CS939-15 Quantum Computing

Introductory description

Quantum computing is an interdisciplinary field that lies at the intersection of computer science, mathematics, and physics. This computational paradigm relies on principles of quantum mechanics, such as superposition and entanglement, to obtain powerful algorithms.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Quantum computing — motivation, foundations, and prominent applications.
Review of linear algebra in the context of quantum information, Dirac’s bracket notation, limitation of classical algorithms.
The four postulates of quantum mechanics, qubits, quantum gates and circuits.
Basic quantum algorithms I — Deutsch’s algorithm, analysing quantum algorithms, and implementing quantum circuits via QISKIT.
Basic quantum algorithms II — Simon’s problem and the Bernstein -V-azirani algorithm.
Grover’s quantum search algorithm, the BBBV Theorem, and applications of Grover’s algorithm.
RSA, and Shor’s integer factorisation algorithm.
Introduction to quantum cryptography (post-quantum security, quantum key distribution).
Introduction to quantum information (superdense coding, nocloning theorem, quantum teleportation) Applications (quantum money, the Elitzur-Vaidman bomb).

Learning outcomes

By the end of the module, students should be able to:

• Understand the quantum computing paradigm:- Have an overview of a range of project management techniques- Understand how failure to correctly manage a project can lead to failure.- Understand how project management techniques provide quantifiable metrics for project progress
• Understand the power and limitation of quantum computers:- Understand the underlying power of quantum mechanics for computation.- Identify problems for which a quantum speedup is possible.- Understand the fundamental limitations of quantum algorithms.
• State the four postulates of quantum mechanics and their application to computation:- Design and analyse quantum algorithms.- Grasp the notions of quantum states, unitary evolution, measurements, andcomposite systems.- Restate the postulates in terms of density matrices.
• Analyse fundamental quantum algorithms:- Shor’s algorithm.- Grover’s search.- The Berstein-Vazirani algorithm.- Simon’s problem.- The Deutsch-Jozsa paradigm.
• Understand the principles of quantum information andquantum communication:- Understand quantum teleportation and its limits.- Describe the framework of quantum error-correcting codes.- Discuss Everett’s many worlds interpretation.
• Understand the implications of quantum computing on cryptography and security:- Understand the foundations of post-quantum cryptography.- Hack the RSA cryptosystem via a quantum computer.- Use quantum mechanics to obtain a monetary scheme.

Indicative reading list

Please see Talis Aspire link for most up to date list.

View reading list on Talis Aspire

Subject specific skills

Designing and analysing quantum algorithms.

Transferable skills

Understanding quantum mechanics and the power of quantum computing.