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Outline1.1. Quantum Braitenberg VehiclesQuantum Braitenberg Vehicles
1. Programmable Braitenberg Vehicles
2. Combinational and Quantum Circuits
3. Deterministic, Probabilistic, and Entangled Behaviors
4. Examples or our Robots
2.2. Quantum Search Quantum Search
3.3. Quantum Emotional RobotsQuantum Emotional Robots
4.4. CurriculumCurriculum
5.5. ResearchResearch
Part 2:Part 2:
QuantumQuantum
SearchSearch
Grover Algorithm Grover Algorithm Reminder in new lightReminder in new light
Graph Coloring• 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
2
4
1
3
5
6 7
2
4
1
3
5
6 7
Color every node with a color. Every two nodes that share an edge should have different colors. Number of colors should be minimum
This graph is 3-colorable
Simpler Graph Coloring Problem
2
1
3
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
12
13
23
24
34
Value 1 for good coloring
We need to give all possible colors here
F(x)
Simpler Graph Coloring Problem
12
13
23
24
34
Value 1 for good coloring
We need to give all possible colors here
H
H
H
H
H
Give Hadamard for each wire to get superposition of all state, which means the set of all colorings
|0>|0>
|0>
Discuss naïve non-quantum circuit with a full counter of minterms
Now we will generate whole Kmap at once using quantum properties - Hadamard
f(x)
“Classical” Quantum Computer Circuit Model for Graph Coloring
inputs
C
C
AND
Sorting/Absorber
Color # Counter
Comparator
Desired number of
colors
AND Output
Simplified schematic of our Graph Coloring Oracle. Simplified schematic of our Graph Coloring Oracle.
We designed 35 oraclesWe designed 35 oracles
Hadamard TransformSingle qubit H
H
H
Parallel connection of two Hadamard gates is calculated by Kronecker Product (tensor product)
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
1/2
=
=
Here I calculated Kronecker product of two Hadamards
Motivating calculations for 3 variables• As we remember, these are transformations of Hadamard gate:
H|0> |0> + |1> H|1> |0> - |1>
H|x> |0> + (-1) x |1>
In general:
For 3 bits, vector of 3 Hadamards works as follows:
(|0>+(-1)a|1>) (|0>+(-1)b|1>) (|0>+(-1)c|1>) =From multiplication
|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>
|abc>
If a = b = c =0 then all phases positive
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
f(x)
oracle
|0>
|0>
This is like a Kmap with every true minterm (1) encoded by -1
And every false minterm (0) encoded by 1
|000> +|001> + |010>+|011> +|100> + |101> +|110> + |111>
What Grover algorithm does?
• Grover algorithm looks to a very big Kmap and tells where is the -1 in it.
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1
1 1 -1 1 1 1 1 1
1 1 1 1 1 1 1 1
Here is -1
Block Diagram for graph coloring and similar problems
Vector Of
Hadamards
Vector Of
Basic States
|0>Oracle with Comparators,
Global AND gate
Work bits
Output of oracle
All good colorings are encoded by negative phase
Think about this as a very big Kmap with -1 for every good coloring
Vector Of
Hadamards
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
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.
