HOMEWORKS FOR SPRING 2005.

• Week 1. March 28 - April 2.
  Homework 1: Design of simple reversible cascades with garbage and input constants. This homework is in slides of the first lecture. In addition, you have to convert every Toffoli gate to a sequence of CV, CV+ and Feynman gates and try to optimize these gates by shifting and cancelling gates.
  Background material:
  • ESOP. Reed-Muller. Positive Polarity Reed-Muller. Fixed-Polarity Reed Muller. Toffoli gate, Feynman gate. Inverter. Reversibility. Kmaps. The CV and CV+ gates are explained in lecture 7.1.1, slides 67 - 69 and next.
  
  
  
• Week 2. April 4 - April 9.
  Homework 2:
  
  Part 1. Simulate the circuit from Homework 1 using quantum simulator QUIDPRO. Remove one CV gate and compare the results. Try to explain what happened.
  
  Part 2. Design of simple quantum circuits. Use of quantum circuits to control simple robots.
  
  THIS IS OUR HOMEWORK TO DO.
  
  Description of Braitenberg vehicles. This is another homework. Just auxiliary.
  
  Description of Braitenberg vehicles. More auxiliary materials.
  
  Work in progress. Description of Braitenberg vehicles. Again only an auxiliary material.
  Background material:
  • ESOP. Reed-Muller. Positive Polarity Reed-Muller. Fixed-Polarity Reed Muller. Unitary and permutative matrices of gates. Hadamard gate and controlled Hadamard gate. What is a Hermitian. Kronecker and standard multiplication. Complex numbers. Conjugates. Analysis of a quantum circuit.
  
  
  
• Week 3. April 11 - April 17.
  No homework assigned. You work on projects.
  
  
• Week 4. April 18 - April 24. Billiard Ball model.
  
  
  HOMEWORK 3.
  Use Switch and Interaction gates only, and their inverses.
  A. Design the Toffoli gate using Switch gates.
  B. Design the Fredkin gate using Interaction gates. There is a bug in lecture slides. You can fix the bug or design the gate from scratch, using the generation of product functions and next summing the disjoint groups.
  C. Design any of the gates below using Switch and Interaction gates: Miller, Kerntopf, Margolus, Miller, Peres, any other non-linear gate.
  
  
  
  
• Week 5. April 25 - May 1. Decision Diagrams.
  
  HOMEWORK 4.
  Use of decision diagrams to synthesize reversible circuits. EXTENDED.
  Use of cascade methods to synthesize reversible circuits.
  
  
  
  
• Week 6. May 2 - May 8.
  No homework assigned. Work on the midterm exam that was assigned.
  
  
• Week 7. May 9 - May 15.
  1. HOMEWORK 5. Optimization. NO homework on optimization this year.
     Optimization methods. Search. Exhaustive search. Informed versus non-informed search. Evolutionary methods. Simulated annealing.
  
  
  
• Week 8. May 16 - May 22.
  1. HOMEWORK 6. Quantum Dot Cellular Automata. Homework to be returned in the week of finals. This is the last homework this year. Please concentrate on projects.
  
  
  
• Week 9. May 24 - May 29.
  1. HOMEWORK 7. Quantum Algorithms. No homework this year.
• Week 10. May 30 - June 5.
  1. Preparation to final exam. No homework.
• Week 11. June 6 - June 12. WEEK OF FINALS!
  1. Final exam. No homework.