The paper is intended to be a survey of all the important aspects and results that have shaped the eld of quantum computation and quantum information. The reader is rst familiarized with those features and principles of quantum mechanics providing a more e cient and secure information processing. Their applications to the general theory of information, cryptography, algorithms, computational complexity and error-correction are then discussed. Prospects for building a practical quantum computer are also analyzed. 1 Introduction and

In the simulation of quantum circuits the matrices and vectors used to represent unitary operations and qubit states grow exponentially as the number of qubits increase. For instance, the evolution of an n-qubit quantum system in an initial superposition state is described by a 2 n x 2 n unitary matrix. However, the evolution of an n-qubit quantum system can be described as well as a composition of single-qubit and controlled-not unitary operations which are equivalent to the 2 n x 2 n unitary matrix. A strategy is suggested for the mapping of onequibit and two-qubit gates onto a three PE systolic array, and then we show how the interconnection of those systolic arrays can be used to implement or describe quantum circuits. As a case study we present the description of the teleportation algorithm. 1.

the solution of trivalent decision problems by

This article is dedicated to the memory of Rob Clifton, with whom I had many pleasant and thoughtprovoking conversations and e-mail exchanges over the past dozen years. I describe a pedagogical scheme devised to teach efficiently to computer scientists just enough quantum mechanics to permit them to understand the theoretical developments of the last decade going under the name of ‘‘quantum computation.’ ’ I then note that my offbeat approach to quantum mechanics, designed to be maximally efficacious for this specific educational purpose, is nothing other than the Copenhagen interpretation.

As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.

The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented aspects of computation and the interplay between them. This report is presented as a Master’s thesis at the department of Computer Science and Engineering at Göteborg University, Göteborg, Sweden. The text is part of a larger work that is planned to include chapters on quantum algorithms, the quantum Turing machine model and abstract approaches to quantum computation. Contents 1