PHYC 571.001  Quantum Computation  Spring 2013

Syllabus

0. Brief review of quantum information theory   [ Lecture note, Sec.0 ]

0.1 Qubit

0.2 Pauli operators

0.3 Mixed states

0.4 Quantum operations

0.5 Two qubits: tensor product

0.6 Purification and complete positivity

0.7 Choi-Jamiołkowski isomorphism

0.8 Schmidt decomposition of quantum states

0.9 Schmidt decomposition of quantum unitary operations

1. Entanglement theory revisited   [ Lecture note, Sec.1 ]

"What are the features of quantum correlation, stronger and weirder than classical correlation?"

1.1 Definition

1.2 Conversions under LOCC: single copy

1.3 Schmidt rank and a coarse-grained characterization

1.4 Conversions under LOCC: identically many copies

1.5 Entanglement in mixed states

1.6 Key protocols: entanglement concentration, dilution, and distillation

1.7 Entanglement measures

1.8 Multipartite entanglement → to be taught with 2.4, 2.5, 4.1, and 4.2

2. Quantum computational models   [ Lecture note, Sec.2 ]

"What is computation physically admissible by the laws of nature? What are the key resources?"

2.1 Church-Turing thesis

2.2 Quantum circuit model

2.3 Quantum teleportation-based model

2.4 Entanglement-based model

2.5 Graph states and their usage in quantum computation

3. Quantum algorithms, classical simulation, and quantum simulation   [ Lecture note, Sec.3 ]

"When can we find quantum advantage in information processing?"

3.1 Oracle problems: exponential speed-up over classical computer

3.2 Grover's algorithm: amplitude amplification

3.3 Shor's integer factorization algorithm

3.4 Quantum simulation

4. Quantum error correction and fault-tolerance   [ Lecture note, Sec.4 ]

"How can we hope a full-scale quantum computer would be built in practice?"

4.1 Classical repetition code for error correction

4.2 Quantum 3-qubit bit-flip code

4.3 Quantum 9-qubit error correction code

4.4 Stabilizer codes

4.5 Fault-tolerance of quantum computation

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