Items related to An Introduction to Quantum Computing Algorithms
Synopsis
The purpose of this monograph is to provide the mathematically literate reader with an accessible introduction to the theory of quantum computing algorithms, one component of a fascinating and rapidly developing area which involves topics from physics, mathematics, and computer science. The author briefly describes the historical context of quantum computing and provides the motivation, notation, and assumptions appropriate for quantum statics, a non-dynamical, finite dimensional model of quantum mechanics. This model is then used to define and illustrate quantum logic gates and representative subroutines required for quantum algorithms. A discussion of the basic algorithms of Simon and of Deutsch and Jozsa sets the stage for the presentation of Grover's search algorithm and Shor's factoring algorithm, key algorithms which crystallized interest in the practicality of quantum computers. A group theoretic abstraction of Shor's algorithms completes the discussion of algorithms. The last third of the book briefly elaborates the need for error-correction capabilities and then traces the theory of quantum error-correcting codes from the earliest examples to an abstract formulation in Hilbert space. This text is a good self-contained introductory resource for newcomers to the field of quantum computing algorithms, as well as a useful self-study guide for the more specialized scientist, mathematician, graduate student, or engineer. Readers interested in following the ongoing developments of quantum algorithms will benefit particularly from this presentation of the notation and basic theory. Series: Progress in Computer Science and Applied Logic, Volume 19 Contents Preface Acknowledgements 1. Quantum Statics 1.1 Context 1.2 Experimental motivation for quantum mechanics 1.3 The basic model 1.4 The basic example: spin-1/2 particles 1.5 Dirac notation 1.6 Unitary transformations 2. Basics of Quantum Computation 2.1 Qubits and tensor products 2.2 The basic strategy of quantum algorithms 2.3 Quantum gates 2.4 Quantum subroutines: addition on a quantum computer 2.5 Quantum subroutines: a teleportation circuit 3. Quantum Algorithms 3.1 Deutsch-Josza algorithm 3.2 Simon's algorithm 3.3 Grover's algorithm 3.4 Shor's algorithm: factoring N=15 3.5 Shor's algorithm: factoring N=pq 3.6 The finite Fourier transform 3.7 Eigenvalues in quantum algorithms 3.8 Group theory and quantum algorithms 4. Quantum Error-Correcting Codes 4.1 Quantum dynamics and decoherence 4.2 Error correction 4.3 Shor's nine qubit error-correcting code 4.4 A seven qubit error-correcting code 4.5 A five qubit error-correction code 4.6 Stabilizers and the five qubit code 4.7 Theoretical aspects of stabilizer codes 4.8 CSS codes 4.9 Abstract quantum error correction 4.10 Further aspects of quantum error-correcting codes Afterword References Index
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Review
"Pittenger's book, as the title suggests, explains the mathematics at the basis of quantum computing and the fundamental algorithms, including Shor's factoring, Grover's search and error correction algorithms....
Since quantum computing is a highly interdisciplinary science, the author has tried to capture the attention of a large variety of readers and he has mostly achieved this objective. The book can be used as a formal introductory text for graduate students as well as a fascinating, but still engaging resource for interested readers who are comfortable with linear algebra.... Pittenger helps the reader into focusing attention on the algorithmic aspects rather than the formal content and uses examples as [an] integral part of the book, illustrating the substantial meaning of quantum theory applied to computing. He also proposes some exercises to stimulate an insightful reading.... The bibliography is complete and the interested reader can improve the understanding of the book and of the entire matter by following the numerous references, acquiring in this way more tools for the comprehension of a subject of such complexity...." ―SIGACT News
"An Introduction to Quantum Computing Algorithms reflects its author's own experience in learning the mathematics and theoretical physics required for the subject, as he writes in the acknowledgements. It is generally written in a pleasant and informal style, with much motivation in between the mathematics.... In just 150 pages this book manages to explain much of the core of quantum computing, and to explain it well." ―Quantum Information and Computation (QIC)
"If you have a general (fuzzy) background on quantum physics and on computer science, I recommend reading this book.... It is well written, easy to read, with many illustrating examples, and many exercises." ―Zentralblatt Math
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- PublisherSpringer Verlag
- Publication date1999
- ISBN 10 3764341270
- ISBN 13 9783764341275
- BindingHardcover
- LanguageEnglish
- Number of pages152
- Rating
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