UCD Home >

# MATH40830

#### Maths of Quantum Computation (MATH40830)

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Dr Rupert Levene
Trimester:
Autumn
Mode of Delivery:
Blended
Internship Module:
No

Curricular information is subject to change.

Designed to be accessible to advanced undergraduate mathematics students, this module will introduce students to the mathematical structures underlying quantum computation, and will explore a variety of applications.

###### 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:
Student Effort Type Hours
Lectures

24

Tutorial

12

Specified Learning Activities

36

Autonomous Student Learning

48

Total

120

###### Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based learning.
Requirements, Exclusions and Recommendations
Learning Requirements:

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.

Module Requisites and Incompatibles
Pre-requisite:
MATH20300 - Linear Algebra 2 (MathSci)

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Continuous Assessment: Continuous Assessment Throughout the Trimester n/a Standard conversion grade scale 40% No

40

No
Examination: 2 hour End of Trimester Exam 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

60

No

Carry forward of passed components
No

Resit In Terminal Exam
Spring Yes - 2 Hour