Introduction to quantum computation and general procedure of Shor`s algorithm

Shihao Zhang, Lvzhou Li

A. Yu. Kitaev

We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an arbitrary finite Abelian group. The paper also contains a rather detailed introduction to the theory of quantum computation.

Keisuke Fujii

Alexei Kitaev

We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an arbitrary finite Abelian group. The paper also contains a rather detailed introduction to the theory of quantum computation.

ARTUR K. EKERT

Nežka Rugelj

In this diploma paper we present the Shor’s algorithm for factorising numbers, which runs on quantum computers. Initially, we explain the basics of quantum computing. Afterwards, we present a general review of the Fourier and the discrete Fourier transform, from which we derive the quantum Fourier transform. In the last part, we first give a short introduction to modular arithmetics. Later on, we describe the concept of factorization that is used in Shor’s algorithm. Diploma thesis ends with a detailed review of how the algorithm works on quantum computers and a simple example.