Studying the “brain” realization and its simulated quantum

implementation for the Cynthia robot

• Introduction to Cynthia robot. • The goal of the research. • Examples of different explanations of the brain

system • The research plan.• Overview on the previous work.• Simulation steps• Current work (Project)• Future work.

Contents

Introduction to Cynthia Robot

Introduction to Cynthia Robot

- That requires us to study the biological brain systems

The goal of the research• To build a block which will act as a brain on top of the MNS and NNS.

• This block will control the behavior of the robot such that it reflects the learning process of the robot as well as the physical phenomena that might happened and affect the robot behavior similar to the real brain.

• Gerald Edelman Neural Darwinism: The Theory of Neural Group Selection.

Examples of different explanations of the brain system

SUM (Wij) AFW31output

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W21

W41

W11

W14

W13

W51

Neural Darwinism: The Theory of Neural Group Selection.

1

1

0

1

0

1

Examples of different explanations of the brain system

• Stapp The Brain as a Quantum Measuring Device

The neural wave function enfolds superposed possibilities, and then consciousness chooses one classical branch and annihilates the others. The choice is "unruly," Stapp (1993, p.32) says.

•Some Physical Phenomena couldn't be represented by any low or mathimatical equations

• Twins spiritual link It is believed that this could be explained using one of the quantum mechanics features, called , Entanglement

Examples of different explanations of the brain system

• Yasue Quantum Brain Dynamics and Consciousness: An Introduction (Advances in Consciousness Research, V. 3 Water Mega molecule• Ben Goertzel Evolutionary Quantum Computation: Its Role in the Brain, Its Realization in Electronic Hardware, and Its Implications for the Pan psychic, Theory of Consciousness Populations of neuronal maps have a quantum aspect as well as a classical. The brain is an evolving population of quantum neural networks

Examples of different explanations of the brain system

•Set up an ensemble of quantum computers, and allow them to evolve. • Create criteria for judging QC's, and then, in the manner of natural selection, allow successful QC's to survive and (probabilistically) mutate and combine to form new candidate QC's, whereas unsuccessful QC's perish. • The result is that one has quantum computers fulfilling desired functions via unknown means.

Quantum System &Theory

• Hilbert Space

X

E14= (1 0 0 0)

E24= (0 1 0 0)

E34= (0 0 1 0)

E1 E2 E3 E4 are orthonormal vectors and called the bases of the Hilbert space

Quantum System &Theory• Hilbert Space

X

E14= (1 0 0 0)

E24= (0 1 0 0)

E34= (0 0 1 0)

r

......4|43|32|21|1| EEEEr

1...|4||3||2||1| 2222

Quantum System &Theory

• Quantum system

• Quantum systems are described by a wave function, r , that exists in a Hilbert space.• The Hilbert space has a set of states, Ei , which is called the set of bases, and the system is described by a quantum state, r , which is said to be in a linear superposition of the basis states Ei , and in general, the coefficients are complex numbers.

Quantum Theory

• State • Super position

• Qubit

• Uncertainty

1|0||

1|||| 22

1|||| 22

Quantum Theory0

1

0

1Classical BIT

QuBIT

Block Sphere

Quantum Theory

• Measures the qubit state

The quantum system is said to be collapsed when we make the projection on one of the basis. That is also called decoherence or the measures. For example, if we take the projection of on the |0> basis then it will be . is the probability of the qubit to collapse on the state |0>.

| 0||

|| 2

Why quantum

• The increasing speed of the computations as well as reducing the size of the computers will lead to the quantum mechanics theory will replace the classical logic theory.

• Implementation of models of the physical phenomena that could not be implemented before.

• Reduction in time and increase in memory capacity.

• Parallelism

Quam using Grover algorithm

Storing Pattern algorithm

Pattern recall algorithm

For a set of m binary patterns with length n, 2n+1 qubits are required

Research algorithm the speed of researching is

O( ). NSPEED

OF WHAT?

??

Storing Pattern algorithm

A quantum algorithm for constructing a coherent superposition of states (bases), that corresponds to the patterns, with the amplitudes of the states in the superposition all being equal.

|f> = |X1 X2……Xn >

Where X1,X2,….,Xn are n qubits to represent the n bits for every binary pattern of the m patterns.

For example

|f > = |10110100> + |11000011> +……..

Storing Pattern algorithm

• To construct this wave function we need to use n+1 qubits to be used in the process of generation the function.

|f> = |X1 X2……Xn, G1G2…..Gn-1, C1C2>

G1, G2, Gn-1 as well as C1 C2 are control registers.

Storing Pattern algorithmThree transformation are used in the process of generating the function

• S state generation

Where s is the values of the F(z) and s {1,-1} and

1 <= P <=m.

explain

Storing Pattern algorithm

• Control flip transformation

]*

0

0

1

1

][

0100

1000

0001

0010

210

[F

Let’s consider two qubits 0|11| 1|0|2|

1|0|2|

Storing Pattern algorithm• Control flip transformation

Let’s consider two qubits 1|11| 1|0|2|

1|0|2|

]*

1

1

0

0

][

0100

1000

0010

0001

211

[F

Storing Pattern algorithm• AND transformation

Let’s consider three qubits 0|11|

1|0|3|

0|12| 1|0|3|

]

*0*0

*0*0

*1*0

*1*0

*0*1

*0*1

*1*1

11

][

1

1

1

1

1

1

01

10

321

00

B

B

B

B

A [

Storing Pattern Algorithm

Explain all symbols

Storing Pattern AlgorithmStep by Step example

To understand the algorithm, let’s assume the following set of learning patterns  D = {f(01) = -1, f(10) = 1, f(11) = -1} From D we can deduce the following Z3 is 01 Z2 is 10 Z1 is 11 n = 2 number of qubit to represent the patterns m=3 number of patterns to be represented 

