1. Outline Quantum Braitenberg Vehicles Quantum Search
Programmable Braitenberg Vehicles
Combinational and Quantum Circuits
Deterministic, Probabilistic, and Entangled Behaviors
Examples or our Robots
Quantum Search
Quantum Emotional Robots
Curriculum
Research

2. Part 2:
Quantum
Search

3. Grover Algorithm Reminder in new light

4. The Graph Coloring Problem
Building oracle for graph coloring is a better explanation of Grover than database search.
This is not an optimal way to do graph coloring but explains well the principle of building oracles.
The Graph Coloring Problem 1
Color every node with a color. Every two nodes that share an edge should have different colors. Number of colors should be minimum 1 3 2 3 2 5 4 5 4 6 7 6 7
This graph is 3-colorable

5. Simpler Graph Coloring Problem1 3 2
We need to give all possible colors here 4
Two wires for color of node 1
Two wires for color of node 2
Two wires for color of node 3
Two wires for color of node 4     
Gives “1” when nodes 1 and 2 have different colors
13
23
24
34
12
F(x)
Value 1 for good coloring

6. Simpler Graph Coloring Problem
We need to give all possible colors here
Give Hadamard for each wire to get superposition of all state, which means the set of all colorings H
|0>
|0> H
|0> H H H     
13
23
24
34
12
Discuss naïve non-quantum circuit with a full counter of minterms
f(x)
Value 1 for good coloring
Now we will generate whole Kmap at once using quantum properties - Hadamard

7. “Classical” Quantum Computer Circuit Model for Graph Coloring
Simplified schematic of our Graph Coloring Oracle.
We designed 35 oracles

8. Hadamard Transform H H H = = 1 -1 Single qubit  1/2
Parallel connection of two Hadamard gates is calculated by Kronecker Product (tensor product)
Here I calculated Kronecker product of two Hadamards

9. Motivating calculations for 3 variables
As we remember, these are transformations of Hadamard gate:
|0> H
|0> + |1>
|1> H
|0> - |1>
In general:
|x> H
|0> + (-1) x |1>
For 3 bits, vector of 3 Hadamards works as follows:
From multiplication
|abc> 
(|0>+(-1)a|1>)
(|0>+(-1)b|1>)
(|0>+(-1)c|1>) =
|000> +(-1)c |001> +(-1)b |001>+(-1)b+c |001>000> +(-1)a |001> +
(-1)a+c |001> + (-1)a+b |001> (-1)a+b+c |001>
If a = b = c =0 then all phases positive

10. |0>
oracle
|000> +|001> + |010>+|011> +|100> + |101> +|110> + |111>
This is like a Kmap with every true minterm (1) encoded by -1
And every false minterm (0) encoded by 1
|0>
f(x)
We can say that Hadamard gates before the oracle create the Kmap of the function, setting the function in each of its possible minterms (cells) in parallel

11. What Grover algorithm does?
Grover algorithm looks to a very big Kmap and tells where is the -1 in it.
Here is -1 1 -1

12. Block Diagram for graph coloring and similar problems
All good colorings are encoded by negative phase
Vector Of
Basic
States
|0>
Vector Of
Hadamards
Oracle with Comparators,
Global AND gate
Vector Of
Hadamards
Output of oracle
Think about this as a very big Kmap with -1 for every good coloring
Work bits

13. 1 in 4 search A practical Example
This presentation shows clearly how to perform a so called 1 in 4 search
We start out with the basics
1 in 4 search

14. Pick your needle and I will find you a haystack
The point of this slide is to show examples of 4 different oracles. Grovers search can tell between these oracles in a single iteration, classically we would need 3 iterations.

15. Properties of the oracle
Let f : {0,1}2  {0,1} have the property that there is exactly one x  {0,1}2 for which f (x) = 1
Goal: find x  {0,1}2 for which f (x) = 1
Classically: 3 queries are necessary
Quantumly: ?
Only after 3 tests can we determine with certainty that the oracles is 1 for only a single input value x

16. f f Black box for 1-4 search: x1 x2 y y  f(x1,x2)
A 1-4 search can chose between 4 oracles in one iteration
Black box for 1-4 search: f
x1
x2
y
y  f(x1,x2)
Start by creating phases in superposition of all inputs to f: f H
1
0
Input state to query:
(00 + 01 + 10 + 11)(0 – 1)
((–1) f(00)00 + (–1) f(01)01 + (–1) f(10)10 + (–1) f(11)11)(0 – 1)
Output state:
Here we clearly see the Kmap encoded in phase – the main property of many quantum algorithms

