Introduction to Quantum Computation

Abstract

In this chapter, we introduce the basic concepts of quantum computation. We first describe the minimum unit of quantum information, the qubit, and define several gate operations for it. Then, we explain the Solovay-Kitaev algorithm, which provides a way to decompose an arbitrary single-qubit unitary operation into an elementary set of single-qubit gates. Using multi-qubit gates, we construct an arbitrary n-qubit unitary operation from an elementary universal set of gates, which we call universal quantum computation. Quantum algorithms, which run on a universal quantum computer, are also presented. One example of this is Shor's prime factoring algorithm based on the phase estimation algorithm. Another is an approximation of the Jones polynomial. Finally, we will introduce quantum noise and see how we can describe a quantum system coupled with an environment.