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
Properties of the oracle
fx1x2y
x2x1
y f(x1,x2)
((–1) f(00)00 + (–1) f(01)01 + (–1) f(10)10 + (–1) f(11)11)(0 – 1)
Output state:
Black box for 1-4 search:
Start by creating phases in superposition of all inputs to f:
Input state to query: (00 + 01 + 10 + 11)(0 – 1)
fH
H
H1
00
A 1-4 search can chose between 4 oracles in one iteration
Here we clearly see the Kmap encoded in phase – the main property of many quantum algorithms
fH
H
H1
00 H
H
H
H
H
X
X H H
X
XM
M
M
Time
state = 0 1 0 0 0 0 0 0
state =0.353-0.3530.353-0.3530.353-0.3530.353-0.353
state =0.353-0.3530.353-0.3530.353-0.353-0.3530.353
state =0.353-0.3530.353-0.3530.353-0.353-0.3530.353
state =-0.3530.3530.353-0.3530.353-0.3530.353-0.353
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
00 01 11 10
ab c 0 11
00 01 11 10
ab c 0 10.3 –0,3
0.3 –0,3
0.3 –0,3
0.3 –0,3
ab c 0 10.3 –0,3
0.3 –0,3
- 0.3 0,3
0.3 –0,3
00 01 11 10
ab c 0 1
0.3 –0,3
- 0.3 0,3
00 01 11 10
0.3 –0,3
0.3 –0,3
ab c 0 1
0.3 –0,3
0.3 - 0,3
00 01 11 10
- 0.3 0,3
0.3 – 0,3
ab c 0 1
- 0.5 0,5
0 0
00 01 11 10
0 0
0.5 – 0,5
ab c 0 1
- 0.5 0,5
0.5 - 0.5
00 01 11 10
0 0
0 0
This slide illustrates how the state of the system is changed as it propagates through the quantum network implementation of Grovers Search algorithm.
fH
H
H1
00 H
H
H
H
H
X
X H H
X
XM
M
M
Time
state =0.353-0.3530.353-0.3530.353-0.353-0.3530.353
state =-0.3530.3530.353-0.3530.353-0.3530.353-0.353
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 =-0.3530.3530.353-0.3530.353-0.353-0.3530.353
state =-0.3530.3530.353-0.3530.353-0.353-0.3530.353
state = 0 0 0 0 0 0 0 -1
state = 0 0 0 0 0 0 0 1
ab c 0 1
0.3 –0,3
- 0.3 0,3
00 01 11 10
0.3 –0,3
0.3 –0,3
ab c 0 1
0.3 –0,3
0.3 - 0,3
00 01 11 10
- 0.3 0,3
0.3 – 0,3
ab c 0 1
- 0.5 0,5
0 0
00 01 11 10
0 0
0.5 – 0,5
ab c 0 1
- 0.5 0,5
0.5 - 0.5
00 01 11 10
0 0
0 0
ab c 0 1
00 01 11 10
ab c 0 1
00 01 11 10
ab c 0 1
00 01 11 10
-1
-0.3 0.3
0.3 -0.3
-0.3 0.3
0.3 -0.3
- 0.3 0.3
0.3 - 0.3
- 0.3 0.3
0.3 - 0.3
Ibverters flip between 00 and 11
Hadamard addis in 00 and 11
Inverter flips second bit when first is 1
Ibverters flip between 00 and 11
Hadamard of affine function
Inversion about the mean
ψ00 = – 00 + 01 + 10 + 11ψ01 = + 00 – 01 + 10 + 11ψ10 = + 00 + 01 – 10 + 11ψ11 = + 00 + 01 + 10 – 11
fH
H
H1
00 H
H
H
H
H
X
X H H
X
XM
M
M
Time
The state corresponding to the input to the oracle that has a output result of 1 is ‘tagged’ with a negative 1.
After Hadamard the solution is “known” in Hilbert space by having value -1. But it is hidden from us
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
Grover LoopGrover Loop
We need to repeat the Grover We need to repeat the Grover Loop Loop N timesN times
Future work
Grover Loop
Had
amard
s
Co
nstan
ts
Measu
remen
ts
Grover SearchGrover Search
Oracle orQuantum
Circuit
Inp
uts-
senso
rs
Measu
remen
ts
Quantum Braitenberg Quantum Braitenberg VehicleVehicle
Ou
tpu
ts - actu
ators
Inp
uts-
senso
rs
Measu
remen
ts
New New ConceptConcept of of
Real-time Real-time Quantum Quantum
SearchSearch
Ou
tpu
ts - actu
ators
Grover Loop
Co
ntro
lled
Had
amard
s
Co
nstan
ts
ControlControl LEARNINGLEARNING
Worst case quadratic speedup on Worst case quadratic speedup on every problem that you can build an every problem that you can build an oracle!oracle!
