INTRODUCTION TO QUANTUM COMPUTERS

by Gennady P. Berman, Gary D. Doolen, Ronnie Mainieri

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 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.

Genres: Physics, Computer Science, Science

196 pages, Paperback

First published July 7, 1998

Reviews

[Jose Brox · Rating 4 out of 5]

This book is quite difficult to rate. Let me start with what it is not: this is not a gentle introduction to quantum computing. The discrete Fourier transform and Shor's factorization algorithms are described, and in a superb way. But apart from quick introductions to Turing machines, classical circuits, and quantum computing in the first eight small chapters (50 pages in total), this short book is devoted to its main subject, quantum *computers*, that is, the computer's architecture. Indeed this little book is a sort of reference guide on the physical implementation of quantum gates, as the state of the art was in 1998, giving theoretical proofs of their operation. So in each chapter we typically study how to implement some gate or system with some physical resource (here mostly ion traps, spin chains, and laser pulses), looking at the specific math behind it. To assess the relative significance of this book today, it is important to note that nowadays the engineering (as by IBM, Google, etc.) of successful quantum computers is more centered around superconducting electronic circuits, although research on ion traps is far from being stopped. That said, this book is a good source to understand how quantum circuits can be actually implemented, for anyone with some knowledge of quantum mechanics.

CONTENTS

1 Introduction
2 The Turing Machine
3 Binary System and Boolean Algebra
4 The Quantum Computer
5 The Discrete Fourier Transform
6 Quantum Factorization of Integers
7 Logic Gates
8 Implementation of Logic Gates Using Transistors
9 Reversible Logic Gates
10 Quantum Logic Gates
11 Two and Three Qubit Quantum Logic Gates
12 One-Qubit Rotation
13 Aj-Transformation
14 Bjk-Transformation
15 Unitary Transformations and Quantum Dynamics
16 Quantum Dynamics at Finite Temperature
17 Physical Realization of Quantum Computations
18 CONTROL-NOT Gate in an Ion Trap
19 Aj and Bjk Gates in an Ion Trap
20 Linear Chains of Nuclear Spins
21 Digital Gates in a Spin Chain
22 Non-resonant Action of pi-Pulses
23 Experimental Logic Gates in Quantum Systems
24 Error Correction for Quantum Computers
25 Quantum Gates in a Two-Spin System
26 Quantum Logic Gates in a Spin Ensemble
at Room Temperature
27 Evolution of an Ensemble of Four-Spin Molecules
28 Getting the Desired Density Matrix
29 Conclusion

[Wael Itani · Rating 4 out of 5]

This short book delivers a non-pretensive introduction to quantum computing best suited for those coming of a background in classical computing, but otherwise accessible to everyone who wants to get started with a book to be read in a single session.