Quantum Computing: A Short Course from Theory to Experiment 2nd Edition by Joachim Stolze | (PDF) Free Download

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Second edition of the successful textbook which has emerged from a lecture series. The compact introduction addresses graduate students with a reasonably good background in physics, notably in quantum mechanics, plus some knowledge in introductory statistical mechanics and solid-state physics. The authors explain basic concepts from quantum mechanics and computer science which are used throughout the whole field of quantum computing and quantum communication. This second edition reflects the rapid development of the main ideas and techniques, e.g. by including the most recent experiments on cold atoms.

User’s Reviews

Editorial Reviews: Review It’s a very good book – it’s by far the best textbook at this level, and will become the principal text for our new course. Jonathan Jones Oxford Centre for Quantum Computation “The authors, experimantalists, being themselves involved in the realization of quantum computers, present with this book a didactically well formed introduction to quantum information processing, including computer architecture, tested and proposed schemes. Clearly, in order to offer this extensive material in a space of only just over 200 pages, the authors had restricted themselves to basic of relevant ideas. The latter are well selected and guide readers attention engagingly in chosen directions. … This textbook has the advantage that it contains both, theoretical as well as experimental, features of quantum computing, that the exposition is well organized, and for beginners that it omits more advanced mathematical tools. It gives … a broad overview … It is an introduction for beginners, a good one, and can be well recommended as such.” Zentralblatt MATH “Generell ist den Autoren die Verbindung unterschiedlicher Bausteine zu einem tragfähigen Ganzen fachlich und didaktisch geglückt … ein nützliches Buch, das den von seinen Autoren intendierten Zweck ohne Zweifel erfüllt.” Physik in unserer Zeit “Das Buch gibt eine beeindruckend aktuelle Beschreibung neuester Experimente … machen die Autoren mit dem sehr gelungenen Buch trotz der hohen Dichte an Information die grundlegenden Konzepte und Methoden verständlich und geben mit zahlreichen Verweisen und Zitaten auch einen soliden Ausgangspunkt für eine eingehende Beschäftigung mit dem Thema.” Physik Journal Review It’s a very good book—it’s by far the best textbook at this level, and will become the principal text for our new course. —Jonathan Jones, Oxford Centre for Quantum Computation From the Inside Flap “The book gives an impressive description of current experiments. Despite of the high density of information, the authors succeeded to describe the fundamental concepts and methods. As it contains numerous references and links, this book also forms a solid starting point for further studies.” Quoted from Physik Journal on the first edition New to this edition – Working with single Photons – Report on progress in the trapping and manipulation of neutral particles – Quantum simulations of strongly correlated many-particle models – End-of-chapter problems From the Back Cover “The book gives an impressive description of current experiments. Despite of the high density of information, the authors succeeded to describe the fundamental concepts and methods. As it contains numerous references and links, this book also forms a solid starting point for further studies.” Quoted from Physik Journal on the first edition New to this edition – Working with single Photons – Report on progress in the trapping and manipulation of neutral particles – Quantum simulations of strongly correlated many-particle models – End-of-chapter problems About the Author Dieter Suter is an experimentalist and well known for his NMR-work. He is currently working on quantum computation projects. Joachim Stolze is an expert on the theory of quantum computation. His topic research area is quantum spin chains. Both authors are known to have excellent didactic skills. Excerpt. © Reprinted by permission. All rights reserved. Quantum ComputingA Short Course from Theory to Experiment, Revised and EnlargedBy Joachim Stolze Dieter SuterJohn Wiley & SonsCopyright © 2008 WILEY-VCH Verlag GmbH & Co. KgaA, WeinheimAll right reserved.ISBN: 978-3-527-40787-3Chapter OneIntroduction and Survey 1.1 Information, Computers, and Quantum Mechanics 1.1.1 Digital Information Storage, interchange and processing of information is a defining feature of human culture as well as the basis of our economic system. Over the last fifty years, all these processes have undergone dramatic changes, driven by the evolution of microelectronics technology. The increasing availability of cheap storage, fast processors and global telecommunication (including the internet) has prompted a shift from a number of different conventional techniques used to store, process and transmit information, which used different, mostly analog techniques, to those which use all-digital forms of representing information. This convergence of technologies has also eased the connection between storage, processing and communication and made most of the ongoing