Emerging Computing Paradigms

3 Quantum Computing Principles and Mathematical Models

Arish Pitchai

Entropik Tech, 600032, Tamilnadu, Chennai, India

3.1 Introduction

Moore’s law, which says integrated circuit density will double every two years, is coming to an end because of the limitations in manufacturing smaller transistors [1]. End of Moore’s law doesn’t mean the computers are not going to become faster anymore. Recent research reveals that a new paradigm of computation called quantum computing is capable of presenting efficient machines. Quantum computing research is interdisciplinary and demands the knowledge of mathematics, physics, and computer science to understand the working of their algorithms and to build better algorithms. Quantum computing research is experiencing rapid growth in both theoretical and practical innovations [2]. Recent developments of hardware and quantum machine learning algorithms are showing a promising future for a quantum era. This chapter provides an overview of quantum computing principles and architectures from a mathematical perspective.

The following section presents an overview to quantum computers, explaining necessary prerequisite topics from mathematics such as vector algebra and the matrix operations. Different representations of simple and composite set of qubits, the building blocks of quantum computers, are presented using Paul Dirac’s bra-ket, column vector and also Bloch sphere notations. The third section contains the operations that can be applied on the ...