Oracle for Quantum Map of Europe ColoringOracle for Quantum Map of Europe Coloring
Spain
France
Germany
Switzerland
Spain
France
Germany
Switzerland
Good Good coloringcoloring
quaternary
Yale Fan extended Deutsch-Jozsa, Bernstein-Vazirani and Grover algorithms to multi-valued quantum logic
Multiple-Multiple-Valued Valued Quantum Quantum CircuitsCircuits
Oracle for Quantum Map of Europe ColoringOracle for Quantum Map of Europe Coloring
0 1 2 3
1 0 3 2
2 3 0 1
3 2 1 0
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
0
1
2
3
0 1 2 3
0 1 2 3
0 1 2 3
0
1
2
3
+2
+3
0
1
2
3
+1
+3
+2
Quaternary Feynman Quaternary input/binary output comparator of equality
1 when A = B
A
B+1
A
B
A BA BA BA B
Oracle for Quantum Map of Europe ColoringOracle for Quantum Map of Europe Coloring
0
1
2
3
+1
+3
+2
A
B
+11
1
0
1
2
3
+1
+3
+2
C
D
+11
1
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
0
Binary signal 1 when all frontiers well colored
Comparator for Comparator for each frontiereach frontier
Quaternary controlled binary target gate
Binary Toffoli
Constraints Constraints Satisfaction ProblemsSatisfaction Problems
S E N D
+ M O R E
M O N E Y
Graph coloringGraph coloringCryptographic Cryptographic
ProblemsProblems
Constraint SatisfactionConstraint Satisfaction for Robotics for Robotics
• Insufficient speedInsufficient speed of robot of robot image processingimage processing and pattern and pattern recognition. recognition.
– This can be solved by special processors, DSP processors, FPGA This can be solved by special processors, DSP processors, FPGA architectures and parallel computing. architectures and parallel computing.
• Prolog allows to write CSP programs very quickly.Prolog allows to write CSP programs very quickly.
• An interesting approach is to An interesting approach is to formulate many problemsformulate many problems using the using the same generalsame general model. model.
• This model may be predicate calculus, Satisfiability, Artificial This model may be predicate calculus, Satisfiability, Artificial Neural Nets or Neural Nets or Constraints Satisfaction ModelConstraints Satisfaction Model..
Constraint Constraint Satisfaction Image Satisfaction Image Analysis by WaltzAnalysis by Waltz
• Huffman and Clowes Huffman and Clowes created an created an approach to approach to polyhedral scene polyhedral scene analysis,analysis, scenes with scenes with opaque, trihedral opaque, trihedral solids, next improved solids, next improved significantly by Waltzsignificantly by Waltz
• Popularized the Popularized the concept of constraints concept of constraints satisfaction and its use satisfaction and its use in problem solving, in problem solving, especially image especially image interpretation. interpretation.
• Objects in this Objects in this approach had always approach had always three plane surfaces three plane surfaces intersecting in every intersecting in every vertex. vertex.
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.
AC-3: State 2
3. Queue:
(2,3)(3,2)(3,4)(4,3)(4,1)(1,4) (1,3)(3,1)
4. Removing (2,3).
5. L3 on 2 inconsistent with 3, so it is removed.
6. Of arcs (k,2), (1,2) is not on queue, so it is added.
Constraint satisfaction model in roboticsConstraint 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
Examples of Examples of CSPCSP in in roboticsrobotics• Scene recognitionScene recognition
• Motion generationMotion generation in presence in presence of constraintsof constraints
– internal (internal (low powerlow power, , don’t hit don’t hit itselfitself))
– external (shape of racing track, external (shape of racing track, wolf-man-cabbage-goatwolf-man-cabbage-goat))
• GestureGesture under emotions under emotions
• Communication in a swarm of Communication in a swarm of robots (robots (graph coloringgraph coloring))
• Robot guard (Robot guard (set coveringset covering) )
Robot Reasoning Robot Reasoning ProblemProblem
New Approach New Approach to Quantum to Quantum
RoboticsRobotics
AdiabaticAdiabatic Quantum Computer Quantum Computer
Constraint Satisfaction ProblemConstraint Satisfaction Problem
Robot Vision Robot Vision ProblemProblem
Robot Robot Communication Communication
ProblemProblem
Robot Robot Obstacle Obstacle AvoidanceAvoidanceProblemProblem
Classical Classical quantum quantum computingcomputing
Adiabatic Adiabatic Quantum Quantum
ComputingComputing to solve to solve
Constraint Constraint Satisfaction Satisfaction
Problems Problems efficientlyefficiently
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 systemOrion 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.