processes transparent or invisible to the person who is actually using them. A search for a picture over an internet search engine, e.g., which typically involves typing a few words and results in a long list of “hits”, involves all three types of processes mentioned several times: The computer on which the person works interprets the input and uses its locally stored information to decide what action it has to take. It communicates with routers to obtain the address of the search engine. It sends the request over the internet to the search engine. The transfer of information over the internet involves multiple steps of processing and using stored information about connections at all nodes. The search engine receives the request and compares the keywords to those stored in its files. It uses stored rules to rank the hits. The result is sent back over the internet. The workstation receives the information and uses stored information to display the information. Each of these steps can be further subdivided into smaller steps that may again include different types of actions on the information being exchanged between many different parties (most of them electronic circuits). These fundamental changes of the way in which information is represented and processed have simultaneously changed the way in which we use information. One consequence is that, very often, information can no longer be localized or associated with a specific physical device. While hand-written notes represented unique instances of the pertinent information, every electronic mail is stored (at least temporarily) on many different computers. It is therefore not only available for later retrieval by the person who wrote it, but also to many others like system managers, hackers, or government agencies. Most users of digital information experience the paradigm shift from conventional forms of information representation to a unified digital form as an exciting possibility for improved communication, easier access to vital information and additional choices for entertainment. This attitude has driven the growth of the microelectronics industry over the last decades and is likely to remain an important economic force for the foreseeable future. At the same time, the global availability of information and the difficulty of controlling one’s personal data have prompted concerns about maintaining privacy. The emerging field of quantum information processing holds promises that are relevant for both issues, the further evolution of microelectronics as well as the concerns about privacy. This field, which combines approaches from physics, mathematics, and computer science, differs from conventional approaches by taking into account the quantum mechanical nature of the physical devices that store and process the information. In this monograph, we concentrate on the aspect of “quantum computers”, which refers to machines built on the basis of explicitly quantum mechanical systems and designed to process information in a way that is much more efficient than conventional computers. While it is still unclear at what time (and if ever) such computers will be more powerful than classical computers, it is quite clear that at least some of the underlying physics will be incorporated into future generations of information processing hardware. The related field of quantum communication, which promises to deliver ways of exchanging information that cannot be tapped by any eavesdropper, will only be mentioned briefly in Section 13. 1.1.2 Moore’s Law The evolution of micro- and optoelectronic devices and the associated digitization of information has relied on improvements in the fabrication of semiconductors that have led to ever smaller and faster components. The decrease in size, in particular, has allowed more components to be packed onto a chip, thus making them more powerful by integrating more functions. Simultaneously, the decrease in size is a prerequisite for making faster devices, as long as they rely on a fixed, systemwide clock. As early as 1965, Gordon Moore noticed that the number of components that could be placed on a chip had grown exponentially over many years, while the feature size had shrunk at a similar rate [Moo65]. This trend continued over the next forty years and is expected to do so for the foreseeable future. Figure 1.1 shows the current expectations: it represents the projections that the semiconductor industry association makes for the coming decade. As shown in Fig. 1.1, the feature size of electronic devices is now less than 100 nm and decreasing at a rate of some 12% per year. This trend could in principle continue for another forty years before the ultimate limit is reached, which corresponds to the size of an atom. Much before this ultimate limit, however, the feature size will become smaller than some less well defined limit, where the electrons that do the work in the semiconductor devices, will start to show that their behavior is governed by quantum mechanics, rather than the classical physical laws that are currently used to describe their behavior. 