Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Apress eBooks

Mathematics Behind Quantum Computing

Bhagvan Kommadi

Published Jan 1, 2020• 1 citation
Publisher

Abstract

In this chapter, we cover the mathematical concepts related to quantum computing. We look at quantum operators, sets, vectors, matrices, and tensors.
DOI
10.1007/978-1-4842-6516-1_2

Related papers

Analysis and Review of Mathematical Concepts in Quantum Computation

M. A. Bashar, Mahmudul Hasan, M. Syduzzaman M. A. Chowdhury

The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data.Mathematics lies at the heart of quantum computation and it is needed in every aspect of the research and development of quantum computation.In this paper we have presented mathematical concepts that are closely related to quantum computation and their relation to quantum mechanics in a way which is innovative and very easy to comprehend.Most of the mathematical concepts presented in this paper are deduced from the postulates of quantum mechanics and linear algebra.

Journal of information engineering and applications•Jan 1, 2015•0 citations

Quantum Computing—Foundations, Principles, and Modern Applications

M. Bharathi, Virupakshi Madhurima, Sandhya Kumari G. +4 more

This chapter explores the rapidly developing field of quantum computing, which essentially devises the power to change science and technology. After an introductory outline, the fundamental ideas of quantum computing are covered, setting it apart from classical computing. The chapter then goes on to describe the features of a quantum computing system, highlighting its unique traits and possible advantages. The reliance on complex numbers and advanced mathematics is a central point of quantum computing [ 1 ]. Fundamental mathematical concepts are important to understand the quantum algorithms, which are explained in more detailed way. In quantum computing, the main idea is that quantum bits can have several states. The quality of quantum processing is extensively explored in this chapter. The chapter also covers a range of quantum computing techniques, highlighting their resourceful methods for tackling problems. Finally, the uses of quantum computing and its influence in many areas, such as optimization, materials research, and cryptography, are described and analyzed. This ample introduction will provide readers with thoughtful principles and the mathematical and practical significance of quantum computing.

CRC Press eBooks•Nov 28, 2025•0 citations

Quantum Computing and Communications

Yongli Zhao

This book explains the concepts and basic mathematics of quantum computing and communication. Chapters cover such topics as quantum algorithms, photonic implementations of discrete-time quantum walks, how to build a quantum computer, and quantum key distribution and teleportation, among others.

IntechOpen eBooks•Nov 6, 2020•5 citations

Basic Concepts in Quantum Physics— Mathematical Tools

Daniel Minoli, Benedict Occhiogrosso

This chapter presents some of the basic mathematical background and nomenclature needed to gain an introductory understanding of Quantum Mechanics (QM). The more direct application of the math to QM per se is covered in chapters that follow.

Auerbach Publications eBooks•Mar 18, 2025•0 citations

Introduction to Quantum Computing

Walid E. Gomaa

This presentation provides a comprehensive overview of the foundational principles of quantum computation. It begins by contrasting classical and quantum information, highlighting how quantum bits (qubits) leverage superposition, entanglement, and interference to process information in ways that surpass classical limits. The document explains the four postulates of quantum mechanics: state space (qubits as unit vectors in a Hilbert space), time evolution (via unitary operators), measurement (probabilistic collapse of the state), and composite systems (tensor products of subsystems). Key concepts such as the Bloch sphere representation, quantum gates (e.g., Hadamard, CNOT, Pauli gates), and quantum circuits are discussed, illustrating how quantum operations manipulate qubit states. The presentation also covers quantum evolution, the gate model for computation, and the universality of certain gate sets, emphasizing the potential for quantum parallelism and the transformative impact of quantum computing on fields like cryptography and optimization.

•Nov 11, 2025•0 citations

Majorization

Gilad Gour

Chapter 4 delves into the concept of majorization, an essential mathematical framework critical for understanding the intricate structures within quantum resource theories. At its core, majorization establishes a preorder relationship between probability vectors, revealing a structured approach to compare the dispersion or concentration of probabilistic distributions. The chapter systematically deconstructs majorization into comprehensible segments, incorporating axiomatic, constructive, and operational perspectives. It further explores the mathematical foundations of majorization through an in-depth look at doubly stochastic matrices and T-transforms. Additionally, the chapter examines various forms of majorization, including approximate, relative, trumping, catalytic, and conditional majorization. This exploration not only encompasses the theoretical facets but also offers practical insights derived from games of chance.

Cambridge University Press eBooks•Apr 10, 2025•0 citations
The basic principle behind quantum computation is that quantum properties can be used to represent data and perform operations on these data.Mathematics lies at the heart of quantum computation and it is needed in every aspect of the research and development of quantum computation.In this paper we have presented mathematical concepts that are closely related to quantum computation and their relation to quantum mechanics in a way which is innovative and very easy to comprehend.Most of the mathematical concepts presented in this paper are deduced from the postulates of quantum mechanics and linear algebra.
This chapter explores the rapidly developing field of quantum computing, which essentially devises the power to change science and technology. After an introductory outline, the fundamental ideas of quantum computing are covered, setting it apart from classical computing. The chapter then goes on to describe the features of a quantum computing system, highlighting its unique traits and possible advantages. The reliance on complex numbers and advanced mathematics is a central point of quantum computing [ 1 ]. Fundamental mathematical concepts are important to understand the quantum algorithms, which are explained in more detailed way. In quantum computing, the main idea is that quantum bits can have several states. The quality of quantum processing is extensively explored in this chapter. The chapter also covers a range of quantum computing techniques, highlighting their resourceful methods for tackling problems. Finally, the uses of quantum computing and its influence in many areas, such as optimization, materials research, and cryptography, are described and analyzed. This ample introduction will provide readers with thoughtful principles and the mathematical and practical significance of quantum computing.
This presentation provides a comprehensive overview of the foundational principles of quantum computation. It begins by contrasting classical and quantum information, highlighting how quantum bits (qubits) leverage superposition, entanglement, and interference to process information in ways that surpass classical limits. The document explains the four postulates of quantum mechanics: state space (qubits as unit vectors in a Hilbert space), time evolution (via unitary operators), measurement (probabilistic collapse of the state), and composite systems (tensor products of subsystems). Key concepts such as the Bloch sphere representation, quantum gates (e.g., Hadamard, CNOT, Pauli gates), and quantum circuits are discussed, illustrating how quantum operations manipulate qubit states. The presentation also covers quantum evolution, the gate model for computation, and the universality of certain gate sets, emphasizing the potential for quantum parallelism and the transformative impact of quantum computing on fields like cryptography and optimization.
Chapter 4 delves into the concept of majorization, an essential mathematical framework critical for understanding the intricate structures within quantum resource theories. At its core, majorization establishes a preorder relationship between probability vectors, revealing a structured approach to compare the dispersion or concentration of probabilistic distributions. The chapter systematically deconstructs majorization into comprehensible segments, incorporating axiomatic, constructive, and operational perspectives. It further explores the mathematical foundations of majorization through an in-depth look at doubly stochastic matrices and T-transforms. Additionally, the chapter examines various forms of majorization, including approximate, relative, trumping, catalytic, and conditional majorization. This exploration not only encompasses the theoretical facets but also offers practical insights derived from games of chance.