Quantum Information and Computation

PHYS30401 Quantum Information and Computation 10 Semester 1 Undergraduate Level 3 Philip Taranto Unit coordinator Department of Physics & Astronomy 1 FHEQ level (Framework for Higher Education Qualifications) ' Last part of a Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 Quantum Information Science is an interdisciplinary field that combines principles from quantum mechanics and information theory to explore new computational paradigms and technologies. This course introduces students to the fundamental concepts of quantum information, including qubits, entanglement, and quantum circuits, and examines how these concepts differ from classical information systems. Students will explore the theoretical foundations of quantum computation and cryptography, and gain insight into the practical challenges and potential applications of quantum technologies. Topics include quantum algorithms, quantum cryptography, and the applications of quantum systems for communication. The course aims to develop a critical understanding of the advantages and limitations of quantum systems, preparing students for advanced study in quantum computing and related fields. <div class="bigtext noneditable" style="-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);border-radius:0.285714rem;border:1px solid rgba(34, 36, 38, 0.15);box-shadow:transparent 0px 0px 0px 0px inset;box-sizing:inherit;color:rgba(0, 0, 0, 0.87);font-family:"Segoe UI", Lato, "Helvetica Neue", Arial, Helvetica, sans-serif;font-size:14px;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;margin:0px;min-height:6rem;min-width:100%;orphans:2;outline:none;padding:0.678571em 1em !important;resize:vertical;text-align:start;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;transition:color 0.1s, border-color 0.1s;white-space:normal;widows:2;word-spacing:0px;" title="Brief description of this Course Unit's content">Part 1: Fundamentals of Quantum Information 1. Review of Quantum Mechanics Foundations (2 lectures). Key postulates of quantum mechanics: states, dynamics, measurements. Linear algebra for quantum mechanics: state vectors, operators, and eigenvalues. Essential basic probability theory. 2. Qubits and Basic Quantum Information Concepts (3 lectures). Qubits: Bloch sphere representation and single-qubit states. Single-qubit operations: Pauli matrices, unitary transformations. Introduction to quantum superposition and coherence. Mixed states / density matrices. Composite systems, reduced states, and introduction to entanglement. 3. Foundations of Information Theory: Classical & Quantum (2 lectures). Basic classical (Shannon) information theory: entropy, mutual information, noiseless coding theorem. Basic quantum information theory: no cloning theorem, Holevo capacity, Schumacher compression.  4. Essential Quantum Information Protocols (2 lectures). State tomography and discrimination tasks, quantum teleportation, superdense coding.  Part 2: Quantum Information in Practice 5. Quantum Correlations (2 lectures). Entanglement, Schmidt decomposition, purification. Entanglement quantification: pure and mixed states. EPR argument: local hidden variables, Bell’s theorem, quantum non-locality. 6. Quantum Cryptography & Metrology (2 lectures). Principles of quantum cryptography: BB84 protocol, quantum key distribution. Phase estimation. Quantum Information Science is an interdisciplinary field that combines principles from quantum mechanics and information theory to explore new computational paradigms and technologies. This course introduces students to the fundamental concepts of quantum information, including qubits, entanglement, and quantum circuits, and examines how these concepts differ from classical information systems. Students will explore the theoretical foundations of quantum computation and cryptography, and gain insight into the practical challenges and potential applications of quantum technologies. Topics include quantum algorithms, quantum cryptography, and the applications of quantum systems for communication. The course aims to develop a critical understanding of the advantages and limitations of quantum systems, preparing students for advanced study in quantum computing and related fields. <div class="bigtext noneditable" style="-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);border-radius:0.285714rem;border:1px solid rgba(34, 36, 38, 0.15);box-shadow:transparent 0px 0px 0px 0px inset;box-sizing:inherit;color:rgba(0, 0, 0, 0.87);font-family:"Segoe UI", Lato, "Helvetica Neue", Arial, Helvetica, sans-serif;font-size:14px;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;margin:0px;min-height:6rem;min-width:100%;orphans:2;outline:none;padding:0.678571em 1em !important;resize:vertical;text-align:start;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;transition:color 0.1s, border-color 0.1s;white-space:normal;widows:2;word-spacing:0px;" title="Brief description of this Course Unit's content">Part 1: Fundamentals of Quantum Information 1. Review of Quantum Mechanics Foundations (2 lectures). Key postulates of quantum mechanics: states, dynamics, measurements. Linear algebra for quantum mechanics: state vectors, operators, and eigenvalues. Essential basic probability theory. 