17. f 0 H H X X H M 0 H H X H H X H M 1 H H M 00 01 11 10
This slide illustrates how the state of the system is changed as it propagates through the quantum network implementation of Grovers Search algorithm.
Time
0 H f H X X H M
0 H H X H H X H M
1 H H M
state =
state =
state =
state =
state =        0        0     -0.5      0.5      0.5     -0.5        0        0
state =        0        0     -0.5      0.5        0        0      0.5     -0.5
state =        0        1        0        0        0        0        0        0
ab c 0 1 1
ab c 0 1
ab c 0 1
ab c 0 1
ab c 0 1
ab c 0 1
ab c 0 1
0.3 –0,3
0.3 –0,3
0.3 –0,3 ,3
0.3 –0,3
0.3 –0,3
0.3 –0,3
–0,3 ,5 ,5
0.3 –0,3 ,3 ,3 ,3
0.3 –0,3
0.3 –0,3
0.3 –0,3
– 0,3
– 0,5

18. f 0 H H X X H M 0 H H X H H X H M 1 H H M 00 01 11 10
Time
0 H f H X X H M
0 H H X H H X H M
1 H H M
state =        0        0     -0.5      0.5        0        0      0.5     -0.5
state =
state =
state =        0        0        0        0        0        0        0       -1
state =
state =
state =        0        0     -0.5      0.5      0.5     -0.5        0        0
state =        0        0        0        0        0        0        0       1
Hadamard of affine function
Ibverters flip between 00 and 11
Inverter flips second bit when first is 1
Hadamard addis in 00 and 11
Ibverters flip between 00 and 11
ab c 0 1
ab c 0 1
ab c 0 1
ab c 0 1
ab c 0 1
ab c 0 1
ab c 0 1
0.3 –0,3 ,3
0.3 –0,3
–0,3 ,5 ,5 -1 ,3 ,3
0.3 –0,3
– 0,3
– 0,5

19. Inversion about the mean
Grover Loop
Time
0 H f H X X H M
0 H H X H H X H M
1 H H M
Inversion about the mean
ψ00 = – 00 + 01 + 10 + 11
After Hadamard the solution is “known” in Hilbert space by having value -1. But it is hidden from us
ψ01 = + 00 – 01 + 10 + 11
ψ10 = + 00 + 01 – 10 + 11
ψ11 = + 00 + 01 + 10 – 11
This was a special case where we could transform the state vector without repeating the oracle.
In general we have to repeat the oracle – general Grover Loop
The state corresponding to the input to the oracle that has a output result of 1 is ‘tagged’ with a negative 1.
We need to repeat the Grover Loop N times

20. Future work Grover Search Quantum Braitenberg Vehicle
Loop
Constants
Hadamards
Measurements
Worst case quadratic speedup on every problem that you can build an oracle!
Oracle or
Quantum
Circuit
Quantum Braitenberg Vehicle
Inputs- sensors
Measurements
Outputs - actuators
New Concept of Real-time Quantum Search
Constants
Grover
Loop
Controlled Hadamards
Measurements
Outputs - actuators
Inputs- sensors
LEARNING
Future work
Control

21. Oracle for Quantum Map of Europe Coloring
Yale Fan extended Deutsch-Jozsa, Bernstein-Vazirani and Grover algorithms to multi-valued quantum logic
Germany
France
Switzerland
Spain
Spain
France
Germany
quaternary
Switzerland    
Multiple-Valued Quantum Circuits
Good coloring

22. Oracle for Quantum Map of Europe Coloring
A B
A B 1 2 3 1 2 3
0+1=1
1+1=0
2+1=3
3=1=2
0+0=0
1+0=1
2+0=2
3+0=3
0+3=3
1+3=2
2+3=1
3+3=0
0+2=2
1+2=3
2+2=0
3+2=1 A A +1
1 when A = B 1 2 3 1 2 3 B +1 B +2 +3 +3 +2
Quaternary Feynman
Quaternary input/binary output comparator of equality

23. Oracle for Quantum Map of Europe Coloring
Comparator for each frontier 1 2 3 +1 +3 +2 A B
1  1 -- when control 1
1 -- for controls 0,2 and 3
Binary qudit =1 for frontier AB when countries A and B have different colors 1 2 3 +1 +3 +2 C D
Binary signal 1 when all frontiers well colored
Quaternary controlled binary target gate
Binary Toffoli

24. Constraints Satisfaction Problems
S E N D
+ M O R E
M O N E Y
Cryptographic Problems
Graph coloring

25. Constraint Satisfaction for Robotics
Insufficient speed of robot image processing and pattern recognition.
This can be solved by special processors, DSP processors, FPGA architectures and parallel computing.
Prolog allows to write CSP programs very quickly.
An interesting approach is to formulate many problems using the same general model.
This model may be predicate calculus, Satisfiability, Artificial Neural Nets or Constraints Satisfaction Model.

