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Lecture 1: Basics. (Qubits, operations on qubits, postulates of quantum mechanics, No-cloning theorem, teleportation, superdense coding, CHSH game.)
- Further reading: Read Chapter 1 of
this book for more background for strong Church-Turing Thesis,
reversible computation, quantum physics, etc.
- Watch
this for fun.
(Theoretical Physicists John Preskill and Spiros Michalakis describe how things are different in the Quantum World and how that can lead to powerful Quantum Computers.)
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Lecture 2: Shor's algorithm. (Quantum Fourier transform on Z_n,
Order finding, phase estimation, Hidden Subgroup Problems for finite Abelian
groups).
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Lecture 3: Hidden Subgroup Problems 1. (Linear representations of finite groups, Fourier transform on non-Abelian groups.)
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Lecture 4: Hidden Subgroup Problems 2. (Mixed states, standard method, weak Fourier sampling, strong Fourier sampling, query-efficient algorithms for HSP)
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Lecture 5: Searching algorithm and quantum adversary method.
(Grover's search, quantum lower bound by quantum adversary method with
negative weight)
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Lecture 6: Quantum query complexity.
(Quantum adversary method continued, matching quantum algorithm)
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Lecture 7: Quantum communication complexity 1.
(Communication complexity, Disjointness, quantum fingerprint)
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Lecture 8: Quantum communication complexity 2.
(Fourier analysis, a recent protocol)
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Lecture 9: Quantum information theory 1.
(Admissible quantum operations, distance measures of quantum states)
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Lecture 10: Quantum information theory 2.
(Classical and quantum entropy, mutual information, basic information theory
concepts)
-
Lecture 11: Quantum information theory 3.
(Classical and quantum source encoding)
-
Lecture
12: Quantum information theory 4. (Classical and quantum noisy
channel encoding)
Note:
- This is a temporary plan. Content may be adjusted.
- Open the lecture note by Microsoft Office 2010 (or any later version).