MATH40830

Learning Outcomes:

Students will learn:

To work with and demonstrate an understanding of the mathematical structures and theory underlying quantum computation.

To communicate and apply the topics covered in the module.

To solve problems involving these topics.

Indicative Module Content:

Topics will be selected from the following, as time allows:

1. Basics: state vectors, qubits, Dirac notation, quantum gates, measurement, superposition, tensor products, entanglement, quantum circuits

2. Quantum algorithms: superdense coding, quantum teleportation, the quantum Fourier transform, algorithms of Deutsch, Deutsch-Josza, Simon, Shor, Grover

3. Density operator formalism: density operators, quantum channels, the partial trace, purification, the Schmidt decomposition, measurements

4. Quantum error correction: Shor’s 9 qubit code, outline of the Knill-Laflamme theorem

5. Nonlocal games and Bell inequalities

6. Quantum key distribution

Student Effort Hours:

Approaches to Teaching and Learning:

In addition to a good standard of linear algebra (including eigenvalues, eigenvectors and the diagonalisation of matrices over the complex numbers), students should be comfortable with mathematical proof techniques, such as are typically picked up during the first half of an undergraduate mathematics degree programme. Any questions about eligibility should be addressed to the module coordinator.

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

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