26. Constraint Satisfaction Image Analysis by Waltz
Huffman and Clowes created an approach to polyhedral scene analysis, scenes with opaque, trihedral solids, next improved significantly by Waltz
Popularized the concept of constraints satisfaction and its use in problem solving, especially image interpretation.
Objects in this approach had always three plane surfaces intersecting in every vertex.
Constraint Satisfaction Image Analysis by Waltz
Thus there are 18 possible trihedral vertices in this problem out of 64 possible.
There are only 3 types of edges between these blocks possible:
(1) obscuring edge is a boundary between objects or objects and background. Boundary lines are found using outlines with no outside vertices,
(2) concave edges are edges between two object’s faces forming an acute angle when seen from outside,
(3) convex edges are those between two faces of an object forming an obtuse angle as seen from outside.

27. Constraint Satisfaction Image Analysis by Waltz
There are only four ways to label a line in this blocks world model.
The line can be convex, concave, a boundary line facing up and a boundary line facing down (left, or right).
The direction of the boundary line depends on the side of the line corresponding to the face of the causing it object.
Waltz created a famous algorithm which for this world model which always finds the unique correct labeling if a figure is correct.
Moreover, the algorithm handled also shadows and cracks in blocks. Mackworth and Sugihara extended this work to arbitrary polyhedra and Malik to smooth curved objects.
This becomes a well-known approach to image recognition based on constraint satisfaction and a prototype of many similar approaches to vision and planning problems in robotics.

28. AC-3: State 2 Queue: (2,3)(3,2)(3,4)(4,3)(4,1)(1,4) (1,3)(3,1)
Removing (2,3).
L3 on 2 inconsistent with 3, so it is removed.
Of arcs (k,2), (1,2) is not on queue, so it is added.

29. Constraint satisfaction model in robotics
Used in main areas of robotics:
vision,
knowledge acquisition,
knowledge usage.
In particular the following:
planning, scheduling, allocation, motion planning, gesture planning, assembly planning, graph problems including graph coloring, graph matching, floor-plan design, temporal reasoning, spatial and temporal planning, assignment and mapping problems, resource allocation in AI, combined planning and scheduling, arc and path consistency, general matching problems, belief maintenance, experiment planning, satisfiability and Boolean/mixed equation solving, machine design and manufacturing, diagnostic reasoning, qualitative and symbolic reasoning, decision support, computational linguistics, hardware design and verification, configuration, real-time systems, and robot planning, implementation of non-conflicting sensor systems, man-robot and robot-robot communication systems and protocols, contingency-tolerant motion control, multi-robot motion planning, multi-robot task planning and scheduling, coordination of a group of robots, and many others

30. Examples of CSP in robotics
Scene recognition
Motion generation in presence of constraints
internal (low power, don’t hit itself)
external (shape of racing track, wolf-man-cabbage-goat)
Gesture under emotions
Communication in a swarm of robots (graph coloring)
Robot guard (set covering)

31. New Approach to Quantum Robotics
Obstacle
Avoidance
Problem
Robot Reasoning
Problem
Robot
Communication
Problem
Robot Vision
Problem
New Approach to Quantum Robotics
Constraint Satisfaction Problem
Adiabatic Quantum Computer
Classical quantum computing

32. Adiabatic Quantum Computing to solve Constraint Satisfaction Problems efficiently

33. Adiabatic Quantum Computing to solve Constraint Satisfaction Problem efficiently.
Will February 13th 2007 be remembered in annals of computing.?
DWAVE company demonstrated their Orion quantum computing system in Computer History Museum in Mountain View, California.
The first time in history a commercial quantum computer was presented.
The Orion system is a hardware accelerator designed to solve in principle a particular NP-complete problem called the two-dimensional Ising model in a magnetic field (for instance quadratic programming).
It is built around a 16-qubit superconducting adiabatic quantum computer (AQC) processor.

34. Orion computer from DWAVE
Conventional front end
The solution of an NP-complete problem:
1. Pattern matching applied to searching databases of molecules.
2. Planning/scheduling application for assigning people to seats subject to constraints.
3. Sudoku 7 3 2 1 8 5 9 4 6

35. Orion Is the Constraint Satisfaction Solver
The company promises to provide free access by Internet to one of their systems to those researchers who want to develop their own applications.
Does it have quadratic speed-up?