1.1.3 Emergence of Quantum Behavior The reduction of feature size also implies a decrease in operation voltage, since the internal fields would otherwise exceed the breakthrough fields of all available materials. Within the next ten years, the operational voltage is expected to decrease to less than one Volt. The capacitance of a spherical capacitor is ITLITL = 4[pi][[epsilon].sub.0]r. For a spherical capacitor with radius 50 nm, the capacitance is therefore of the order of 5 x [10.sup.-18] F. A change in the voltage of 0.1 V will then move less than four electrons in such a device, again making quantization effects noticeable. While the capacitance of real capacitors is higher, the number of electrons stored in a memory cell will become a small integer number in the near future, again bringing quantum physics into play. Classical physics is an approximation of the more fundamental laws of quantum mechanics, which, until today, has proved sufficiently accurate for all fields of engineering. Quantum mechanics is required in order to understand the properties of semiconductors, such as current – voltage curves of diodes, from their microscopic structure. Once these properties are established, however, it becomes possible to describe the operation of semiconductor devices on the basis of the classical theory of electrodynamics. This classical description of the operation of semiconductor devices will become impossible when the feature size reaches the coherence length. This quantity depends on the details of the material, the processing and the temperature at which the device operates, but typically is in the range of a few nanometers to some tens of nanometers. Figure 1.2 shows how the transition to the quantum regime will change the way in which typical electronic devices operate. Capacitors, which are present in many electronic circuits, exhibit a direct proportionality between applied voltage and stored charge in all classical devices. When the capacitance becomes small enough, the transfer of a single electron will change the potential of the capacitor by a large enough amount that it takes a significantly larger voltage to transfer additional charges. This makes it obvious that the progress that we have today will soon lead to a situation where it is no longer possible to describe the flow of electricity as a classical current. While a classical device, such as the workhorse FET, requires a continuous relationship between current and voltage, this will no longer be the case in the quantum mechanical regime, as experimental prototypes clearly show. 1.1.4 Energy Dissipation in Computers Possibly even more impressive than the reduction in feature size over time is a corresponding trend in the energy dissipated in a logical step, which is represented in Figure 1.3. Over the last fifty years, this number has decreased by more than ten orders of magnitude, again following an exponential time dependence. The reduction of energy dissipation is a requirement for a continuing improvement: if today’s processors had the energy efficiency of 1950, even a single computer would require more power than a large power station can generate. As a result, it would become too hot to operate and disintegrate within a fraction of a second. Even with today’s efficiency, heat dissipation is often the limiting factor for the speed of microprocessors. While the continued reduction of energy dissipation is thus a necessity, it will take only about 10 more years until a fundamental limit is reached: Any computer working with Boolean logic (which includes all of today’s digital computers) must dissipate at least an amount of kT ln 2 whenever it performs an AND or OR operation, since these operations are not reversible. The kT limit could be overcome by using so-called reversible logical operations. As we will discuss in Section 5, devices that operate by the laws of quantum mechanics are inherently reversible. The principles on which it operates may thus well find applications also in electronic circuits for classical computers. The two trends – reduction of dissipated power and reduction of size – therefore appear to converge towards devices that use quantum mechanics for their operation. While the limitations that force the use of quantum devices in the future may appear as a nuisance to many engineers, they also represent an enormous potential, since these future devices may be much more powerful than conventional (classical) devices. They can implement all the algorithms that run on today’s classical computers, but in addition, they also can be used to implement a different class of algorithms, which explicitly use the quantum mechanical nature of the device. A few such quantum algorithms have been designed to solve specific problems that cannot be solved efficiently on classical computers. While many questions remain unanswered concerning the feasibility of building devices that fulfil all the stringent requirements for a useful quantum computer, the possibilities offered by this emerging technology have generated a lot of attention, even outside the scientific community. 