Quantum Information - MAT00007M
- Department: Mathematics
- Credit value: 10 credits
- Credit level: M
- Academic year of delivery: 2022-23
Related modules
Additional information
Pre-requisite modules for Natural Sciences students: Linear Algebra for the Natural Sciences (MAT00041I), and Quantum Mechanics 1 (MAT00024H)
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Spring Term 2022-23 |
Module aims
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To complement the traditional approach to quantum mechanics based on particle dynamics.
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To study quantum mechanics in a finite-dimensional space in its own right.
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To explain that information is physical and explore the consequences thereof.
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To introduce basic ideas of quantum computation and quantum information.
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To see the interplay between mathematics and physics at work in an active research area.
Module learning outcomes
Subject content
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be familiar with quantum mechanics in finite-dimensional spaces;
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appreciate the differences between classical and quantum mechanical processing of information;
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understand paradigms of quantum information theory such as the no-cloning theorem, teleportation and simple quantum algorithms;
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be able to understand and construct simple quantum circuits;
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understand what a universal quantum computer is;
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understand examples of tasks for which quantum protocols can outperform classical ones;
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understand more advanced concepts and protocols such as density matrices, generalized measurements, non-locality, Bell inequalities or Grover’s algorithm
Academic and graduate skills
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Academic skills: this course requires students to apply abstract mathematical techniques and concepts to describe counter-intuitive physical phenomena.
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Graduate skills: through lectures, examples, classes, students will develop their ability to assimilate, process and engage with new material quickly and efficiently. They develop problem solving-skills and learn how to attach physical meaning both to previously known and to new mathematical structures.
Module content
In recent years, a quantum mechanical theory of information has emerged. The central idea is that all processing of information, ultimately, requires physical objects to carry it. If implemented microscopically, the quantum mechanical nature of the carriers becomes relevant and must be taken into account. Interestingly, this insight does not limit the possibilities to process information but opens up new, classically unexpected ways to proceed.
The first part of the module presents quantum mechanics in finite-dimensional spaces where most of quantum information processing takes place. Important concepts such as entanglement and Bell inequalities will be introduced. The second part is dedicated to quantum information proper. It includes topics such as quantum circuits, teleportation, quantum cryptography and basic quantum algorithms.
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
None
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Module feedback
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
M. A. Nielsen, I. L. Chuang: Quantum Computation and Quantum Information (Cambridge University Press, Cambridge 2000) (SK 30 NIE)
N. David Mermin: Quantum Computer Science (Cambridge University Press, Cambridge 2007) (SK 30 MER)
G. Alber: Quantum Information - An introduction to basic theoretical concepts and experiments (Springer, London 2001) (SK 30 ALB)