Quantum Robot for Teenagers Arushi Raghuvanshi Yale Fan

Quantum Robot for Teenagers Arushi Raghuvanshi Yale Fan Michal Woyke Marek Perkowski Presentation at ISMVL 2007 May 14 -16

Outline 1. 2. 3. 4. Introduction to Braitenberg Vehicles Programmable Braitenberg Vehicles Combinational and Quantum Circuits Deterministic, Probabilistic, and Entangled Behaviors 6. Examples or our Robots 7. Next steps

Classic Braitenberg Fear Aggression

Programmable Braitenberg A B H P A = Left Light Sensor Ultrasonic Sensor B = Right Light Sensor Circuit Implemented by Program Q P = Motor for Left Wheel Sound/Touch Sensor Q = Motor for Right Wheel

Representing Gates via Matrices A B P Q Behavior 0 0 Robot stays stationary. 0 1 Robot moves left. 1 0 1 1 Robot moves forward. 1 1 1 0 Robot moves right. Input Output

Using Binary Gates Feynman Gate And-OR Gates A P B Q 00 01 10 11 1 0 0 0 0 0 1 1 0 00 01 10 11 0 0 0 1 0 00 01 10 11 A B P Q Behavior 0 0 0 0 Robot stays stationary. 0 1 0 1 Robot moves left. 1 0 1 1 Robot moves forward. 1 1 1 0 Robot moves right. This behavior is deterministic because it can be determined how the robot will react to a given input.

Using Quantum Gates Hadamard A H P Input A=0 X Output = Which in Dirac Notation is, A P Behavior 0 ½ 1 Motor stops or moves. 1 ½ 0 ½ 1 Motor stops or moves. Which after Measurement means, ½ probability of ‘ 0’ & ½ probability of ‘ 1’

Entanglement Example A B H P Q

Entanglement Example – Step 1 Hadamard A Hadamard in parallel with wire A P H Q B 00 01 10 11 A P Behavior 0 ½ 1 Motor stops or moves. 1 ½ 0 ½ 1 Motor stops or moves. Wire A P Behavior 0 0 Stopped 1 1 Moving = 1 √ 2 1 0 0 1 -1 0 0 -1 00 01 10 11 A B P Q Behavior 0 0 0 1 0 0 Robot stays stationary. Or, moves tight 0 1 1 1 Robot moves left. Or, moves forward 1 0 0 Robot stays stationary. Or, moves tight 1 1 0 1 1 1 Robot moves left. Or, moves forward

Entanglement Example – Step 2 Einstein-Podolsky-Rosen Feynman Gate A A P B Q 00 01 10 11 1 0 0 0 0 0 1 0 00 01 10 P H Q B 00 01 10 11 1 0 0 11 A B P Q Behavior 0 0 Robot stays stationary. 0 1 Robot moves left. 1 0 1 1 Robot moves forward. 1 1 1 0 Robot moves right. 0 0 0 1 0 00 01 10 X 11 1 √ 2 1 0 0 1 -1 0 0 -1 00 01 10 11 00 01 10 = 1 √ 2 11 1 0 0 1 0 -1 -1 0 A B P Q Behavior 0 0 ½ 1 ½ 0 ½ 1 Stationary or moves forward. 0 1 ½ 0 ½ 1 ½ 0 Turns left or turns right. 1 0 ½ 1 ½ 0 ½ 1 Stationary or moves forward. 1 1 ½ 0 ½ 1 ½ 0 Turns left or turns right. 00 01 10 11

Putting it together A B Vector ‘I’ A B False True 00 01 10 11 0 0 Selected Combination 00 01 10 11 H Matrix ‘M’ 1 P √ 2 Q Either the robot will turn left or turn right with equal probability. Measurement P Q False True 1 True False √ 2 True 0 1 1 0 1 0 -1 -1 0 00 01 10 11 Vector ‘O’ O=M*I

Robot. C Program Walkthrough

Light sensors Braitenberg Demo Avoids Light Ultrasonic Sensor Feynman Gate P But. . destroys objects that emit light Avoids Objects Q

Braitenberg Demo Light sensors Ultrasonic Sensor Goes towards light but turns away before hitting P Q

Braitenberg Demo Sound sensor Ultrasonic Sensor Avoids Obstacles P Dances with Music But. . Hits obstacles when Music is playing Q

Quantum Potato Head Happy Face S 1 L 1 S 2 M 6 M 5 M 3 L 2 M 4 M 2 Sad Face M 1 Confused Face

Quantum Potato Head Behavior using Einstein-Podolsky-Rosen Circuit Response to Touch Response to both Light and Touch Response to Light

Old Duck Biped

Next: Quantum Automaton Robot

Key Learnings We learned l About Braitenberg Vehicles l How to program robots to demonstrate probabilistic, deterministic, and entangled behavior l About quantum theory and quantum computing l How to represent circuits with matrices l Programming Robots in C language l Trigonometry, complex numbers, matrix and vector multiplication, and digital circuits.

Backup

Video l Link to video (5 -8 minutes) l Video of Quantum Potato head (show Feynman, EPR) l Video of Braitenberg Vehicle (show Feynman, EPR)

Selected Circuits Direct Connection Feynman Gate Swap Gate A P A P B Q B Q 00 01 10 11 Identity Matrix 1 0 0 0 0 1 00 1 0 01 10 11 Feynman+Swap 0 0 1 00 01 10 11 00 1 0 01 10 11 A P Einstein-Podolsky-Rosen A H P B Q 00 01 10 11 1 0 0 0 1 0 0 00 01 10 11 1 √ 2 1 0 0 1 0 -1 -1 0 0 0 0 0 1 0 00 01 10 11 And-OR Gates A P B Q 00 01 10 11 1 0 0 0 0 1 00 01 10 11

Robot Configuration – Additional Sensors Sound Sensor Left Light Sensor Right Light Sensor Ultrasonic Sensor Touch Sensor

Selected Configurations l Configuration 1 (classic) ¡ ¡ l Configuration 2 (light + distance) ¡ ¡ l A = Left Light Sensor B = Right Light Sensor A = True, if the sum of both light sensor values > 75; Otherwise False B = True, if close to an obstacle (<50 cms), Otherwise False Configuration 3 (sound + distance) ¡ ¡ A = True, if noisy (value > 50), Otherwise False B = True, if close to an obstacle (<50 cms), Otherwise False