1.2 Quantum Computer Basics 1.2.1 Quantum Information We discuss here exclusively digital representations of information. Classically, information is then encoded in a sequence of bits, i.e., entities that can be in two distinguishable states, which are conventionally labeled with 0 and 1. In electronic devices, these states are encoded by voltages, whose values vary with the technological basis of the implementation (e.g., TTL: 0 ~ low is represented by voltages <0.8 V and 1 ~ high by voltages > 2.4 V). The same principle applies to quantum systems that represent information: to represent a single bit of information, two distinguishable states of the system are needed. “Distinguishable” means, in a quantum system, that the two states must differ in some quantum numbers, i.e., they must be different eigenstates of at least one operator. A typical example is a spin 1/2, which has two possible states. Another example is a photon, which can be polarized either vertically or horizontally. One of these states is identified with the logical value 0 (or false), the other with the value 1 (or true). The main difference between quantum mechanical and classical information is that, in the quantum mechanical case, the system is not necessarily in the state 0 or 1. Instead it can be in an arbitrary superposition (linear combination) of these states. To emphasize this difference between quantum and classical bits, the term “qubit” (short for quantum bit) has been adopted for the quantum mechanical unit of information. The power of quantum computers is directly related to this possibility of creating super-positions of states and applying logical operations to them: this allows one to perform many operations in parallel. A system consisting of N qubits has [2.sup.N] mutually orthogonal basis states, and it is possible to bring such a system into a state that is a superposition of all these basis states. Logical operations such as multiplications can then be applied to this superposition. In a sense to be discussed later, such a transformation is equivalent to transforming all the states in parallel, i.e., performing [2.sup.N] operations in parallel. Becoming slightly more formal, we find that the information, which is encoded in a quantum mechanical system (or quantum register), is described by a vector in Hilbert space. For the simplest case of a single qubit, the state is [absolute value of [psi] > = a] [[psi].sub.0] + b|[[psi].sub.1]>. The two parameters a and b are both complex numbers. Taking normalization into account, the system is therefore described by three continuous variables. The fact that the state is described by three continuous variables does not imply that a single qubit can store an infinite amount of information. To obtain the information content, one has to take the measurement process, which retrieves the information, into account: it is never possible to measure exactly the quantum state of a single photon. A single measurement (more precisely: an ideal quantum mechanical measurement as postulated by von Neuman) can only measure one degree of freedom and returns a single bit (particle found or not). A complete measurement of the state of a single qubit would thus require repeated measurements, which were possible if one could prepare copies of the actual quantum mechanical state. However, this is prohibited by the “no-cloning theorem”, which states that no process can duplicate the exact quantum state of a single particle. While the details of the calculation are rather involved, it is possible to show that a single quantum mechanical two-level system can transfer up to two classical bits of information. Without a complete analysis, this can be rationalized by the consideration that we can make two independent measurements on a photon, corresponding, e.g., to the measurement of the polarization horizontal/vertical or at 45 degrees. 1.2.2 Quantum Communication One of the most active areas of quantum information processing is quantum communication, i.e., the transfer of information encoded in quantum mechanical degrees of freedom. This is typically done by encoding the information in photons. Semiclassically, a photon can carry a bit: it can be transmitted or not, thus corresponding to a logical 0 or 1. Other encoding schemes include the polarization of the photon, which may be vertical or horizontal. (Continues…) Excerpted from Quantum Computingby Joachim Stolze Dieter Suter Copyright © 2008 by WILEY-VCH Verlag GmbH & Co. KgaA, Weinheim. Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐So the gold-standard is now more or less Nielsen and Chuang right? (circa 2014), why this one? well, say you dont want a super-technical phone book sized text to read: this is your book.It doesn’t always prove things or give you all the details, but it’s not terribly long and it’s very readable. This book is ideal for a foundation/overview and I’ve looked back over time to refresh things easily and quickly, while I usually turn to Preskill or other sources for the full-blown details.

⭐Overview and practical implementation chapters were quite good. Quantum algorithm chapters were impossible for me to understand, even after following other treatments. Other books like Kaye_2007 and Nielsen_2010 build on linear operators with equivalent matrix and circuit representations to build the needed concepts. This reviewed book uses nested summations, up to four deep, to describe something mathematically equivalent but nearly impervious to intuitive understanding.

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