Quantum Information Science II, Part 3 - Advanced quantum algorithms and information theory

Proof of the noiseless coding theorem – size of the typical set

The non-Abelian hidden subgroup problem – statement

Shannon's noisy coding theorem – setup and noisy channel examples

HSP and polytime quantum algorithms – lecture overview

Shannon's noisy coding theorem – statement

The non-Abelian hidden subgroup problem – the gentle measurement lemma

Proof of the noiseless coding theorem – the idea of typical sequences

Hypothesis testing – briefly

Pros and cons of different models of quantum algorithms

The non-Abelian hidden subgroup problem – towards the gentle measurement lemma

Shannon's noisy coding theorem – statement

Information theory II – lecture overview

QFT caveat – the requirement for controlled-U to some power

The non-Abelian HSP – fast quantum algorithms for Heisenberg and dihedral groups

Simon's quantum algorithm – briefly

Interpretation of noisy coding theorem

Quantum algorithm for the Abelian hidden subgroup problem I

The nonabelian quantum Fourier transform – application to HSP

The Abelian hidden subgroup problem – proof of algorithm complexity

The nonabelian quantum Fourier transform – definition

Lower bound on the complexity of the hidden subgroup problem

Quantum algorithms – lecture overview

The Abelian hidden subgroup problem – statement and claim

Quantum algorithms for the hidden subgroup problem – lecture overview

The nonabelian quantum Fourier transform – intro