Over the past half century wires and logic gates in computers have halved in size every year and a half, creating a phenomenon known as the Moore’s law. As the size of computer components reduces towards the atomic scale, however, the classical laws of thermodynamics are no longer able to predict the real behavior of electronic devices. In this context, the theory of quantum mechanics becomes increasingly important to characterize how circuits operate. Quantum information is the theory of communication and computation born to study the potential arising from information encoded in elementary particles, such as photons. The essential goal of quantum information is to determine how the quantum laws ruling the peculiar phenomena happening at an atomic scale can be used to enhance the capabilities of computers and communication systems.
Over the past half century wires and logic gates in computers have halved in size every year and a half, creating a phenomenon known as the Moore’s law. As the size of computer components reduces towards the atomic scale, however, the classical laws of thermodynamics are no longer able to predict the real behavior of electronic devices. In this context, the theory of quantum mechanics becomes increasingly important to characterize how circuits operate. Quantum information is the theory of communication and computation born to study the potential arising from information encoded in elementary particles, such as photons. The essential goal of quantum information is to determine how the quantum laws ruling the peculiar phenomena happening at an atomic scale can be used to enhance the capabilities of computers and communication systems.
Information is physical. Today’s information processing and communication are classical: they are based upon the laws of Newton’s and Maxwell’s classical physics. This assertion holds all the way, from commercial computers and networks, up to their most abstract models, e.g. Turing machines. Research in quantum information was born some twenty five years ago, with the encounter of two major scientific achievements of the 20th century, namely quantum physics and information sciences. A technological motivation for that is an extrapolation of Moore’s law which seems to indicate that the amount of matter needed for one bit will be reduced to one particle sometimes before year 2020. A deeper, scientific driving force of this interdisciplinary research is that of looking for the consequences of having computation and communication based directly upon the laws of quantum physics, i.e. our current ultimate knowledge of the world of elementary particles, as described by quantum mechanics. Breakthroughs in cryptography, communications, information theory and algorithmics have shown that this transplantation from classical to quantum has far reaching consequences, both quantitative and qualitative, and opens new avenues for research within the foundations of computer science and physics. The principles 388 and most striking results and hot topics of this promising way of encoding, processing and communicating information are briefly introduced in this chapter from a mostly computer science point of view, with detailed examples in algorithmics and in cryptography. At the end of the chapter, a short list of some significant articles, textbooks and reports on quantum information are suggested for further reading.
In the preceding chapter we established that a suitable set of quantum gates, complemented by quantum error correction, allows us to produce a desired multiqubit unitary transformation. This transformation is one of the three steps in a quantum computation; the others, of course, are the preparation of the qubits in their initial state and the measurement of them after the transformation has been implemented. A quantum computation is designed to solve a problem or class of problems. The power of quantum computers is that they can do this, at least for some problems, very much more efficiently and quickly than any conventional computer based on classical logic operations. If we can build a quantum computer then a number of important problems which are currently intractable will become solvable. The potential for greatly enhanced computational power is, in itself, reason enough to study quantum computers, but there is another. Moore’s law is the observation that the number of transistors on a chip doubles roughly every eighteen months. A simple corollary is that computer performance also doubles on the same timescale. Associated with this exponential improvement is a dramatic reduction in the size of individual components. If the pace is to be kept up then it is inevitable that quantum effects will become increasingly important and ultimately will limit the operation of the computer. In these circumstances it is sensible to consider the possibility of harnessing quantum effects to realize quantum information processors and computers. We start with a brief introduction to the theory of computer science, the principles of which underlie the operation of what we shall refer to as classical computers. These include all existing machines and any based on the manipulation of classical bits. The development of computer science owes much to Turing, who devised a simple but powerful model of a computing device: the Turing machine. It its most elementary form, this consists of four elements. (i) A tape for data storage, which acts as a memory. This tape has a sequence of spaces, each of which has on it one of a finite set of symbols. (ii) A processor, which controls the operations of the machine.
