## Lecture Notes for 8.370/18.435 Quantum Computation from Fall 2022

## Peter Shor

#### Lecture Notes

Here are the 2022 Lecture notes. I never got around to writing the notes for
Lecture 26 --- I may or may not do that at some point in the future.

Lecture 1
--- Introduction and History

Lecture 2
--- The Superposition Principle

Lecture 3
--- Unitary Evolution and the Bloch Sphere

Lecture 4
--- Quantum Measurements

Lecture 5
--- Joint Quantum Systems and Tensor Products

Lecture 6
--- More Tensor Products (Measurements of Joint Systems)

Lecture 7
--- Classical Boolean circuits

Lecture 8
--- Reversible Boolean circuits

Lecture 9
--- Quantum gates I

Lecture 10
--- Quantum gates II

Lecture 11
--- Quantum Teleportation

Lecture 12
--- Density Matrices I

Lecture 13
--- Density Matrices II

Lecture 14
--- The GHZ Experiment (theory)

Lecture 15
--- Quantum Optics and the GHZ Experiment

Lecture 16
--- The Deutsch-Jozsa Algorithm

Lecture 17
--- Classical computational complexity theory

Lecture 18
--- Simon's algorithm

Lecture 19
--- The quantum Fourier transform

Lecture 20
--- Phase Estimation

Lecture 21
--- Quantum factoring algorithm

Lecture 22
--- The Number Theory Needed for the Factoring Algorithm

Lecture 23
--- The Discrete Log Algorithm

Lecture 24
--- Grover's search algorithm

Lecture 25
--- Proof that Grover Search is Optimal

Lecture 26
--- Lecture on Hamiltonian Simulation; Notes Unwritten

Lecture 27
--- Introduction to Quantum error correcting codes --- the 9-qubit code

Lecture 28
--- More on the 9-qubit code

Lecture 29
--- The 7-qubit Quantum Hamming Code

Lecture 30
--- Quantum CSS Codes

Lecture 31
--- The BB84 Quantum Key Distribution Protocol and the Proof of Its Security