36. Orion computer from DWAVE
The plans are that by the end of year 2008 the Orion systems will be scaled to more than 1000 qubits.
Company plans to build in 2009 processors specifically designed for quantum simulation, which represents a big commercial opportunity.
These problems include: protein folding, drug design and many other in chemistry, biology and material science.
Thus the company claims to dominate enormous markets of NP-complete problems and quantum simulation.

37. We plan to concentrate on robotic applications of the Constraint Satisfaction Model.
Adiabatic Quantum Computing was proved equivalent to standard QC circuit model.
Each of the developed by us methods can be transformed to an adiabatic quantum program and run on Orion.
We developed logic minimization methods to reduce the graph that is created in AQC to program problems such as Maximum Clique or SAT.
This programming is like on “assembly level” but with time more efficient methods will be developed in our group.
This is also similar to programming current Field-Programmable Gate Arrays.

38. Future work on Adiabatic Quantum Controller for a robot
In the second research/development direction the interface to Orion system will be learned
How to formulate front-end formulations for various robotic problems as constraint-satisfaction problems for this system?

39. New Research Direction
New approach to quantum robotics based on reduction to Constraint Satisfaction Model
Some ideas of quantum computing can be used to build sophisticated robot controllers.
Intelligent biped robots will be an excellent medium to teach emotional robotics, robot theatre, gait and movement generation, dialog and many other computational intelligence areas that have been not researched yet because of high costs of biped robots.
Well-known problems
New problems

40. Quantum Emotional Robots
Part 3
Quantum Emotional Robots

41. Emotional Robot Helpers
Because humans attribute emotions to other humans and to animals, future emotional robots should perhaps be visually similar to humans or animals,
otherwise their users would be not able to understand robots’ emotions and correctly communicate with them.
Observe that the whole idea of emotional robot helpers is to enable easy communication between humans and robots.

42. Robot emotions
The research on robot emotions and methods to allow humanoid robots to acquire complex motor skills is recently advancing at a very fast pace.
Simple emotions like “fear” or “anger” or behaviors like obstacle-avoidance for wheeled mobile robots.
Subsumption architecture.
Practically insufficient to cover all necessary behaviors of future household “helper robots”.

43. Larger biped robots are very expensive
Emotions can be
best expressed
by a biped robot with
human-like face
Larger biped robots are very expensive
hundreds thousands dollars.
Recent small humanoid robots.
We acquired two KHR-1 robots and integrated them to our robot theatre system with its various capabilities such as:
sensors,
vision,
speech recognition and synthesis
Common Robot Language.

44. Humanoid robots to express emotions:
Walking biped robot can express the fullness of human emotions:
body gestures,
dancing,
jumping,
gesticulating with hands.
Emotions can be:
Emergent - Arushi
Programmed – Martin Lukac ISMVL
Mimicked – ULSI
Learned – Martin Lukac Reed-Muller
Humanoid robots to express emotions:
M. Lukac uses human-like faces and head/neck body combinations.
KAIST theatre used whole-body stationary robots with hands.

45. Synthesis of quantum circuits and state machines from examples
Quantum mappings – Quantum Braitenberg Vehicles – Arushi ISMVL 2007
Quantum Oracles such as Grover – Yale ISMVL 2007
Emotional State Machines – Lukac ISMVL 2007
Quantum Automata and Cellular Quantum Automata – Lukac ULSI 2007
Motion – Quay and Scott

46. Quantum Emotional Facial Gestures

47. First View: Emotion as synthesized behavior
Serchuk et al (2006) discuss emotion as mapping from internal state to observable output behavior.
We want to design these mappings well, so that they wil be similar to humans
Physical variables = positions,
speeds, accelerations, words,
Emotional state =
state of all emotion variables

48. Wheel of emotions Active - Passive Positive - Negative
Internal representation of emotions by vectors in multi-dimensional space
Mapping from internal to external representation of emotions

49. Second View: Emotion as emergent, evolvable behavior
Here emotion is an emergent behavior that arises from sensors, drives, effectors and logic.
This may look like human, animal behavior but also as an entirely new “other world” behavior, behavior as it may be.
Degrees of freedom
Sensors, vision and fusion =
features and patterns
Evolved “emotional”
behavior of robot
Drives and effectors
Main input-output mapping
(perception, internal state, behavior)
Precise motion generation (behavior)

50. Human Emotions Perceived by Robot
Robot perceives emotions of a human
Emotional aspect of speech
Text from speech recognition
(I hate you example)
Facial gestures
Body language and hand upper body gestures.
Camera with software
Microphones with speech recognition/speech analysis system
You do not need robot, this may be done by laptop with microphone and camera.

