Quantum Information Science is a cross-disciplinary subject that has arisen in the last twenty years. It concerns itself with the consequences of our most complete description of the physical world (that is, quantum mechanics) for the reliable, secure, private, and rapid processing of information, both in communication and computation. While its invention is often ascribed to the famous theoretical physicist Richard Feynman in the 1980s, his contributions were only one of many that initiated the field around that time. While he perceived that new types of physical devices, in which the quantum laws of superposition and entanglement function at the logical level, could give new power in the simulation of quantum physics, it was others (Bennett, Brassard) who showed that the uncertainty principle led to fundamentally more secure ways of communicating secret messages. It was yet others (Deutsch, Vazirani) who understood that quantum theory defined a new kind of Turing machine, and that not only quantum physics simulations, but potentially many other computational problems, are sped up in this machine. And it was yet another (Shor) who found a simple, very fast algorithm for prime factorization. The word "qubit" was coined only in 1995. Its introduction is indicative of a new mindset that has developed in recent years for studying and using quantum systems. "Qubit" now stands for a durable paradigm that spans a very wide variety of fields. It thus has many sub-meanings: first, it is the basic abstract unit of information for workers ranging from optical communication engineers to NMR spectroscopists to black-hole theorists. Second, it is the name we now routinely give to physical two level systems, as they are realized by photons, atomic and ionic eigenlevels, electronic and nuclear spin, structural defects in solids, and circulating-current states of superconducting devices. Physics has long dealt with some of these two-level systems, but calling them qubits implies a whole suite of interrelated ideas and capabilities that we ascribe to these systems: the ability to precisely set, and to precisely measure, the quantum state of one unique specimen, to avoid its coupling with the environment while at the same time strongly and controllably coupling the qubits together, to exploit the resulting quantum entanglement as a resource for metrological, cryptographic, and computational tasks. Quantum Information is a very diverse subject pursued today in many different directions, by many hundreds of researchers internationally: In theoretical physics, it has enlivened and sharpened the understanding of efficient representations of entangled many-particle wavefunctions, and has provided the prospect of applications for new concepts such as anyons and majorana fermions. Information theorists has benefitted from having a rigorous extension of the basis of their field, in which classical information theory is subsumed into a greatly broader subject. Theoretical computer scientists continue the search for new quantum algorithms, and have used quantum concepts to prove new results about the classification of computational complexity. Coding theorists have had the new and subtle problem of quantum error correction to analyse and conquer. Most strikingly, the program of experimental physics has been influenced in many directions by Quantum Information Science. State-of-the-art optics experiments transmit quantum states over long distances and perform precision manipulations in single quanta (atomic ions, impurity spins, quantum dots) in the quest to have working quantum cyptography and quantum computing. Quantum Hall systems, and topological insulators, are being assiduously examined for new elementary excitations for use as qubits. In the course of ten years, superconducting devices have improved by over four orders of magnitude in their quantum coherence, a metric made precise by the ideas of quantum computing. [...] DiVincenzo, David
Quantum Information Science is a cross-disciplinary subject that has arisen in the last twenty years. It concerns itself with the consequences of our most complete description of the physical world (that is, quantum mechanics) for the reliable, secure, private, and rapid processing of information, both in communication and computation. While its invention is often ascribed to the famous theoretical physicist Richard Feynman in the 1980s, his contributions were only one of many that initiated the field around that time. While he perceived that new types of physical devices, in which the quantum laws of superposition and entanglement function at the logical level, could give new power in the simulation of quantum physics, it was others (Bennett, Brassard) who showed that the uncertainty principle led to fundamentally more secure ways of communicating secret messages. It was yet others (Deutsch, Vazirani) who understood that quantum theory defined a new kind of Turing machine, and that not only quantum physics simulations, but potentially many other computational problems, are sped up in this machine. And it was yet another (Shor) who found a simple, very fast algorithm for prime factorization. The word "qubit" was coined only in 1995. Its introduction is indicative of a new mindset that has developed in recent years for studying and using quantum systems. "Qubit" now stands for a durable paradigm that spans a very wide variety of fields. It thus has many sub-meanings: first, it is the basic abstract unit of information for workers ranging from optical communication engineers to NMR spectroscopists to black-hole theorists. Second, it is the name we now routinely give to physical two level systems, as they are realized by photons, atomic and ionic eigenlevels, electronic and nuclear spin, structural defects in solids, and circulating-current states of superconducting devices. Physics has long dealt with some of these two-level systems, but calling them qubits implies a whole suite of interrelated ideas and capabilities that we ascribe to these systems: the ability to precisely set, and to precisely measure, the quantum state of one unique specimen, to avoid its coupling with the environment while at the same time strongly and controllably coupling the qubits together, to exploit the resulting quantum entanglement as a resource for metrological, cryptographic, and computational tasks. Quantum Information is a very diverse subject pursued today in many different directions, by many hundreds of researchers internationally: In theoretical physics, it has enlivened and sharpened the understanding of efficient representations of entangled many-particle wavefunctions, and has provided the prospect of applications for new concepts such as anyons and majorana fermions. Information theorists has benefitted from having a rigorous extension of the basis of their field, in which