2. Qubits and Basic Quantum Information Concepts (3 lectures). Qubits: Bloch sphere representation and single-qubit states. Single-qubit operations: Pauli matrices, unitary transformations. Introduction to quantum superposition and coherence. Mixed states / density matrices. Composite systems, reduced states, and introduction to entanglement. 3. Foundations of Information Theory: Classical & Quantum (2 lectures). Basic classical (Shannon) information theory: entropy, mutual information, noiseless coding theorem. Basic quantum information theory: no cloning theorem, Holevo capacity, Schumacher compression.  4. Essential Quantum Information Protocols (2 lectures). State tomography and discrimination tasks, quantum teleportation, superdense coding.  Part 2: Quantum Information in Practice 5. Quantum Correlations (2 lectures). Entanglement, Schmidt decomposition, purification. Entanglement quantification: pure and mixed states. EPR argument: local hidden variables, Bell’s theorem, quantum non-locality. 6. Quantum Cryptography & Metrology (2 lectures). Principles of quantum cryptography: BB84 protocol, quantum key distribution. Phase estimation. 7. Quantum Computation (4 lectures). Quantum circuits: entangling gates, universal gate sets. Overview of Deutsch-Jozsa, Grover’s search, and Shor’s factoring algorithms. Computational complexity: quantum speedup compared to classical approaches. Implications of quantum algorithms for cryptography and other fields. 8. Noise & Quantum Error Correction (2 lectures). Quantum channels and decoherence. Quantum error correction basics: syndrome measurements and CSS code. 9. Experimental Implementations (scattered throughout). Physical platforms: photonic/optical systems, ion traps, superconducting circuits. Challenges in building scalable quantum systems. </div><div class="ui fluid accordion" style="-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);box-sizing:inherit;color:rgba(0, 0, 0, 0.87);font-family:"Segoe UI", Lato, "Helvetica Neue", Arial, Helvetica, sans-serif;font-size:14px;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;max-width:100%;orphans:2;scrollbar-color:auto;text-align:start;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;white-space:normal;widows:2;width:1069.67px;word-spacing:0px;"><div class="title active" style="box-sizing:inherit;color:rgba(0, 0, 0, 0.87);cursor:pointer;font-family:"Segoe UI", Lato, "Helvetica Neue", Arial, Helvetica, sans-serif;font-size:1em;padding:0.5em 0px;">  </div></div> To provide a foundational understanding of quantum mechanics in the context of quantum information science. To explore key concepts such as qubits, entanglement, and quantum circuits. To introduce students to practical applications, including quantum cryptography, algorithms, and communication tasks. To develop the ability to critically analyse the advantages and limitations of quantum systems compared to classical ones for information processing tasks.  On the successful completion of the course, students will be able to:  ILO 1Explain the fundamental principles of quantum information theory and their relation to classical information theory.ILO 2Describe and apply concepts such as qubits, entanglement, and quantum circuits in the characterisation of quantum systems and their advantages for information processing tasks.ILO 3Evaluate the principles and practical applications of quantum cryptography and communication.  ILO 4Critically assess the challenges of scaling quantum systems, including decoherence and error correction. Two one hour, live in-person lectures per week where the core material with examples will be delivered. The recordings of these lectures will be on the course online page. The lectures are accompanied by brief summary notes and for some of the material explanatory videos that the students are expected to assimilate before the lecture. This is augmented by a weekly online quiz (where the students get automatic feedback), and fortnightly problems. A Piazza discussion forum is also provided where students can ask questions with answers provided by other students and the unit lead.  1 Written exam 100% PHYS20302 Quantum Mechanics 2 Pre-Requisite Compulsory N Quantum Computation and Quantum Information, by Michael A. Nielsen and Isaac L. Chuang:https://doi.org/10.1017/CBO9780511976667 Quantum Information, Computation and Communication, by Jonathan A. Jones, Dieter Jaksch:https://doi.org/10.1017/CBO9781139028509  Assessment written exam 2 Lectures 22 0 76