MIT

Noisy coding theorem – proof of joint typicality

Overview of known quantum algorithms

Efficient algorithm for Fourier transform over any decomposable Abelian group

Quantum entropy inequalities that still hold

Grover search for multiple marked items

Polynomial quantum speedups in the oracle model

Quantum information theory 

Polynomial quantum speedups in the oracle model – AND OR tree

Quantum noisy coding theorem: quantum channel coding scenarios

Hamiltonian simulation – problem statement

Polynomial quantum speedups in the oracle model – collision problem

Hamiltonian simulation – using amplitude amplification

Quantum versions of Shannon's theorems: quantum data compression

The non-Abelian hidden subgroup problem – amplifying correctness probability

Polynomial quantum speedups in the oracle model – element distinctness

Realizing the QFT over Z_N using quantum phase estimation I

Hamiltonian simulation with amplitude amplification – linear combination of unitaries

The non-Abelian hidden subgroup problem – quantum algorithm and query complexity

Polynomial quantum speedups in the oracle model – graphs

Realizing the QFT over Z_N using quantum phase estimation II

Hamiltonian simulation with amplitude amplification – setup

The non-Abelian hidden subgroup problem – quantum algorithm idea

Proof of the converse of Shannon's noisy coding theorem – step 1

Reversible classical computation of x * y / N

Hamiltonian simulation with amplitude amplification – success probability amplification