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Quantum Computing
This course will try to answer three questions:
- What is a quantum computer? (A computer where ordinary bits are replaced by qubits, the key feature of which is that they can be in a quantum superposition of 0 and 1.)
- Can you do anything interesting with one? (In principle---the famous examples are Shor's quantum Fourier transform which relates to code-breaking, and Grover's quantum phone book.)
- Can you do in practice what you can do in principle? (Maybe---the prospects lie in quantum error correction.)
The main prerequisite is a sound understanding of linear algebra and finite-dimensional vector spaces. No prior knowledge of quantum mechanics or informatics is required; we will cover what we need along the way.
Our text will be the lecture notes by the inimitable David Mermin.
- Mermin's chapter 1 is an introduction to essential concepts from quantum mechanics. This is a small subset of the whole subject of quantum mechanics, but within its limited scope quite thorough.
- Chapter 2 introduces some toy problems and basics of quantum computing algorithms.
- Chapter 4 (which we cover before 3) covers the quantum phone book, a search algorithm.
- Chapter 3 covers quantum Fourier transforms, and the implications for code-breaking.
- Chapter 5 cover quantum error-correction.
- Chapter 6 covers some miscellaneous topics, such as quantum encryption.
Summary of lectures.
Text by David Mermin
Notes by U. Vazirani
Some TeX macros for drawing quantum circuits.