classical information theory is subsumed into a greatly broader subject. Theoretical computer scientists continue the search for new quantum algorithms, and have used quantum concepts to prove new results about the classification of computational complexity. Coding theorists have had the new and subtle problem of quantum error correction to analyse and conquer. Most strikingly, the program of experimental physics has been influenced in many directions by Quantum Information Science. State-of-the-art optics experiments transmit quantum states over long distances and perform precision manipulations in single quanta (atomic ions, impurity spins, quantum dots) in the quest to have working quantum cyptography and quantum computing. Quantum Hall systems, and topological insulators, are being assiduously examined for new elementary excitations for use as qubits. In the course of ten years, superconducting devices have improved by over four orders of magnitude in their quantum coherence, a metric made precise by the ideas of quantum computing. [...] DiVincenzo, David
In order to provide novel techniques for processing, storing, and transmitting information, the multidisciplinary field of quantum information science (QIS) integrates ideas from quantum physics [ 4 ] with information science. However, due to a number of events, including Peter Shor’s invention of quantum algorithms and the rise in interest in quantum computing, the history of QIS started to expand quickly in the early to middle 1990s. Peter Shor, a physicist and mathematician, developed the first quantum algorithm that could factor big numbers exponentially more rapidly than any classical algorithm in 1994. This finding triggered strong interest in quantum computing’s potential to tackle issues that are currently unsolvable for classical computers. Since then, QIS has advanced due to the development of novel quantum algorithms and enhancements in the hardware used for quantum computing. Understanding complex quantum phenomena like entanglement and superposition and developing novel strategies for utilizing them for information processing and communication are the core goals of QIS. Quantum bits (qubits) can exist in superpositions of 0 and 1 simultaneously, which enables far more efficient computation than classical bits, which can only be in one state or the other at a given time. Superposition is a key concept in quantum computing. In addition to superposition, entanglement, coherence, and quantum algorithms are other important QIS concepts. Entanglement is a key feature of quantum mechanics and has been observed experimentally in a wide range of physical systems, including photons, atoms, and superconducting qubits. Two particles can get entangled with one another through a phenomenon called entanglement in which their quantum states exhibit a high correlation. This indicates that even if two particles are separated by a considerable distance, modifying the state of one can change the state of the other. No matter how far away two separate particles are from one another when they are entangled, measuring the state of one particle immediately gives the state of another particle. It plays a central role in many quantum technologies, including quantum computing for solving complex problems that take classical computers a long time to solve, quantum cryptography for secure communications, quantum sensing for quantum properties of particles to enable more precise measurements, and quantum networking to improve communication and processing speed over both short and long distances. Quantum metrology methods use the principles of quantum mechanics to improve the accuracy of measurements in fields like gravity sensors, timekeeping, and frequency standards. Some of the benefits of QIS are enhanced computing power, improved communication, advanced cryptography, more precise scientific measurements, and better logistics optimization.
Information is a physical. Physical systems register and process information. These facts generated enormus interest in the development of novel quantum tecnologies, especially because the construction of smaller electronic devices ultimately leads to a consideration of quantum mechanical effects in electronic and computer desingns. The notion of the classical bit of information theory was formally pushed into the realm of the quanta with the introduction of the quantum bit or qubit, in the seminal works of Deutsch (Deutsch, 1985) and Shor (Shor, 1994). They demostrated that, indeed, controlled multipartite qubit interference effects could provide the means for a radical new way of computing, allowing the computation of many intractable computational problems, such as the factoring of large number or exact simulation of large quantum systems. The field of experimental and theoretical research in quantum information and computation has emerged as very important player in the understanding of quantum phenomena the both the basic and technological levels. This has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineerin, to the physical sciences, and we now have an interdisciplinary field where great efforts are being made in order to build devices that allow the progressing of information at a quantum level. A concise introduction to the field of quantum information and quantum computation is presented. This stars with the bassic definitions of bits, quantum registers, through to the universal gate-set for building the universal quantum computer, from a quantum network model of computation. The work shows how two-qubit gates suffice for quantum computation, emphasing the power of the quantum circuit representation for entagling and disentagling quantum states. This leads to the “no-cloning theorem”, which leads us to many interesting applications, such as quantum cryptography. Two alternative approaches or performing quantum computation are also described i) the one-way or measurement based quantum computer method, and ii) holonomic or geometric quantum computation. Following this, quantum entaglement quantification is highlighted, particulary its usefulness as a communication resource, in order to describe some of its most celebrated practical applications to date: quantum teleportation, cryptography, dens coding, and data compression. Deutsch’s concept of quantum parallelism is enphasized in order to gain insight into the potential for efficiently solving certain classically intratable algorithms. A subject central to the field of QIP- quantum decoherence- is then introduced.. Possible ways to overcome it, in particular quantum error correction, are discussed. A descriptios of some of the currently available hardware of the practical implementation of quantum computation is provided with a discussion of the main physical quantum bits that are currently employed (or proposed) for a such a purpose.