51. happiness (H) - surprise (U)
Robot perceives human mood
From top to bottom, the continua shown in each row are…
happiness (H) - surprise (U)
surprise (U) - fear (F)
fear (F) - sadness (S)
sadness (S) - disgust (D)
disgust (D) - anger (A)
and anger (A) - happiness (H)

52. Why we need Robot-Generated Emotions?
Robot presents its emotions to a human
Why we need it?
Robot who helps elderly
Assistive robot for disabled
Robot that works with mentally challenged children (autism, Asperger Syndrome, ADD),
Robot receptionist
Robot barman
Robot astronaut helper
Robot museum guide
Robot theatre (mostly in interactive theatres)
Imitation of human emotions
Interaction with human based on emotion
Improvisation of theatrical plays, texts, stories
Interpretation of human behavior in psychological terms, negotiation and cheating

53. Emotions in Humanoid Robots
Humanoid Robotics focuses on communication with humans that includes:
Behavioral changes and emotional expressions,
Emotional alterations of text-to-speech,
Facial mimics and gestures,
Overall body language (posture) and hand upper body gestures (hands, neck).
Member postures and movements

54. Symmetry of emotion transmission
Robot reconstructs Human emotion
Human emotion
Robot perceives Human behavior
Human behavior
Robot creates its emotion
Human perceives robot behavior and emotion
Start with arrow - Human emotion affects human behavior
Robot expresses its behavior
Emotions as emergent behaviors
Emotions as learned behaviors
Two aspects – two approaches

55. Traditional and modern theories of emotion
Observable (traditional) emotions: emotional behaviors, moods, content changes (speech variations, etc)
Modern Hypothesis: emotions and feelings are influencing decision making, problem solving, memory efficiency and so on.

56. Two level representation of the Cognitive-Emotional robot Structure
Flow of emotions
Flow of actions

57. Quantum Mechanics to model emotions

58. Quantum Mechanics to Model Emotions
The problem being considered here is the synthesis of logic controller allowing the robot to modify its actions and express unique emotional states
The emotional expression is desired to be compelling the human user to communicate with the robot,
the behaviors should be original and non-repeating
Standard classical approaches can be compared to an FSM approach;
the robot action space (behavioral space) is a finite set of states that the robot learns or just uses in a input driven mapping

59. Concept: Emotional Quantum State Machine
Design a machine that will simulate the articulation of human social behavior:
Subjective
Non repetitive
Innovative
But still:
Socially acceptable or not
Behaviorally understandable
Safe (the framework of this behavior is purely virtual – no contact)

60. Quantum Hierarchical Model of Emotions
Because the concept of emotional expression can be extended to a functional model; emotional expression affects the robot functioning.
Here the concept of QFSM is extended to a Quantum Cellular Automata based on the quantum emotional state machine
The quantum string rewriting is extended to a complete robot hierarchy rewriting schema

61. One Machine Model in Our Approach

62. Definition of Emotion
Emotion is the result of measurements of a hybrid classical/quantum system
In terms of quantum mechanics, emotions are represented by quantum states that we (observe) know only after measurement,
but we can operate on them deterministically in the Hilbert space.
Emotional evolution is represented by quantum operator (unitary and non-unitary, including the measurement)

63. Simulating emotions for practical applications
Simulating emotions as only observable behaviors is not sufficient to make emotional robots
Definition: Emotional State Machine is a model of FSM that can modify its state and output independently of the content of the input, but based solely on its current state.
Definition: Robotic Emotions are simulated emotional states allowing the robot to perform a given action in a way that satisfies its current emotional state.
We propose a emotional model as computational process distributed across the robot software controller allowing to use emotions to modify all robot actions

64. Emotional Quantum Automata
A network of Emotional State Machines is called an Emotional Quantum Automata (plural - per similarity to Cellular Automata)
This network can be regular or not.
If regular, it can be:
One-dimensional and one-directional (pipelined)
One-dimensional (like one-dimensional cellular automata)
Two-dimensional (like Game of Life and Two-Dimensional cellular Automata of Wolfram)
more dimensional.
Emotional Quantum Automaton is therefore a generalization of Cellular Automata, Random Boolean Networks and Quantum Cellular Automata
Example of one- dimensional and one-directional Cellular Quantum Automata

65. Complex space vs. Real States
Neighbors
Emotional states travels across the robot body
Time
Simulation of a quantum emotional automata. The dots represents real states (observables) and the surrounding represents complex components.
Of interest is the fact that even in a variants that the automata communicate exclusively via classical data channels, the complex part can travel through space.
Thus, emotions encoded by such a complex state can be moving across robot controller and create unexpected local effects

66. Emotional Parameters for control in Cynthea Robot
Device Parameters Other
This slide shows which parameters are affected by which input and output devices

