Mathematics of quantum computation (Q2782239)

To some extent, this book presents a state-of-the-art of quantum computing which becomes a reality as the miniaturization of electronic circuits and chips increases. It is a collection of fifteen papers written by twenty-three authors, which can be clustered into nine parts: Quantum Entanglement (Ch 1,2 and 3), Universality of Quantum Gates (Ch 4), Quantum Search Algorithms (Ch 5, 6, and 7), Quantum Computational Complexity (Ch 8), Quantum Error-Correcting Codes (Ch 9 and 10), Quantum Computing Algebraic and Geometric Structures (Ch 11 and 12), Quantum Teleportation (Ch 13), Quantum Secure Communication and Quantum Cryptography (CH 14), Commentary on Quantum Computing (Ch 15). It is not a comprehensive textboook and it is intended to quantum mechanically literate readers only. NEWLINENEWLINEIn a more detailed manner, the topics addressed by the book are the following: Contents:NEWLINENEWLINEQuantum entanglement: Ch. 1: Jean-Luc Brylinski, Algebraic measures of entanglement (3--23); Ch. 2: Berthold-Georg Englert and Nasser Metwally, Kinematics of qubit pairs (25--75); Ch. 3: David A. Meyer and Noland Wallach, Invariants for multiple qubits: the case of 3 qubits (77--97).NEWLINENEWLINEUniversality of quantum gates: Ch. 4: Jean-Luc Brylinski and Ranee Brylinski, Universal quantum gates (101--116).NEWLINENEWLINEQuantum search algorithms: Ch. 5: Lov K. Grover and Anirvan M. Sengupta, From coupled pendulums to quantum search (119--134); Ch. 6: Goong Chen, Stephen A. Fulling and Jeesen Chen, Generalization of Grover's algorithm to multiobject search in quantum computing. I. Continuous time and discrete time (135--160); Ch. 7: Goong Chen and Shunhua Sun, Generalization of Grover's algorithm to multiobject search in quantum computing. II. General unitary transformations (161--168).NEWLINENEWLINEQuantum computational complexity: Ch. 8: Stephen A. Fenner, Counting complexity and quantum computation (171--219).NEWLINENEWLINEQuantum error-correcting codes: Ch. 9: Markus Grassl, Algorithmic aspects of quantum error-correcting codes (223--252); Ch. 10: Andreas Klappenecker and Martin Rötteler, Clifford codes (253--273) .NEWLINENEWLINEQuantum computing algebraic and geometric structures: Ch. 11: Jean-Luc Brylinski and Ranee Brylinski, Invariant polynomial functions on \(k\) qudits (277--286); Ch. 12: Michael H. Freedman, David A. Meyer and Feng Luo, \(Z_2\)-systolic freedom and quantum codes (287--320).NEWLINENEWLINEQuantum teleportation: Ch. 13: Kishore T. Kapale and M. Suhail Zubairy, Quantum teleportation (323--355).NEWLINENEWLINEQuantum secure communication and quantum cryptography: Ch. 14: Almut Beige, Berthold-Georg Englert, Christian Kurtsiefer and Harald Weinfurter, Communicating with qubit pairs (359--401).NEWLINENEWLINECommentary on quantum computing: Ch. 15: Stephen A. Fulling, Transgressing the boundaries of quantum computation: a contribution to the hermeneutics of the NMR paradigm (405--419). NEWLINENEWLINEThe book is easy to read, the notations are consistent from a chapter to another one, but the reference lists are not. If I were the editor I would begin the book with an introductory chapter (fifteeen-twenty pages) on the basics of quantum computation. I would suggest to the new reader to begin with the chapters 13 and 15.