It was Richard Feynman who first proposed, in 1982, the far-reaching concept of \na ”quantum computer”—a device more powerful than classical computers. The idea \nof a quantum computer is to employ the fascinating and often counterintuitive \nlaws of quantum mechanics to process information. It is far from obvious that \nthe proposed concept of a quantum computer is more powerful than its classical \ncounterpart, it was only in 1994 when Peter Shor theoretically demonstrated the \nexistence of a quantum algorithm for factorizing integers into prime factors \nthat runs in polynomial time unlike its classical counterpart which works in \nsub-exponential time. The factorization of integers into prime factors is the \nbasis of asymmetric cryptography. These early theoretical results lunched an \nimmense interest of the scientific community. Already during ’90s, the first \nproposals for the physical implementation of quantum computation emerged. Ever \nsince, many experimental groups around the world pursued different physical \nimplementations of quantum bits (qubits). The first decade of the new century \nsaw a steady improvement in the control and decoherence time (the time over \nwhich the information carried by the qubit is lost) for various qubits by many \norders of magnitude. The natural next step in this context is to answer the \nquestion of how to scale the system up to include many qubits and thus build a \nquantum computer? One of the main parts of this thesis addresses exactly this \nquestion, namely the question of architecture and scalability of future quantum \ncomputer. \n \nAmong various different physical realizations of qubits, the idea of using \nelectron spins trapped in electrostatic semiconductor quantum dots as the \nbuilding blocks of a quantum computer (the so-called spin qubits), put forward \nby Daniel Loss and David DiVincenzo in 1997, triggered tremendous interest in \nscientific community. Nevertheless, the implementation of the original \nLoss-DiVincenzo proposal posed a considerable technical challenge. It used \nquantum tunneling between qubits to enable their communication with each other, \nand thus required that the qubits to be placed very close to each other. This \nrequirement not only leaves little \nspace for the placement of the vast amount of gates and wirings needed to define \nthe electrostatic quantum dots, but also makes it challenging to control the \nlocal magnetic field needed for single-qubit operations. For these reasons, no \nsystem with more than a couple of spin qubits has been \nsuccessfully implemented thus far. In the first part of this thesis, we leap \nover this long-standing problem with an entirely different strategy of using \nmetallic floating gates or ferromagnets to couple together qubits that are \nseparated over a long distance. Our scheme works for any type of \nspin qubits, including the qubits based on nitrogen-vacancy center (NV-center) \nin diamond and technologically very important silicon qubits. \n \nThe main topic of this thesis is related to quantum computer. Still, quite \nunexpectedly, some of the ideas we employed in order to tackle the problem of \nquantum computer scalability can be utilized in a completely different field of \nresearch, namely, in the field of magnetic field sensing. Qubit are not only a \nnecessary ingredient of quantum computer but they also provide a way to measure \nvery accurately magnetic fields. The magnetometer build upon the qubit based on \nNV-center, so-called NV-magnetometer, emerged in recent years as most sensitive \nmagnetic moment sensor. These magnetometers are able to detect about hundred \nnuclear spins within a minute of acquisition time. In the second part of this \nthesis, we propose an entirely novel experimental realization of \nNV-magnetometers which increases present NV-center sensitivities by four orders \nof magnitude at room temperature. This unprecedented amplification of \nsensitivity will render magnetometers capable of detecting individual nuclear \nspins. This amplification is achieved by introducing a ferromagnetic particle \nbetween the nuclear spin that needs to be detected and the NV-magnetometer. Our \nsetup, in contrast to existing schemes, is particularly advantageous because, \ndue to the large amplification of sensitivity, the nuclear spin need not lie \nwithin a few nanometers of the surface but rather can be detectable at a \ndistance of 30 nm. With these novelties, our scheme provides chemically \nsensitive spin detection under ambient conditions allowing nanoscale resolution \nof nuclear magnetic moments in biological systems—the holy grail of nuclear \nmagneticresonance. \n \nIn the last part of the thesis we focus our attention to a new direction in \nquantum computer implementation that deals with topological quantum computer \nintroduced by Alexei Kitaev in 1997; in this approach the idea is to use \nquasiparticles with ”fractional” statistics and to perform the single- and \ntwo-qubit gates by merely exchanging these quasiparticles. Additionally, \ninformation in this system is stored non-locally thus it mitigates the problem \nof decoherence caused by local noise from the environment. Majorana fermions are \none of the most well known examples of such excitations. We analyze transport \nsignatures of different topological states in one-dimensional systems, like \nMajorana fermions and fractionally charged states. We envision an Aharonov-Bohm \nsetup wherein conductance measurement provides a clear signature of presence of \nfractionally charged fermionic states, since oscillations with double period \nemerge in this case. Additionally, we propose a very simple setup that enables \nexistence of degenerate mid-gap states, so-called Tamm-Shockley states that are \ncharacterized by fractional charge and discuss possible ways of detecting these \nstates experimentally. \n
