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Introduction to quantum physics and information processing
Vathsan R., CRC Press, Inc., Boca Raton, FL, 2015. 264 pp. Type: Book (978-1-482238-11-2)
Date Reviewed: Jul 25 2016

Quantum mechanics (QM) is the study of subatomic phenomena that began in the 20th century and has steadily added to the knowledge of mankind, providing us with such technologies as the transistor and the laser, both of which have changed the course of human existence. The former, of course, is the primary component of modern computers; the latter has applications in many fields, including medicine, communications, and optical data storage.

As the field grew, researchers began investigating how QM objects might be used in making computations. In so-called classical computers, data is stored as binary numbers, bits, which take the logical values of one or zero. Physically, bits are stored as presence or absence of charge in a capacitor, presence or absence of magnetization on a rotating disk, pits in an optical disk, and so on. Electronic circuits retrieve data or act to change the state of bits to record data. At the quantum level, bit-like objects are called qubits. Physically, a qubit may be the spin direction of an electron, the polarity of a quantum of light, a photon, or some other property of a quantum entity that can be measured. Quantum computing grew from the observation that manipulations of the mathematical constructs that describe the properties of quantum objects can produce computations. Moreover, algorithms developed using these constructs appear to offer significant speed increases in certain cases when compared to algorithms that carry out the same calculation using a classical computing system. Perhaps the most famous example is Shor’s algorithm for factoring large integers. The computational difficulty of such factoring on classical computers is at the heart of current encryption systems used for secure communications. Reducing that difficulty would make the encryption systems obsolete.

This book introduces QM theory in the context of information and computation. It ties experimental observations from experiments that demonstrate quantum states to the mathematics that describe them. The tie between experiment and theory is very nicely presented with clear and very well-written text. Further, illustrations are plentiful and well done.

With basic QM theory in hand, models of classical and quantum computation are treated using Turing and quantum Turing machines, along with a discussion of computational complexity. As noted above, addressing the latter is the primary reason to consider quantum computation.

Classical computing is done by movement of electrons in circuits. An analogy called the “quantum circuit” permits visualization of an action taken on a qubit to effect a computational operation. Beginning with classical circuits, the author shows how they can be applied to the mathematical model that describes operations on qubits, and then moves into a theoretical treatment of quantum circuits. From here on, the treatment remains theoretical. One can understand the reason for this: qubits do not travel along wires as electrons do in a classical computer, hence the circuit analogy breaks down in this regard. In fact, handling physical qubits is at present quite difficult; only very simple quantum computing systems have been implemented due to the technical difficulties of manipulating and maintaining the states of subatomic entities. One wishes that in an otherwise excellent book, the author had addressed the state of physical QM computing systems even with just a few paragraphs.

With the quantum “equivalents” to classical circuits in hand, the author turns to quantum algorithms, treating the most well known--Deutsch, Deutsch-Josza, Bernstein-Vazirani, Simon, the quantum Fourier transform, Shor’s factorization, and Grover’s search.

The book concludes with three chapters on quantum information and communication. As before, the author presents the classical forms, showing how the quantum analogs are defined and manipulated. Here, we find treatment of communication of data, encryption, cryptography, quantum key distribution, quantum error correction, and finally the relation of information to entropy based on the work of Claude Shannon.

All in all, this is an excellent exposition of introductory QM and its application to computing and information. The material is well integrated, flows well from beginning to more advanced topics, and is beautifully written. Each chapter provides exercises and deeper problems at the end. A decent bibliography follows the final chapter. The book would be a suitable text for students with some background in linear algebra; background in QM is not required.

Reviewer:  G. R. Mayforth Review #: CR144627 (1610-0743)
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Physics (J.2 ... )
 
 
Error-Checking (B.1.3 ... )
 
 
Physics (J.2 ... )
 
 
Models Of Computation (F.1.1 )
 
 
Analysis Of Algorithms And Problem Complexity (F.2 )
 
 
Data Encryption (E.3 )
 
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