In Part II of this book we show how computations can be implemented using quantum systems. As we will see, the differences between bits and qubits, briefly outlined in Part I, lead to some important consequences for quantum computing. We begin with a brief introduction to the fundamental principles underlying quantum computing: specific implementations will be considered in later chapters. Reversible computing While quantum computation in its modern form is still a relatively young discipline, researchers have been interested in the relationship between quantum mechanics and computing for a long time. Early workers were not interested in the ideas of quantum parallelism , which will be explored in the next section, but rather in the question of whether explicitly quantum mechanical systems could be used to implement classical computations. In addition to its intrinsic interest, there are two technological reasons why this might be considered an important question. The first reason is a direct consequence of Moore's laws. After the development of integrated circuits, computing technology began its headlong dash down the twin roads of ever-faster and ever-smaller devices. These two phenomena are closely related: as computing devices must communicate within themselves, and as the speed of information transfer cannot exceed the speed of light, faster computers must indeed be smaller. There is, however, a limit to this process, defined by the atomic scale: once the size of individual transistors becomes comparable with that of atoms, the old-fashioned approach of micro-electronics becomes completely untenable.
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.
Information is physical: the laws which govern its encoding, processing and communication are bound by those of its unavoidably physical embodiment. In today's informatics, information obeys the laws of Newton's and Maxwell's classical physics: this assertion holds all the way from commercial computers down to (up to?) their most abstract models, e.g. Turing machines and lambda-calculus. Today's computation and communication are classical. Research in quantum information processing and communication was born some twenty five years ago, as a child of two major scientific achievements of the 20th century, namely quantum physics and information sciences. The driving force of this interdisciplinary research is that of looking for the consequences of having information encoding, computation and communication based upon the laws of quantum physics, i.e. the ultimate knowledge that we have, today, of the foreign world of elementary particles, as described by quantum mechanics. Breakthroughs in cryptography, communications, information theory, algorithmics and, more recently, in abstract computational models, programming languages and semantics frameworks, have shown that this transplantation of information from classical to quantum has far reaching consequences, both quantitative and qualitative, and opens new avenues for research within the foundations of computer science.From a computer scientist's point of view, which is my point of view, I will explain the basics, survey the main achievements, and outline the current hot topics and major challenges of this promising and stimulating research. I will not assume any prior knowledge in quantum mechanics from the audience.
Information is physical: the laws which govern its encoding, processing and communication are those of its unavoidable physical embodyment. In today's computing, information obeys the laws of Newton's and Maxwell's classical physics: this assertion holds all the way from commercial computers down to their most abstract models, e.g. Turing machines and lambda-calculi. Today's computation is classical.Research in quantum information processing and communication (QIPC) was born some twenty years ago, as a child of two major scientific achievements of the 20th century, namely quantum physics and information sciences. The driving force of this interdisciplinary research is that of looking for the consequences of having information encoding, computation and communication obey the laws of quantum physics, i.e. the ultimate knowledge that we have, today, of the foreign world of elementary particles, as described by quantum mechanics. Breakthroughs in algorithmics, cryptography, information theory and abstract computational models have shown that this rerooting of information from classical to quantum has far reaching consequences, both quantitative and qualitative, and opens new avenues for research within the foundations of computer science.The aim of this tutorial is to give a survey of the principles, main results and long term perspectives of current research in QIPC, from a computer science point of view. No prior knowledge in quantum mechanics is required to follow this tutorial. There will be two parts:1 - Computation, the quantum way: quantum bits and quantum operations; two major quantum algorithms: quadratic speedup for unordered database search (Grover's algorithm), exponential speedup for integer factoring (Shor's algorithm);2 - Communication, the quantum way, and longer term perspectives: quantum state teleportation; a quantum cryptographic protocol for secret key distribution. Hot topics in QIPC research, state of the art in physical implementation of quantum computers.