quantum mechanics; (2) Examining the first principles; (3) Researching device physics; (4) Fostering fundamentally-consistent and practical microscopic hardware solutions. Vertebrates and invertebrates exhibit extraordinary information processing which is performed by biomolecules and molecular aggregates. Information processing in natural systems has not been comprehended, while engineered quantum processing is an emerging paradigm. This paradigm focuses on developments of a great number of new solutions such as microscopic devices, processing arithmetics (calculi), system architectures, etc. The microscopic processing primitives must exhibit utilizable quantum-effect state transitions on observables which result in computable transforms from viewpoints of processing arithmetics, calculus and design. The reported paradigm: (i) Eases enormous challenges; (ii) Overcomes foremost inconsistencies of naive algorithmically-centric computing; (iii) Enables new inroads; (iv) Promises unprecedented processing capabilities ensuring far-reaching benchmarks; (v) Significant advances theory and practice of natural and engineered processing. Our findings support a broad spectrum of transformative research activities.
For electronic, MEMS and electronic systems, we examine emerged technologies, research novel solutions and apply new transformative findings. To enable communication and processing schemes, nano and molecular technologies are applied. Transformative findings and developments are substantiated by analyzing and evaluating multi-physics microscopic systems. We advance physical foundations, engineering premises and information technology of classical, quantum and mixed sensing, communication and processing on quantum transductions. This paper examines fundamentals of quantum data processing on measurable and processable real-valued physical quantities. The developed paradigm: (1) Unifies and enables concepts of theoretical computer science, computer engineering and quantum mechanics; (2) Consistent with the first principles of quantum informatics, communication and processing; (3) Coherently examines device physics, switching algebra, processing arithmetics and calculus; (4) Enables practical microscopic hardware solutions for electronics, MEMS and electronic systems.
The theoretical, experimental and technological areas covering the use of quantum mechanics for communication and computation.Quantum information processing includes investigations in quantum information theory, quantum communication, quantum computation, quantum algorithms and their complexity, and quantum control.The science of quantum information processing is a highly interdisciplinary field.In the context of mathematics it is stimulating research in pure mathematics (e.g.coding theory, *algebras, quantum topology) as well as requiring and providing many opportunities for applied mathematics.The science of quantum information processing emerged from the recognition that usable notions of information need to be physically implementable.In the 1960s and 1970s researchers such as R. Landauer, C. Bennett, C. Helstrom and A. Holevo realized that the laws of physics give rise to fundamental constraints on the ability to implement and manipulate information.Landauer repeatedly stated that "information is physical", providing impetus to the idea that it should be possible to found theories of information on the laws of physics.This is in contrast to the introspective approach which led to the basic definitions of computer science and information theory as formulated by A. Church, A. Turing, C. Shannon and others in the first half of the 20th century.Early work in studying the physical foundations of information focused on the effects of energy limitations and the need for dissipating heat in computation and communication.Beginning with S. Wiesner's work on applications of quantum mechanics to cryptography in the late 1960s, it was realized that there may be intrinsic advantages to using quantum physics in information processing.Quantum cryptography and quantum communication in general were soon established as interesting and non-trivial extensions of classical communication based on bits.That quantum mechanics may be used to improve the efficiency of algorithms was first realized when attempts at simulating quantum mechanical systems resulted in exponentially complex algorithms compared to the physical resources associated with the system simulated.In the 1980s, P. Benioff and R. Feynman introduced the idea of a quantum computer for efficiently implementing quantum physics simulations.Models of quantum computers were developed by D. Deutsch, leading to the formulation of artificial problems that could be solved more efficiently by quantum than by classical computers.The advantages of quantum computers became widely recognized when P.
