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Contents

1 Linear Algebra (short review)
2 Postulates of Quantum Mechanics
2.1 Postulate 1: A quantum bit . . . . .
2.2 Postulate 2: Evolution of quantum systems . . .
2.3 Postulate 3: Measurement . . .
2.4 Postulate 4: Multi-qubit systems . . .
3 Entanglement
4 Teleportation
5 Super-dense Coding
6 Deutsch’s Algorithm
6.1 Deutsch-Jozsa Algorithm . .
7 Bloch Sphere
7.1 Phase traveling backwards through control operations . . .
7.2 Phaseflips versus bitflips . . .
8 Universal Quantum Gates
8.1 More than two qubit controlled operations . .
8.2 Other interesting gates . . .
8.3 Swap . . . .
9 Shor’s Algorithm
9.1 Factoring and order-finding . . .
9.2 Quantum Fourier Transform (QFT) . . .
9.3 Shor’s Algorithm – the easy way . . .
9.4 Phase estimation . . . .
9.5 Shor’s Algorithm – Phase estimation method . . .
9.6 Continuous fraction expansion . . .
9.7 Modular Exponentiation . . . .
10 Grover’s Algorithm
11 Error Correction
11.1 Shor’s 3 qubit bit-flip code . .
11.2 Protecting phase . . . .
11.3 7 Qubit Steane code . . . .
11.4 Recursive error correction and the threshold theorem . . .

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