Orion computer from DWAVEOrion 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
73
2
182
59
82
34
93
75
87
66
2644
5
Orion Is the Constraint Satisfaction Orion Is the Constraint Satisfaction Solver 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 Does it have quadratic speed-quadratic speed-up?up?
• The plans are that by the end of year 2008 the Orion systems will be scaled to more than 1000 qubitsmore than 1000 qubits.
• Company plans to build in 2009 processors specifically designed for quantum simulation, which represents a big commercial opportunity.
Orion computer from DWAVE
• 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.
• Adiabatic Quantum Computing was Adiabatic Quantum Computing was proved equivalentproved equivalent to standard QC to standard QC circuit model.circuit model.
• Each of the developed by us methods Each of the developed by us methods can be transformed to an can be transformed to an adiabaticadiabatic quantum program and run on Orion. quantum program and run on Orion.
• We developed We developed logic minimization methodslogic minimization methods to reduce the graph that is to reduce the graph that is created in AQC to program problems such as created in AQC to program problems such as Maximum CliqueMaximum Clique or or SATSAT. .
• This programming is like on “This programming is like on “assembly levelassembly level” but with time more ” but with time more efficient methodsefficient methods will be developed in our group. will be developed in our group.
– This is also similar to programming current This is also similar to programming current Field-Programmable Gate Field-Programmable Gate Arrays. Arrays.
We plan to concentrate We plan to concentrate on robotic applications of on robotic applications of the Constraint the Constraint Satisfaction Model. Satisfaction Model.
Future work on Adiabatic Quantum Controller for a robot
• In the second research/development direction the interface to Orion systeminterface to Orion system will be learned
• How to formulate front-end formulations front-end formulations for various robotic problemsfor various robotic problems as constraint-satisfaction problems for this system?
New Research DirectionNew Research Direction
• New approach to New approach to quantum robotics based quantum robotics based on reduction to on reduction to Constraint Satisfaction Constraint Satisfaction ModelModel •Well-known Well-known
problemsproblems
•New problemsNew problems
Part 3Part 3Quantum Quantum EmotionEmotion
al al RobotsRobots
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.
Robot emotionsRobot emotions
• 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”.
The research on robot emotions and methods to allow humanoid robots to acquire complex motor skills is recently advancing at a very fast pace.
• 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.
Emotions can be best expressed
by a biped robot withhuman-like face
• 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 Humanoid robots to robots to express express emotions:emotions:
• M. Lukac uses human-like faces and head/neck body combinations.
• KAIST theatre used whole-body stationary robots with hands.
Synthesis of quantum circuits and Synthesis of quantum circuits and state machines from examplesstate 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
Quantum Emotional Facial Quantum Emotional Facial GesturesGestures
First View: Emotion as synthesizedsynthesized behavior
Emotional state = state of all emotion variables
Physical variables = positions, speeds, accelerations, words,
Serchuk et al (2006) discuss Serchuk et al (2006) discuss emotion as mappingemotion as mapping from from internal state internal state to to observable output behavior. observable output behavior.