67. Emotional Model
Emotional
Robot controller
Robot actuators
Robot sensors
Robot controller
Robot sensors
Robot actuators
Formal Language
Each element in the robot is represented as Quantum Emotional State Machine (EQSM), such that on each level of robot control hierarchy the emotions can influence both the visible (perceptible) and the non-visible robot processes

68. Emotional Model
Energy – simulated energy representing the emotional state of the robot
Emotional State
Energy
Strategy – the translation function mapping the emotional state to a state parameters, (function dependent)
Emotional State
State Parameters
The input command - represents the robot command such as one obtained from a sensor (user input, other robot), specified in the CRL language
The emotional parameters translated to particular variables, are used to modify the global state of the robot and also the local function (Command rewriting)
Emotional Parameters
State of the robot

69. Project Overview KHR-1 Biped robot 17 servos
2 RCB-1 servo controllers (each 12 servos)
Serial port connectivity

70. Common Robot Language.
We developed symbolic approach to robot specification based on a Common Robot Language.
While the syntax of this language specifies rules for generating sentences, the semantic aspects describe structures for interpretation.
Every movement is described on many levels, for instance every joint angle or face muscle are at low level and complete movements such as pushups or joyful hand waving are at a high level.

71. Common Robot Language.
These aspects serve to describe interaction with environment at various levels of description.
It uses also the constraint satisfaction problem creating movements that specify constraints of time, space, motion style and emotional expression.

72. Describing movements, behaviors and emotions
The goal of our Common Robot Language is to describe human-oriented movements
But it exceeds these behaviors to those like anthropomorphic animals and fairy tale characters.
We created new GUI interface and robot controlling language specific to KHR-1.
Editing functions.
Testing functions.
The ability to read information back from the robot by serial communication was added.
There are two main functions that we achieved:
mimicking,
behavior state machine.

73. Using HBP robot vision software for human mimicking.
Control behaviors mimicked from a human standing in front of the camera.
(with state machine or not)
We wanted the KHR-1 to mimic human motion that was being shown on the screen by the HBP software.
The HPB works by taking an image of a person’s upper body. It then will try and identify the face.
Once it can recognize a face it will then look at the body.
The image that it acquires is converted to a set of feature (parameters) values assigned to several groups of variables.

74. What is wrong with our vision software?
HBP is slow
OPENCV is slow
Robot responds with delay
HBP is not accurate
That one great thing about HPB, is that you have the option of modifying the original code to some extent and make your own features.
To speed up the image recognition we will use the Orion quantum computer in the next project

75. Inductive Quantum Learning

76. Quantum computing basics
Units are qubits, quantum bits, represented by wave function, on real (observable bases) in the complex Vector Space H.
Unitary transformations on single and two qubits (rotations in the Complex Hilbert Space), example rotation around X axis :
Because quantum states are complex, they are measured (or observed) before they can be recorded in the real world. The measurement operation describe this fact:
Difference of complete measurement and expected measurement in a robot.

77. Quantum computing basics
Because the coefficients of the states are complex positive and negative), interference occurs allowing to sum or subtract probabilities of observation of each state. Gates such as CV can be used to synthesize permutative functions with real state transition coefficients (boolean reversible functions)
On of the particular properties of Quantum Computation is the superposition of states: allowing to synthesise quantum probabilistic logic functions
and entanglement (initially known as EPR)
Meaning of entanglement in terms of gestures

78. Three Types of Quantum Inductive Learningab c 1 00 01 11 10 -
Classical Deterministic Learning
Probabilistic and Quantum Probabilistic Learning ab c 1 00 01 11 10 ab c 1 00 01 11 10 ab c 1 00 01 11 10
Quantum Probabilistic and Measurement Dependent Learning

79. Controlled [V/V*] gates
V, V*, C-V, C-V*, are well know elements of quantum logic synthesis for pseudo-boolean (permutative) functions. V* V V* V* X * V* V I V* V V X
CNOT

80. Various types of measurement
V, V*, C-V, C-V*, are well know elements of quantum logic synthesis for pseudo-boolean (permutative) functions. V0
Non-deterministic measurement 1
0 or 1 V* V M

81. Various types of measurement
Measurement here is deterministic
1 for V0 M V V V*
V0 or V1
Operator built-in the measurement
Measurement here would be non-deterministic

82. Inductive Learning Model for Quantum Circuits

83. Simulations and results
Example 1:
Classical Synthesis of reversible functions
applied as a classical Machine Learning ab cd 00 01 11 10 1 -
abc
000
001
011
010
110
111
101
100 -
VV* VV
VVVV* d I
NOT
NOT *I 1
Symbolic synthesis Method

