Topic  Readings  
Lecture #1 (08/24)  Turing Machine Strong ChurchTuring Thesis Circuit Model 
Section 3.1.2 Circuits 
Lecture #2 (08/26)  Circuit Complexity of Boolean Functions Uniform Families of Circuits 

Lecture #3 (08/31)  Fredkin Gate Computing Functions Reversibly 
Section 3.2.5

Lecture #4 (09/02)  Euler Formula Dirac Notation Quantum Bits Blochsphere 
Section 1.2

Monday (09/07)  No Class (Labor Day Holiday) 

Lecture #5 (09/09)  Euler Formula Applications Multiple Qubits Single Qubit Gates Multiple Qubits Gates 
Section 1.2.11.3.2

Lecture #6 (09/14)  Change of Basis NoCloning Theorem 
Section 1.3.31.3.5

Lecture #7 (09/16)  Bell States Teleportation Quantum Parallelism Deutsch Algorithm 
Section 1.3.61.4.3

Lecture #8 (09/21)  Deutsch Algorithm 
Section 1.4.3

Lecture #9 (09/23)  DeutschJozsa Algorithm 
Section 1.4.4

Lecture #10 (09/28)  BernsteinVazirani Algorithm 

Lecture #11 (09/30)  Measurement (Probabilities, Postmeasurement States) 

Lecture #12 (10/05)  Vector Spaces over Finite Fields Linear Error Correcting Codes Simon's Algorithm 

Lecture #13 (10/07) 


Lecture #14 (10/12)  

Lecture #15 (10/14)  Examples of Reduction of Factoring to Order Finding 

Lecture #16 (10/19)  Chinese Remainder Theorem Group of Units, Modular Inverses Euclid's Algorithm Proof of Reduction of Factoring to Order Finding 

Lecture #17 (10/21)  Proof of Reduction of Factoring to Order Finding 

Lecture #18 (10/26)  Shor's Algorithm for Period Finding Definition of Fourier Transform 

Lecture #19 (10/28)  Properties of Fourier Transform (Unitarity, Shift Invariance) Fourier Transform of Comb Functions Visualization of Disturbances Due to Nonperiodic Cutoff 
DFT Simulation Code (Matlab) 
Lecture #20 (11/02)  Quantum Fourier Transform 
Section 5.1 
Lecture #21 (11/04)  Grover's Algorithm 
Section 6.1.1 
Lecture #22 (11/09)  Grover's Algorithm  Known Number of Solutions 
Section 6.1.2 
Wednesday (11/11)  No Class (Veterans Day) 

Lecture #23 (11/16)  Discussion of Topics for Class Presentations 

Lecture #24 (11/18)  Grover's algorithm  Known Number of Solutions 
Section 6.1.2 
Lecture #25 (11/23)  Grover's algorithm  Unknown Number of Solutions 
Section 6.1.3 
Lecture #26 (11/25)  Quantum Amplitude Amplification 
Section 6.1.4 
Lecture #27 (11/30)  Quantum Phase Estimation 
Section 5.2 
Topic  Material 
1. Simulation of Quantum Circuits  
2. Shor's Approach to Period Finding  KLM book, pages 139  142 
3. Quantum Circuits for Implementing Fourier Transforms of Arbitrary Length  The article 
4. Quantum Algorithm for Solving the Discrete Logarithm Problem (Visualization of 2D Fourier Transform)  
5. Quantum Algorithms for Solving Abelian Hidden Subgroup Problems & Determining the Structure of Abelian BlackBox Groups  KLM book, pages 146  151; The article 
6. Eigenvalue Estimation Approach to Order Finding  KLM book, pages 134  139 
7. Quantum Counting  KLM book, pages 170  175 