We want to design these mappings well, so that they We want to design these mappings well, so that they wil be wil be similar to humanssimilar to humans
Wheel of emotions
Internal representation of emotions by vectors in multi-dimensional space
Active - PassiveActive - Passive
Positive - Positive - NegativeNegative
Mapping from internal to external representation of emotions
Second ViewSecond View: Emotion as: Emotion as emergent, evolvableemergent, evolvable behaviorbehavior
Evolved “emotional” behavior of robot
Sensors, vision and fusion = features and patterns
Drives and effectors
Main input-output mapping (perception, internal state, behavior)
Precise motion generation (behavior)
Deg
rees
of f
reed
om
• Here emotion is an emergent behavior that arises from sensors, Here emotion is an emergent behavior that arises from sensors, drives, effectors and logic.drives, effectors and logic.
• This may look like This may look like human, animal behaviorhuman, animal behavior but but also as an entirely also as an entirely new “other world” behaviornew “other world” behavior, behavior as it may be., behavior as it may be.
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.
• 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)
Robot perceives human moodRobot perceives human mood
Why we need Robot-Generated Emotions?
• Robot Robot presents its emotionspresents its emotions to a human 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 RoboticsHumanoid 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
Symmetry of emotion transmission
Human emotion
Human behavior
Robot perceives Human behavior
Robot reconstructs Human emotion
Robot creates its emotion
Robot expresses its behavior
Human perceives robot behavior and emotion
Emotions as emergent behaviors
Emotions as learned behaviors
Two aspects – two Two aspects – two approachesapproaches
55
Traditional and modern theories of emotion
• Observable (traditional) emotions:Observable (traditional) emotions: emotional emotional behaviors, moods, content changes (speech behaviors, moods, content changes (speech variations, etc)variations, etc)
• Modern Hypothesis:Modern Hypothesis: emotions and feelings emotions and feelings are influencing decision making, problem are influencing decision making, problem solving, memory efficiency and so on.solving, memory efficiency and so on.
Two level representation of the Two level representation of the Cognitive-Emotional robot Cognitive-Emotional robot
StructureStructure
Flow of Flow of actionsactions
Flow of Flow of emotionsemotions
Quantum Mechanics to model emotions
58
Quantum Mechanics to Quantum Mechanics to Model EmotionsModel 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 Emotional Quantum State MachineState 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 EmotionsQuantum 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
One Machine Model in One Machine Model in Our ApproachOur Approach
rejacc S,Ssqδ,Θ,E,S,Q,=M 0,0,
Sin S_rej states rejecting ofset
Sin S_acc states accepting ofset
state classical initial
state quantum initial
functionn transitiostate
functionevolution quantum
alphabet
states classical
states quantum
0
0
rej
acc
S
S
s
q
δ
Θ
E
S
Q
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 quantum operatoroperator (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
• DefinitionDefinition: 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
Emotional Quantum Automata• A network of Emotional State Machines is called an A network of Emotional State Machines is called an Emotional Quantum Automata Emotional Quantum Automata
((pluralplural - - per similarity toper similarity to Cellular Automata) Cellular Automata)• This network can be regular or not.This network can be regular or not.
• If regular, it can be:If regular, it can be:– One-dimensionalOne-dimensional and and one-directionalone-directional (pipelined) (pipelined)
– One-dimensionalOne-dimensional (like one-dimensional cellular automata) (like one-dimensional cellular automata)
– Two-dimensional Two-dimensional (like Game of Life and Two-Dimensional cellular Automata of Wolfram) (like Game of Life and Two-Dimensional cellular Automata of Wolfram)
– more more dimensional.dimensional.
• Emotional Quantum Automaton is therefore a generalization of Emotional Quantum Automaton is therefore a generalization of Cellular AutomataCellular Automata, , Random Boolean Networks and Random Boolean Networks and Quantum Cellular AutomataQuantum Cellular Automata
Example of one-Example of one-dimensional and dimensional and one-directional Cellular Quantum Automata
65
Complex space vs. Real StatesComplex space vs. Real States
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
Time
Neighbors
Emotional states travels across the robot body
Emotional Parameters for control in Cynthea Robot
Device Parameters OtherDevice Parameters Other
This slide shows which parameters are affected This slide shows which parameters are affected by which input and output devicesby which input and output devices
67
Emotional Model
• 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
Robot controller
Formal Language
Robot actuatorsRobot sensors
Emotional
Robot controller
Emotional
Robot actuators
Emotional
Robot sensors
68
Emotional Model
• Strategy – the translation function mapping the emotional state to a state parameters, (function dependent)
• Energy – simulated energy representing the emotional state of the robot
Emotional State Energy
• The input command - represents the robot command such as one obtained from a sensor (user input, other robot), specified in the CRL language
Emotional State State Parameters
• The emotional parametersThe 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
Project Overview
• KHR-1– Biped robot– 17 servos– 2 RCB-1 servo
controllers (each 12 servos)
– Serial port connectivity
Common Robot Language. • We developed We developed symbolic approach symbolic approach
to robot specificationto robot specification based on a based on a Common Robot Language. Common Robot Language.