At the most microscopic level, all physical systems are governed by the laws of quantum mechanics. Quantum information processing is the study of how information is gathered, transformed, and transmitted at the quantum level—in atoms, ions, photons, elementary particles, and microscopic solid-state systems, which obey fundamentally quantum mechanical laws. Quantum computers, quantum communication channels, and quantum sensors are devices that can attain the ultimate limits of information processing. The laws of quantum mechanics give rise to counterintuitive effects. Quantum information processors use “quantum weirdness” to perform tasks that classical information processors cannot. Quantum computers are conceived to process information stored on atomic, optical, and solid-state systems: they aim to use counterintuitive effects including quantum superposition and entanglement to perform tasks such as quantum simulation, quantum search, and factoring/code-breaking to solve problems that are hard or impossible on conventional classical computers. Quantum communication systems transmit information encoded in individual photons: they exploit the fact that quantum measurement is inevitably stochastic and destructive to enact quantum-encrypted communication whose security is guaranteed by the laws of physics. Quantum sensors and measurement devices operate at the greatest possible sensitivity and precision allowed by physical law: from magnetometers to quantum clocks to advanced gravitational interferometers (e.g., LIGO), quantum metrology supplies the techniques required to push measurement to its ultimate limits.
Quantum technologies harness the properties of controlled quantum mechanical systems for applications in computation, communication and metrology, and enable us to further our understanding of fundamental physics. Quantum hardware is designed to manipulate complex and fragile many-particle quantum states, which requires exquisite control machinery, advanced software and near-complete isolation from the surrounding environment. With sufficient capabilities, quantum computers with large registers of quantum bits will perform classically intractable calculations such as quantum chemistry simulations. Quantum key distribution will provide completely secure communications across the world and quantum metrology will enable measurement precision beyond today's capabilities. While quantum technologies are far from surpassing classical hardware today, the vision and potential impact has sparked a world-wide research effort, both theoretical and experimental, to develop a quantum computer. The most sophisticated current quantum technologies have control over small numbers of quantum bits and are limited by environmental decoherence processes. While progress in developing quantum hardware is ongoing, designing and demonstrating new algorithms and protocols for quantum information is a thriving research field. Photonics provides an ideal platform for small-scale proof-of-concept quantum experiments, which are the focus of this thesis. In the coming decades, we will see the realisation of quantum hardware capable of applications that outperform any classical computer. In this thesis, I present several protocols and algorithms for quantum information science and technology, which are implemented in quantum photonic experiments. The applications of these works include robust quantum tomography, quantum state relocation, quantum enhanced data recovery and probing fundamental causality in quantum mechanics. The works presented here are based on two photon experiments from a prototypical spontaneous parametric down-conversion source, which provides an excellent test-bed for quantum information experiments. Photons can be used to encode quantum information in a range of different degrees of freedom. This versatility, along with compatibility with existing technology gives photonics a great advantage in the development of quantum hardware.
A computer is a physical device that helps us process information by executing algorithms. An algorithm is a well-defined procedure, with finite description, for realizing an information-processing task. An information-processing task can always be translated into a physical task. When designing complex algorithms and protocols for various information-processing tasks, it is very helpful, perhaps essential, to work with some idealized computing model. However, when studying the true limitations of a computing device, especially for some practical reason, it is important not to forget the relationship between computing and physics. Real computing devices are embodied in a larger and often richer physical reality than is represented by the idealized computing model. Quantum information processing is the result of using the physical reality that quantum theory tells us about for the purposes of performing tasks that were previously thought impossible or infeasible. Devices that perform quantum information processing are known as quantum computers. In this book we examine how quantum computers can be used to solve certain problems more efficiently than can be done with classical computers, and also how this can be done reliably even when there is a possibility for errors to occur. In this first chapter we present some fundamental notions of computation theory and quantum physics that will form the basis for much of what follows. After this brief introduction, we will review the necessary tools from linear algebra in Chapter 2, and detail the framework of quantum mechanics, as relevant to our model of quantum computation, in Chapter 3. In the remainder of the book we examine quantum teleportation, quantum algorithms and quantum error correction in detail. We are often interested in the amount of resources used by a computer to solve a problem, and we refer to this as the complexity of the computation. An important resource for a computer is time. Another resource is space, which refers to the amount of memory used by the computer in performing the computation. We measure the amount of a resource used in a computation for solving a given problem as a function of the length of the input of an instance of that problem.