ENGLISH ABSTRACT: What are the information processing capabilities of physical systems? As recently as the first half of the 20th century this question did not even have a definite meaning. What is information, and how would one process it? It took the development of theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate mathematically what it means to compute or communicate. Yet these theories were abstract, based on axiomatic mathematics: what did physical systems have to do with these axioms? Rolf Landauer had the essential insight - "Information is physical" - that information is always encoded in the state of a physical system, whose dynamics on a microscopic level are well-described by quantum physics. This means that we cannot discuss information without discussing how it is represented, and how nature dictates it should behave. Wigner considered the situation from another perspective when he wrote about "the unreasonable effectiveness of mathematics in the natural sciences". Why are the computational techniques of mathematics so astonishingly useful in describing the physical world [1]? One might begin to suspect foul play in the universe's operating principles. Interesting insights into the physics of information accumulated through the 1970s and 1980s - most sensationally in the proposal for a "quantum computer". If we were to mark a particular year in which an explosion of interest took place in information physics, that year would have to be 1994, when Shor showed that a problem of practical interest (factorisation of integers) could be solved easily on a quantum computer. But the applications of information in physics - and vice versa - have been far more widespread than this popular discovery. These applications range from improved experimental technology, more sophisticated measurement techniques, methods for characterising the quantum/classical boundary, tools for quantum chaos, and deeper insight into quantum theory and nature. In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.
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.
Quantum computing exists at the intersection of mathematics, physics, chemistry, and engineering; the main goal of quantum computing is the creation of devices and algorithms which use the properties of quantum mechanics to store, manipulate and measure information. There exist many families of algorithms, which, using non-classical logical operations, can outperform traditional, classical algorithms in terms of memory and processing requirements. In addition, quantum computing devices are fundamentally smaller than classical processors and memory elements; since the physical models governing their performance are applicable on all scales, as opposed to classical logic elements, whose underlying principles rely on the macroscopic nature of the device in question. \n \nQuantum algorithms, for the most part, are predicated on a theory of resources. It is often assumed that quantum computers can be placed in a precise fiducial state prior to computation, and that logical operations are perfect, inducing no error on the system which they affect. These assumptions greatly simplify algorithmic design, but are fundamentally unrealistic. In order to justify their use, it is necessary to develop a framework for using a large number of imperfect devices to simulate the action of a perfect device, with some acceptable probability of failure. This is the study of fault-tolerant quantum computing. In order to pursue this study effectively, it is necessary to understand the fundamental nature of generic quantum states and operations, as well as the means by which one can correct quantum errors. Additionally, it is important to attempt to minimize the use of computational resources in achieving error reduction and fault-tolerant computing. \n \nThis thesis is concerned with three projects related to the use of error-prone quantum systems to transmit and manipulate information. The first of these is concerned with the use of imperfectly-prepared states in error-correction routines. Using optimal quantum error correction, we are able to deduce a method of partially protecting encoded quantum information against preparation errors prior to encoding, using no additional qubits. The second of these projects details the search for entangled states which can be used to transmit classical information over quantum channels at a rate superior to classical states. The third of these projects concerns the transcoding of data from one quantum code into another using few ancillary resources. The descriptions of these projects are preceded by a brief introduction to representations of quantum states and channels, for completeness. \n \nThree techniques of general interest are presented in appendices. The first is an introduction to, and a minor advance in the development of optimal error correction codes. The second is a more efficient means of calculating the action of a quantum channel on a given state, given that the channel acts non-trivially only on a subsystem, rather than the entire system. Finally, we include documentation on a software package developed to aid the search for quantum transcoding operations.