1. Homework 2
This homework is the first use of quantum gates. In lectures we learned about the following gates: inverter, Feynman (controlled NOT), Toffoli (Controlled-Controlled NOT), Hadamard, Fredkin (Controlled Swap), Swap, Controlled Hadamard. You should know the behavior of each of these gates and a unitary matrix of each of them. Moreover, you should understand the matrix and the Kronecker multiplication. The homework has several points. First read slides about classical Braitenberg Vehicles.
1. Given is the circuits below. S1 and S2 are sensors. M1 and M2 are motors. We are designing a controller for a Quantum Braitenberg Vehicle. Write the matrix of the entire circuit. Analyze formally (calculate output vector) for every pure input vector. Describe in your own words the behavior of the vehicle with this control. Simulate (by hand or software) the behavior of the robot for the following inputs sequence: (S1,S2) = 00, 00, 10, 10, 10, 11, 11, 01, 00, 01. Use random number generator. H S1 M1 S2 M2

2. H C1 Garbage 1 C2 Garbage 2 S1 M1 S2 M2
2. Given is the circuits below. S1 and S2 are sensors. M1 and M2 are motors. C1 and C2 are controls from switches. The user selects one of four possible behaviors of the robot by assigning values 0 and 1 to C1 and C2.
(C1,C2) = 00, 01, 10, 11.
We are designing a controller for a controlled Quantum Braitenberg Vehicle. Write the matrix of the entire circuit. Analyze formally (calculate output vector) for every pure input vector. Describe in your own words the behavior of the vehicle with this control. Simulate (by hand or software) the behavior of the robot for the following inputs sequence: (S1,S2) = 00, 00, 10, 10, 10, 11, 11, 01, 00, 01. Use random number generator for every control C1 C2. C1
Garbage 1 C2
Garbage 2 H S1 M1 S2 M2

3. PSU Braitenberg Vehicle
3. Given are all gates from first slide. You can add your own quantum gates. Build arbitrary quantum circuit that will create interesting behaviors of QBV or Quantum Portland Faces. S1 and S2 are sensors. You can add more sensors. M1 and M2 are motors. You can add more motors. C1 and C2 are controls from switches. You can add more controls.
Write the matrix of the entire circuit. Analyze formally (calculate output vector) for every pure input vector. Describe in your own words the behavior of the vehicle with this control. Simulate (by hand or software) the behavior of the robot for some interesting (your choice) inputs sequences.
Toffoli
Fredkin
PSU Braitenberg Vehicle

4. Portland Quantum Faces
Toffoli
Fredkin
In these faces you will have from 4 to 12 motors. They have any numbers of sensors. You decide where to put sensors and motors.