84. Simulations and results (contd.)
Observe that this is a generalization of the well-known realization of Toffoli invented by Barenco et al a b c d V V V V*
Circuit for the function from previous slide, realizing a symmetric function on the output (D) qubit:
We can create this type of functions for any number of variables
They are inexpensive in quantum but complex in Reed-Muller
Observe:
All controls are linear only
All targets are square roots and their adjoints only

85. Two Approaches to Quantum Learning
We proposed two complementary mechanisms for learning: Symbolic and Measurement Dependent.
Measurement Dependent method assumes known output events and their probabilities – there are several unitary matrices for the same input-output probabilistic behavior (H or V)
Symbolic method assumes known hidden states, predicts probabilistically the output events
Symbolic quantum learning
Measurement dependent Learning
Quantum Circuit
Measurement
Boolean Inputs
Probabilities
Environment

86. Results – The MIN and MAX Gate
The following two gates are the MIN and MAX gates
They can be used to build up a PLA like structure (using Mod-Sum)
Their drawback is the required ancilla qudit, but contemporary circuit CAD systems may be reused to start building quantum circuits out of MIN/MAX gates
2-qudit ternary MAX gate A B
|0> +1 12 R
MAX
MAX (A,B)
2-qudit ternary MIN gate
MIN A B
|0>
MIN (A,B) 01 +1 12 02 +2 R

87. Synthesis Examples.
The 3-qudit SWAP gate was not possible to find with the exhaustive search and therefore indicates the ability of the GA
The 3-qudit SWAP exchanges the 3 input to the output
(b)
3-qudit ternary SWAP gate; Realization (a) and Symbol (b) A B C
(a) B C +1 12 +2 A 02 01

88. Part 4:
Curriculum

89. Teen Program About Braitenberg Vehicles
Programming Robots in C language
Quantum Circuits: analysis and synthesis
How to program robots to demonstrate probabilistic, deterministic, and entangled behavior
Quantum theory and quantum computing
How to represent circuits with matrices
Trigonometry, complex numbers, matrix and vector multiplication, and digital circuits.

90. New classes New class teaches quantum computing and quantum robotics
One of the goals of this lecture is to help others to start with this new and exciting research area.
KHR-1 like robot can become a widely accepted international education platform.
Some ideas of quantum computing can be used to build sophisticated robot controllers.
Intelligent biped robots will be an excellent medium to teach emotional robotics, robot theatre, gait and movement generation, dialog and many other computational intelligence areas that have been not researched yet because of high costs of biped robots.

91. Generalized Circuit Ideas
Basic Binary Logic Gates
Basic Multiple-valued Logic Gates
Basic Fuzzy Logic Gates
Basic Binary Quantum Gates
Square Root of Not and Rotation gates
Logic Circuits
Binary Quantum Circuits
MV Logic Circuits
Fuzzy Logic Circuits
Logic Blocks
MV Logic Blocks
Binary Quantum Blocks
measurement
Logic Oracles
MV Logic Oracles
Binary Oracles
Pauli Rotation Level design
Binary State Machines
MV State Machines
Fuzzy State Machines
Binary Quantum Automata
Binary Oracles
MV Oracles
Binary Quantum
Permutative Oracles
Quantum Oracles detailed design and simulation
Binary Robot
Controller
Multi-valued
Robot
Controller
Fuzzy Robot
Controller
Quantum Robot
Controller
Quantum
Simulator
Subsumption architecture

92. Generalized Quantum Circuit Ideas
Basic Binary Quantum Gates
Basic MV Quantum Gates
Basic Fuzzy Quantum Gates
Square Root of Not and Rotation gates
Binary Quantum Circuits
Muthukrishnan-Stroud and Picton/Fredkin level
MV Quantum Circuits
Fuzzy Quantum Circuits
Binary Quantum Blocks
MV Quantum Blocks
Pauli Rotation Level design
Binary Oracles
MV/Binary Oracles
Binary Quantum Automata
MV Quantum Automata
Quantum Oracles detailed design and simulation
Binary Quantum
Permutative Oracles
MV/Binary Quantum
Permutative Oracles
Binary
Quantum Robot
Controller
Quantum
Simulator
MV/Hybrid
Quantum Robot
Controller
Fuzzy
Quantum Robot
Controller
Subsumption architecture