• While the While the syntax of this language syntax of this language specifies rules for generating specifies rules for generating sentencessentences, the semantic aspects , the semantic aspects describe structures for describe structures for interpretation. interpretation.
• Every Every movement is described on movement is described on many levels,many levels, for instance every for instance every joint angle or face muscle are at joint angle or face muscle are at low level and complete movements low level and complete movements such as pushups or joyful hand such as pushups or joyful hand waving are at a high level. waving are at a high level.
Common Robot Language. • These aspects serve to describe These aspects serve to describe
interaction with environmentinteraction with environment at at various levels of description. various levels of description.
• It uses also the It uses also the constraint constraint satisfaction problem creating satisfaction problem creating movementsmovements that specify constraints that specify constraints of time, space, motion style and of time, space, motion style and emotional expression. emotional expression.
• 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.
Describing movements, behaviors and emotions
Using HBP robot vision software for Using HBP robot vision software for human mimicking.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.
What is wrong with our vision What is wrong with our vision software?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 we will use the Orion quantum computer in the next projectOrion quantum computer in the next project
Inductive Quantum Learning
Quantum computing basics
• Units are qubits, quantum bits, represented by wave function, on real (observable bases) in the complex Vector Space H.
2cos
2sin
2sin
2cos
2sin
2cos2/
i
iXiIeR Xi
x
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: 1
5probability of observing output state |0>
45
probability of observing output state |1>
1|0||
1|5
20|
5
1|
||
||'|
*nn
n
MM
MMDifference of complete
measurement and expected measurement in a robot.
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)
Quantum computing basics
• On of the particular properties of Quantum Computation is the superposition of states: allowing to synthesise quantum probabilistic logic functions
2
1
2
12
1
2
1
*
ii
i
iii
V
and entanglement (initially known as EPR)
11
11
2
1H
2
1
2
100
2
1
2
100
0010
0001
iii
ii
iVControlled
1||,||2
i
ii
i cic
11|00|2
1|
Meaning of entanglement in terms of gestures
Three Types of Quantum Inductive Learning
ab c 0 1
00
01
11
10
0
1
1
1
1
0
0
0
ab c 0 1
00
01
11
10
0
1
1
1
-
-
-
-
ab c 0 1
00
01
11
10
0
1
1
1
V1
V0
V0
V1
ab c 0 1
00
01
11
10
0
1
1
1
V0
V1
M0,1
M0,1
Classical Deterministic Learning
Probabilistic and Quantum Probabilistic Learning
Quantum Probabilistic and Measurement Dependent Learning
V0=V |0>=V * |1>
V1=V |1>=V * |0>
M0,1 - output reading dependent on wether the result is 0 or 1
Controlled [V/V*] gates
• V, V*, C-V, C-V*, are well know elements of quantum logic synthesis for pseudo-boolean (permutative) functions.
10
01** VVVV
V* V* X
V* V I V* V X
CNOT
2
1
2
100
2
1
2
100
0010
0001
iii
ii
iVControlled
01
10, ** VVXVVX
V*
*
V
V
• V, V*, C-V, C-V*, are well know elements of quantum logic synthesis for pseudo-boolean (permutative) functions.
