Course Outline for Physics 229
Quantum Information and Computation

John Preskill, Caltech
Fall, 1997


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Contents

Foundations of Quantum Theory
Quantum Entanglement
Classical Information Theory
Quantifying Entanglement
Quantum Information Theory
Quantum Computers
Quantum Algorithms
Quantum Error Correction
Some Novel Aspects of Measurement
Physical Implementations of Quantum Computation


Foundations of Quantum Theory

Axioms of quantum theory:

Simple quantum systems:

Open systems:

Master equation and decoherence:

Quantum measurement:



Quantum Entanglement

Nonseparability of EPR pairs:

Three particle entanglement:

Entanglement as a resource:



Classical  Information Theory

Data compression and Shannon entropy

The noisy channel and the channel capacity



Quantifying Entanglement

Number of Bell pairs as a measure of entanglement:

Mixed state entanglement:



Quantum Information Theory

Quantum data compression theorem:

Sending classical information over a quantum channel:

Holevo's theorem:

The quantum channel capacity:

Parameter estimation



Quantum Computers

Turing machines:

Universal gates:



Quantum Algorithms

Classical complexity theory

Deutsch-Jozsa algorithm:

Quantum simulation:

Database search:

Simon Algorithm

Quantum Fourier transform:

Factoring:

Quantum communication complexity



Quantum Error Correction

The need for quantum error correction:

Classical error-correcting codes:

Quantum error-correcting codes:

Stabilizer codes:

Fault-tolerant quantum computation:

Topological quantum computation:



Some Novel Aspects of Measurement

Homodyne detection

Quantum Zeno effect

Quantum nondemolition

Protective measurement

Quantum eraser and delayed choice

Interaction-free measurement

Coincidence and interferometry


Physical Implementations of Quantum  Computation

Quantum optics:

Ion Trap:

Cavity QED:

NMR:


I would welcome comments and suggestions concerning the content of the course (which is still evolving).

preskill@theory.caltech.edu

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