Abstract Quantum information and quantum computing are based on the concept and manipulation of qubits. In this pedagogical Tutorial–written with the aim of assisting self-motivated undergraduate mathematics, physics, and engineering students–transformation of these qubits, especially the Hadamard transformation (H) and the phase shifter transformation (Φ), is illustrated. Two-qubit gates and their application in production of entangled states, along with quantum algorithms (including Deutsch–Jozsa algorithm), are included as well. With 2025 being declared as the International Year of Quantum Science and Technology (IYQ) by the United Nations General Assembly (UNGA), under the leadership of United Nations Educational, Scientific and Cultural Organization (UNESCO), the timeliness and relevance of this Tutorial, in order to nudge the budding researchers in the “quantum” direction, cannot be emphasized enough.
Abstract Quantum information and quantum computing are based on the concept and manipulation of qubits. In this pedagogical Tutorial–written with the aim of assisting self-motivated undergraduate mathematics, physics, and engineering students–transformation of these qubits, especially the Hadamard transformation (H) and the phase shifter transformation (Φ), is illustrated. Two-qubit gates and their application in production of entangled states, along with quantum algorithms (including Deutsch–Jozsa algorithm), are included as well. With 2025 being declared as the International Year of Quantum Science and Technology (IYQ) by the United Nations General Assembly (UNGA), under the leadership of United Nations Educational, Scientific and Cultural Organization (UNESCO), the timeliness and relevance of this Tutorial, in order to nudge the budding researchers in the “quantum” direction, cannot be emphasized enough.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
This paper investigates the core principles of quantum computation, providing an in-depth understanding of quantum phenomena and illustrating how these principles form the scientific foundation of the field. The pivotal physical concepts, such as properties of subatomic particles, including electrons and photons, as well as their mathematical description through linear algebra are examined. It focuses on the qubit, the quantum analogue of a classical bit, featuring properties like superposition, entanglement, and wave function collapse, which redefine the traditional concept of information processing. The mathematical structures that underlie quantum system modelling—vector spaces, tensor products, and Dirac notation—are also systematically explained. Essential components of quantum computation involve logic gates such as Pauli matrices and Hadamard gates, which demonstrate the novel application of qubits in unique ways. This sets up an important theme of the interdependence and potential for transformation of quantum states through the illustration of advanced ideas of quantum entanglement and teleportation. Quantum circuits serve as an outstanding example of how reversibility and superposition are exploited to solve complex problems at unprecedented levels of efficiency. The paper also highlights the Deutsch-Jozsa algorithm as a compelling example of quantum superiority over traditional computational approaches. Together, these findings emphasize the transformative potential of quantum computing for science and industry.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.