93. Generalized Quantum Algorithm Ideas
Binary Deutsch Algorithm
MV Deutsch Algorithm
Simon Algorithm
MV Grover
Binary Grover
BinaryDeutsch-Jozsa Algorithm
Generalized MV Deutsch-Jozsa Algorithm
Binary Quantum Graph Coloring Oracle
MV Quantum Graph Coloring Oracle
Generalized Deutsch-Jozsa Algorithm
Binary Quantum FFT
SEND+MORE=MONEY Oracle
Shor Algorithm
Generalized Transforms
Texture Analysis
Paths in Graphs Oracles
Other oracles for Grover
Convolution
Quantum Filtering
Quantum Robot
Planning
Quantum Motion
Generation
Quantum Image Matching
Quantum Robot
Vision
Quantum Constraint
Satisfaction
Quantum
Robot
Quantum Emotional
Models
Quantum
Braitenberg
Vehicles

94. Generalized Quantum Algorithm Ideas
Kets
Shannon Expansion and BDD
Complex numbers and trigonometry
Brakets and Hilbert Space
Operators
Fixed Polarity Reed-Muller Circuits
Bloch Sphere
Davio Expansions and KFDD
Serial gates and Matrix Products
MMD Algorithm
Synthesis of
one-qubit circuits
ESOP Circuits
Parallel gates and Tensor Products
Synthesis of Quantum Arrays from Toffoli and Feynman gates
Synthesis of
two- qubit circuits
Quantum Circuit Analysis
Synthesis of
three-qubit circuits and larger
Quantum Circuit
Synthesis
….. and finally…..

95. Part 5:
Research

96. Research areas Quantum Braitenberg Robots
Quantum Subsumption Architecture
Quantum Emotional Robotics
Other quantum robot architectures such as probabilistic
Quantum Search
Quantum Image Processing and Pattern Recognition
Quantum Spectral Transforms
Quantum Games
Quantum Theorem Proving
Quantum Learning (QNN, Quantum Automata, Markov Models, Bayesian Networks, Associative Memories, etc.
Quantum Holographic memories
Models of Quantum Physical Processes in biology, chemistry, etc.

97. Additional Slides

98. Conclusions and future work.
Didactic Aspects
KHR-1 is now able to mimic upper body human motions.
Students who work on this project learn about robot kinematics, robot vision, state machines (deterministic, non-deterministic, probabilistic and quantum - entangled) robot software programming and commercial robot movement editors.
The most important lesson learned is the integration of a non-trivial large system and the appreciation of what is a real-time programming.
It is important that the students learn to develop a “trial and error” attitude and also how to survive using a non-perfect and incomplete documentation.
It was also emphasized by the professor that students create a very good documentation of their work for the next students to use.

99. Disclaimer – do not worry!
We talk here about emotions of these:
And not these
Words such as “memory, emotion, knowledge, remember, solve, prove” carry human-like meaning but with time we are used to use them in a broader sense

100. Our Main New Idea: Two Layer Action-Emotion FSM Model
Emotions are not something “additional” to rational thinking and acting
Emotions are intimately intertwined in every process of a robot on any level of hierarchy
Instead of a hierarchy of state machines we have a hierarchy of Emotional State Machines
Simplified model of
Emotional State
Machine

101. Emotional State Machine
Deterministic classical physics/compute science world (Turing compatible)
Measurement of the machine state
Quantum memory
Emotional evolution (operator)
Quantum (Hilbert Space) (Quantum Turing Machine Compatible)

102. Quantum computing Basics
In quantum computing the system (circuit) is represented in the form of a wave:
The space of the system is complex Hilbert space H of dimension N. The basis states are orthonormal, for boolean logic:
The operations on the system are in the form of Unitary matrices being rotations of the state vectors in the space H:
To retrieve the result the system has to be observed or measured.
Measurement is an outside operation on the system, and destroys the quantum state.
This operation projects the system onto real basis states such as defined above.
Because the measurement is completely random, the information is extracted from the collapsed state that has the form of:

103. Quantum Computing Basics (contd.)
Special phenomena can be observed in quantum:
The system can be in superposition (being in all states at the same time)
The system can be entangled, the outcome of the whole system or of its subparts is dependent on the measured output qubit(s).
Despite the fact that before measurement both qubits have the probability of 0.5 of being in state 0 or 1, after one of the qubit is measured the state of the second one is instantaneously determined

104. Disclaimer: Definition of Emotion
We use, among other concepts, the quantum concepts to define and use emotions
In our model emotions are formally defined, you can think about them as quantum states or quantum operators.
Then, in this work there is no implication that our “emotions” are related to human emotions
other than that we want to emulate human behavior by a humanoid robot.
So what are robotic emotions?

105. Motivations for Emotional Robotics
Human-Human interaction is highly variable, individual, unique, non-repeating, etc.
Emotional Robot, Humanoid Robot
Quantum emotional state machine
Control logic for robotic quantum controllers in order to increase interactivity and quality of communication
Logic synthesis of such circuits is in the middle of this paper