2
1
2
100
2
1
2
100
0010
0001
iii
ii
iVControlled
01
10, ** VVXVVX
V*V M 0 or 1
Various types of measurement
1
0
VV00
Non-deterministic measurement
Various types of measurement
2
1
2
100
2
1
2
100
0010
0001
iii
ii
iVControlled
V*V M
Operator built-in the measurement
V
V0 or V1
1 for V0
Measurement here would Measurement here would be non-deterministicbe non-deterministic
Measurement here is Measurement here is deterministicdeterministic
e
Inductive Learning Model for Quantum Inductive Learning Model for Quantum CircuitsCircuits
Simulations and results
• Example 1:Example 1:
abcd 00 01
00
01
11
10
0
0
1
0
-
1
-
0 0 1
--
0 1
1 0
11 10
abc
000
001
011
010
110
111
101
100
-
VV*
VV
VV*
VV
VVVV*
VV
VV*
d dd
-
I
NOT
NOT
NOT
I
I
NOT *I
0
0
1
0
1
1
1
0
Symbolic synthesis Method
Classical Synthesis of reversible functions applied as a classical Machine Learning
Simulations and results (contd.)
• Circuit for the function from previous slide, realizing a symmetric function on the output (D) qubit:
V V V*V
a
b
c
d
dcbaSf ),,(3,2
Observe:● All controls are linear only
● All targets are square roots and their adjoints only
Observe that this is a generalization of the well-known realization of Toffoli invented by Barenco et al
We can create this type of functions for any number of variables
They are inexpensive in quantum but complex in Reed-Muller
Two Approaches to Quantum Learning
Quantum Circuit Measurement
Environment
Measurement dependent Learning
Symbolic quantum learning
Boolean Inputs
Probabilities
Symbolic method assumes known hidden states, predicts probabilistically the output events
• 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)
Results – The MIN and MAX Gate
2-qudit ternary MAX gate
A
B
|0>
A
B
+1+1
12
12
+1
+1 R
MAX
A
B
|0>
A
BMAX (A,B)
2-qudit ternary MIN gate
MIN
A
B
|0>
A
BMIN (A,B)
A
B
|0>
A
B
01+1
12
02
+2
+2
R
• 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
Synthesis Examples.
3-qudit ternary SWAP gate; Realization (a) and Symbol (b) A
B
C
B
C
A
• 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)
(a)
B
C+1
+1
12
+1
+2A
B
+1
+1
+1
+1
+1
+1
+1
02
01
12
02
01
C A
+1 +2
Part 4:Part 4:
CurriculumCurriculum
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.
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.
Generalized Circuit IdeasBasic Binary Logic Gates
Logic Circuits
Logic Blocks
Logic Oracles
Binary State Machines
Binary Oracles
Basic Multiple-valued Logic Gates
MV Logic Circuits
MV Logic Blocks
MV Logic Oracles
MV State Machines
MV Oracles
Basic Fuzzy Logic Gates
Fuzzy Logic Circuits
Fuzzy State Machines
Basic Binary Quantum Gates
Binary Quantum Circuits
Binary Quantum Blocks
Binary Oracles
Binary Quantum Automata
Binary Quantum
Permutative Oracles
Square Root of Not and Rotation gates
Pauli Rotation Level design
Fuzzy Robot Controller
Binary Robot Controller
Multi-valued Robot
Controller
Subsumption architecture
Quantum Oracles detailed design and simulation
Quantum Simulator
Quantum Robot Controller
measurement
Generalized Quantum Circuit IdeasBasic Binary Quantum Gates
Binary Quantum Circuits
Binary Quantum Blocks
Binary Oracles
Binary Quantum Automata
Binary Quantum
Permutative Oracles
Square Root of Not and Rotation gates
Pauli Rotation Level design
Subsumption architecture
Quantum Oracles detailed design and simulation
Quantum Simulator
BinaryQuantum Robot
Controller
Basic MV Quantum Gates
MV Quantum Circuits
MV Quantum Blocks
MV/Binary Oracles
MV Quantum Automata
MV/Binary Quantum
Permutative Oracles
Muthukrishnan-Stroud and Picton/Fredkin level
MV/HybridQuantum Robot
Controller
