Studying at York
(NS) Introduction to Quantum Computing - PHY00020H
Related modules
Pre-requisite modules
- None
Co-requisite modules
- None
Prohibited combinations
Module will run
| Occurrence | Teaching cycle |
|---|---|
| A | Spring Term 2018-19 |
Module aims
The field of Quantum Computation has been expanding exponentially over the last decade. At its core is the idea of finding a physical system with the right characteristics to build the "quantum computer", a device which can improve computer performance to levels unreachable by standard (i.e. "classical") computer. There are proposals for quantum computers based on semiconductors, superconductors, cold ions or atoms, molecules in a solvent, fullerenes and so on. Each of the proposals has advantages and disadvantages, and has been partially tested experimentally. The requirements to build a quantum computer are experimentally very challenging, so that the experiments performed in this area are at the very edge of modern techniques. The "quantum computer" is in fact based on the smallest possible quantum system (the two-level system or "quantum-bit") and on exquisite quantum mechanical properties, such as state superposition.
The Introduction to Quantum Computation part of this module aims to provide an introduction to this booming research field.
Module learning outcomes
discuss the fundamentals of quantum computation: concept of quantum bit (qubit); single and two qubit gates; role of superposition principle (quantum parallelism); concept of entanglement; concept of density matrix and its properties; differences between pure and mixed states
understand and been able to use circuit representation of quantum gates
understand and describe some of the quantum algorithms and the basics of quantum-error correction
understand teleportation and describe the simplest teleportation protocol
describe the requirements for physical systems to be used as quantum computers;
understand the main physical limitations to quantum computation (decoherence and scalability); understand how decoherence influences density matrices
describe specific proposals on quantum computers
understand and describe some experimental results related to specific proposals
describe basic ideas behind one-way quantum computing
Module content
- Fundamentals of quantum computation:
- concept of quantum bit (qubit);
- concept of basis set
- examples of physical systems used as qubits;
- Bloch sphere and single qubit representation
- single qubit gates
- Pauli matrices
- circuit representation of single qubit gates
- two qubit states: Dirac and vectorial representation
- two qubit gates and their matrix representation
- tensor product between qubit gates and between qubit states
- circuit representation of two qubit gates
- role of superposition principle (quantum parallelism);
- concept of entanglement; differentiating between entangled and non-entangled states
- Bell states; EPR paradox and Bell inequality; significance of Bell inequality for Quantum Mechanics
- Concept of teleportation; teleportation protocol for one qubit
- quantum circuits
- improvements of quantum over standard 'classical' computation and problem complexity
- concept of density matrix and its properties; concept and differences between pure and mixed states; density matrix and decoherence
- Quantum algorithms
- Concept of quantum error correction; three-qubit code error correction
- Requirements for physical systems to be used as quantum computers: Di Vincenzo check list
- physical systems proposed as quantum computers: ion trap quantum computer, quantum- dot-based quantum computer, silicon-based NMR quantum processor, liquid state NMR quantum processor
- For each proposal: how two qubit gates translate into physical interactions; main physical limitations to quantum computation (decoherence and scalability)
- Experiments related to specific proposals based on semiconductor structures.
- Generalities on one-way quantum computation
Assessment
| Task | Length | % of module mark |
|---|---|---|
| Essay/coursework Physics Practice Questions |
N/A | 14 |
| University - closed examination Introduction to Quantum Computing |
1.5 hours | 86 |
Special assessment rules
None
Reassessment
| Task | Length | % of module mark |
|---|---|---|
| University - closed examination Introduction to Quantum Computing |
1.5 hours | 86 |
Module feedback
Physics Practice Questions (PPQs) - You will receive the marked scripts via your pigeon holes. Feedback
solutions will be provided on the VLE or by other equivalent means from your lecturer. As feedback
solutions are provided, normally detailed comments will not be written on your returned work, although
markers will indicate where you have lost marks or made mistakes. You should use your returned scripts
in conjunction with the feedback solutions.
Exams - You will receive the marks for the individual exams from eVision. Detailed model answers will be
provided on the intranet. You should discuss your performance with your supervisor.
Advice on academic progress - Individual meetings with supervisor will take place where you can discuss
your academic progress in detail.
Indicative reading
Articles from literature:
M.A. Nielsen and I. L. Chuang: Quantum Computation and Quantum Information (Cambridge University Press)
N. D. Mermin: Quantum Computer Science (Cambridge University Press)
