Quantum Theory & Quantum Information - MAT00122M
Module summary
This module will introduce quantum theory for finite-dimensional spaces in an axiomatic way. This setting is particularly appropriate to discuss recent and important applications of quantum theory. Examples drawn mainly from quantum information, will include powerful quantum algorithms and novel quantum cryptographic protocols that have no classical counterparts.
Related modules
Additional information
Cannot be taken in year 4 of MMath; the M-level option is MSc only.
Previous exposure to quantum mechanics would be useful at a conceptual level but all the technical content needed will be provided within the module.
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Semester 1 2023-24 |
Module aims
This module will introduce quantum theory for finite-dimensional spaces in an axiomatic way. This setting is particularly appropriate to discuss recent and important applications of quantum theory. Examples drawn mainly from quantum information, will include powerful quantum algorithms and novel quantum cryptographic protocols that have no classical counterparts.
Module learning outcomes
By the end of the module, students will be able to:
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State the axioms of quantum theory in a finite-dimensional setting;
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Work with quantum states and measurements in bra-ket notation, and calculate probabilities;
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Describe the ways in which quantum information is more powerful than classical;
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Construct simple quantum circuits and convert between circuit diagrams and the corresponding operators;
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Explain what a universal quantum computer is.
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Apply an advanced quantum information concept such as quantum operations.
Module content
In the past few decades a quantum mechanical theory of information has emerged. The central idea is that processing of information requires physical objects and hence physics provides the ultimate limitations on information processing. For microscopic systems, quantum mechanics provides the correct physical description and opens up new possibilities to perform tasks in ways that would be impossible based on classical information alone. This course will systematically develop the required tools from quantum theory before presenting applications such as quantum computing and quantum cryptography that are active research areas.
M-level variant will have an additional independent study component with formative assignment and seminar, and a compulsory exam question on the additional material. Since this part of the module is not a pre-requisite for anything, the additional material will be at the discretion of the lecturer, but could be quantum operations for example
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
None
Additional assessment information
M-level: 3hr exam (100%)
One question on the exam will be compulsory for M-level students and assess the additional M-level material. The M-level students will be able to skip one of the H-level questions
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 Chang, Quantum Computation and Quantum Information. Cambridge University Press, 2000