Basic Fuzzy Quantum Gates
Fuzzy Quantum Circuits
Fuzzy Quantum Robot
Controller
Generalized Quantum Algorithm IdeasBinary Deutsch Algorithm
BinaryDeutsch-Jozsa Algorithm
Generalized Deutsch-Jozsa Algorithm
Quantum Image Matching
Texture Analysis
Simon Algorithm
Binary Quantum FFT
Quantum Robot Vision
Generalized MV Deutsch-Jozsa Algorithm
Other oracles for Grover
SEND+MORE=MONEY Oracle
Convolution
Quantum Filtering
Binary Grover
Quantum MotionGeneration
MV Grover
Binary Quantum Graph Coloring Oracle
Quantum Robot Planning
Generalized Transforms
MV Deutsch Algorithm
MV Quantum Graph Coloring Oracle
Shor Algorithm
Paths in Graphs Oracles
QuantumRobot
Quantum ConstraintSatisfaction
Quantum Emotional Models
Quantum BraitenbergVehicles
Generalized Quantum Algorithm IdeasKets
Operators
Serial gates and Matrix Products
Quantum Circuit Analysis
ESOP Circuits
Fixed Polarity Reed-Muller Circuits
Synthesis of
one-qubit circuits
Davio Expansions and KFDD
Brakets and Hilbert Space
MMD Algorithm
Synthesis of Quantum Arrays from Toffoli and Feynman gates
Shannon Expansion and BDD
Bloch Sphere
Complex numbers and trigonometry
Quantum Circuit Synthesis
Parallel gates and Tensor Products
Synthesis of
two- qubit circuits
Synthesis of
three-qubit circuits and larger
…….. and finally….... and finally…..
Part 5:Part 5:
ResearchResearch
Research areasResearch areas1. Quantum Braitenberg Robots
2. Quantum Subsumption Architecture
3. Quantum Emotional Robotics
4. Other quantum robot architectures such as probabilistic
5. Quantum Search
6. Quantum Image Processing and Pattern Recognition
7. Quantum Spectral Transforms
8. Quantum Games
9. Quantum Theorem Proving
10.Quantum Learning (QNN, Quantum Automata, Markov Models, Bayesian Networks, Associative Memories, etc.
11.Quantum Holographic memories
12.Models of Quantum Physical Processes in biology, chemistry, etc.
Additional Additional SlidesSlides
Conclusions and future work.Conclusions and future work.
• 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.
Didactic AspectsDidactic Aspects
Disclaimer – do not worry!• We talk here about emotions of these:
And not theseAnd 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
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 ofSimplified model of Emotional State Emotional State
MachineMachine
Emotional State MachineDeterministic classical physics/compute science world (Turing compatible)
Quantum (Hilbert Space) (Quantum Turing Machine Compatible)
Quantum Quantum memorymemory
Emotional evolution (operator)
Measurement of the machine state
102
The operations on the system are in the form of Unitary matrices being rotations of the state vectors in the space H:
In quantum computing the system (circuit) is represented in the form of a wave:
Quantum computing BasicsQuantum computing Basics1||>|>| 2=c,ic=ψ i
ii
>1|>0|>| +βα=ψ
1
0>1|
0
1>0| =,=
>|>| ii
i mc=ψU
The space of the system is complex Hilbert space H of dimension N. The basis states are orthonormal, for boolean logic:
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:
>||<
>|>|
* ψMMψ
ψM=ψ'
103
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).
Quantum Computing Basics (contd.)Quantum Computing Basics (contd.)
1||>|>| 2=c,ic=ψ ii
i
0000
0100
0000
00010 =M
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
2
>11|>00|>|
+=φ
1
0
0
1
2
0
0
0
1
2
1
0
0
0
1
2
1
1
0
0
1
0000
0100
0000
0001
2
1>|0 ===φM
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?So what are robotic emotions?
Motivations for Emotional RoboticsMotivations 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
