Introduction to quantum computers

Gary D. Doolen, Ronnie Mainieri, Vldimir I. Tsifrinovich, Gennady P. Berman9810234902, 9789810234904, 9780585459158, 9810235496

Quantum computing promises to solve problems which are intractable on digital computers. Highly parallel quantum algorithms can decrease the computational time for some problems by many orders of magnitude. This important book explains how quantum computers can do these amazing things. Several algorithms are illustrated: the discrete Fourier transform, Shor’s algorithm for prime factorization; algorithms for quantum logic gates; physical implementations of quantum logic gates in ion traps and in spin chains; the simplest schemes for quantum error correction; correction of errors caused by imperfect resonant pulses; correction of errors caused by the nonresonant actions of a pulse; and numerical simulations of dynamical behavior of the quantum Control-Not gate. An overview of some basic elements of computer science is presented, including the Turing machine, Boolean algebra, and logic gates. The required quantum ideas are explained.

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Table of contents :
Contents……Page 8
Chapter 1 Introduction……Page 10
Chapter 2 The Turing Machine……Page 17
Chapter 3 Binary System and Boolean Algebra……Page 22
Chapter 4 The Quantum Computer……Page 29
Chapter 5 The Discrete Fourier Transform……Page 40
Chapter 6 Quantum Factorization of Integers……Page 45
Chapter 7 Logic Gates……Page 47
Chapter 8 Implementation of Logic Gates Using Transistors……Page 53
Chapter 9 Reversible Logic Gates……Page 60
Chapter 10 Quantum Logic Gates……Page 68
Chapter 11 Two and Three Qubit Quantum Logic Gates……Page 73
Chapter 12 One-Qubit Rotation……Page 78
Chapter 13 Aj 205 Transformation……Page 87
Chapter 14 B jk 205 Transformation……Page 92
Chapter 15 Unitary Transformations and Quantum Dynamics……Page 94
Chapter 16 Quantum Dynamics at Finite Temperature……Page 99
Chapter 17 Physical Realization of Quantum Computations……Page 110
Chapter 18 CONTROL-NOT Gate in an Ion Trap……Page 118
Chapter 19 A j and B jk Gates in an Ion Trap……Page 125
Chapter 20 Linear Chains of Nuclear Spins……Page 129
Chapter 21 Digital Gates in a Spin Chain……Page 133
Chapter 22 Non-resonant Action of – Pulses……Page 136
Chapter 23 Experimental Logic Gates in Quantum Systems……Page 145
Chapter 24 Error Correction for Quantum Computers……Page 152
Chapter 25 Quantum Gates in a Two-Spin System……Page 163
Chapter 26 Quantum Logic Gates in a Spin Ensemble at Room Temperature……Page 169
Chapter 27 Evolution of an Ensemble of Four-Spin Molecules……Page 176
Chapter 28 Getting the Desired Density Matrix……Page 183
Chapter 29 Conclusion……Page 187
Bibliography……Page 189