Storing Pattern AlgorithmStep by Step example

1- |f > = |00,0,00 > X1=0 X2=0 g1=0 , C1=0 and C2 =02 2-    do the for loop P=3 Z3= 01 Z31=0 Z32=1 Z4= 00 Z41=0 Z42=0 Z32 not equal Z42 flip X2

220

XcF

Then |f > = |01,0,00 >

C2

X2

X2

Storing Pattern AlgorithmStep by Step example

3- Flip C1 state

120

ccFThen |f > = |01,0,10 >

C2

C1

C1

4-  Generate a new state by applying S on C2 C1

Storing Pattern Algorithm

]*

0

][

3/23/100

3/13/200

0010

0001

21

20

21

20

1

1

01321

C

C

C

C

cCS

[

then |f > = -1/ |01,0,11 > + |01,0,10>3 3/2

C1

C2

• 5-   Flip g1 to mark the register 

1@2@1]0

0101

01gXX

I

FgA [

then |f > = -1/ |01,1,11 > + |01,1,10> 3/23

X1

X2

g1

g1

Storing Pattern Algorithm

26-   Flip C1 which is controlled by g1

 

]*][

0100

1000

0010

0001

11

10

11

10

1

1

0

0

11

1

C

C

C

C

cgF [g1

C1

C1

then |f > = -1/ |01,1,01 > + |01,1,00>3 3/2

Storing Pattern Algorithm

• 5-   Flip g1 again to the normal state  

 

1@2@1]0

0101

01gXX

I

FgA [

then |f > = -1/ |01,0,01 > + |01,0,00> 3/23

X1

X2

g1

g1

Saved Go to step 1Again

Storing Pattern Algorithm

• The whole process repeated again with start

|f > = -1/ |01,0,01 > + |01,0,00>

after the 3rd loop

|f> =

 

that is what is called storing the pattern.

3 3/2

Storing Pattern Algorithm

5 qubit Quam Network Implemantation

?F0

F0

S

F1

A0

A0

X1X2

g1

C1

C2

?F0

7 qubit Quam Network Implemantation

Pattern recall Algorithm

• The idea of pattern recall is collapsing the function |f > on the required basis (pattern).

• Grover used his quantum search in data base algorithm in recalling the pattern. The idea of this search is to change the phase of the desired state and then rotate the entire |f > around the average. This process repeated (3.14/4)* Where N is the total possible state.

 

N

• The algorithm steps:

Pattern recall Algorithm

 1-change the phase of the desired state.

2- compute the average A

3- rotate the entire quantum set around the average. |f>= 2A-|f >

4- repeat 1-3 for (3.14/4)*

5- Measure the desired state.

 

N

• Step By Step example

 

Pattern recall Algorithm

Let’s continue on the same example, used in the learning phase.

Let’s assume we want to recall the pattern 01.

Since we have only 2 qubits then the possible combination is 4.

|f> will collapse on the desired state after repeat the algorithm for (3.14/4)*2, which roughly 1 times.

 

• Step By Step example

Pattern recall Algorithm

1- |f >

2  2- f > 1/ (0,-1,1,1)

3- 3-   Average =1/4

4- 4-   |f > 1/2 (1,3,-1,-1)

5- 5-   Measure the desire state |f >= ( /2) |01>

  

3

3

3

Pattern recall Algorithm

• It is obvious that the probability of the system to collapse on the desired state is ¾= 75%.

• The system collapse in the O( ).

• Which means it is faster than the classical NN which takes O(N)

N

Comparison between the Quam and the

NN Hope field Associative memory.

Quam Hopfield

Max memory capacity

.15*n

Number of neurons

2n+1 n

Pattern recall speed

O( ) O(N)

Phase learning speed

O(mn) O(mn)

2n

N

Comparison between the Quam and the

NN Hope field Associative memory.

The research plan

•Phase One

•Phase Two

• Insert a quantum circuit in the command execution data path, in the MNS in figure.1. The quantum circuit will alter the command slightly.

•Phase Three

Phase One

Robot (CRL parcel translator)

MNS ( command initiation)

Servos (Motion)

Quantum Circuit

( Command alteration)

Phase Two

• Study designing the quantum circuit such that it reflects the learning process of the robot brain and matches the behavior, mode and the emotion of the robot.

Robot (CRL parcel translator)

MNS ( command initiation)

Servos (Motion)

Quantum Circuit

( Command alteration)

Phase Two

Quantum Circuit

( Design the matched Quantum circuit to the required behavior )

• Generalize the Idea by built in a complete block on top of the MNS , which will act as a brain to the robot.

Phase Three

Robot Brain

• A quantum circuit was introduced using the QUASI quantum simulator. •The theatre robots communicate using CRL (Common Robotic Language). •The inputs for the Quantum circuit will be the data between the command tags in the CRL file.

• The present version supports only the following command tags for the recognition of inputs to the Quantum Circuit.

–They are wait, flush, move, normal, smile, frown, cry, look, speak, speed, accel, open and close.

Overview on the previous work

Simulation steps:

Robot (CRL parcel Command translator)

Save input data into XML File

Choose Quantum circuit using Quasi Simulator

Save the circuit into XML data File

Load the XML files Using Quasi Simulator

Generate the Output sequence from the circuit and save in a file to be used as an alter command to

the servo

Current work (project)

• Integrate the software which was done in the previous work. (current)

Robot (CRL parcel Command translator)

Choose Quantum circuit using Quasi Simulator

Generate the Output sequence from the circuit and as an alter command to the servo

Future work

• Design the quantum circuit according to the learning process of the brain.

• Implement the brain block in the Cynthia Robot.

END

Introduction to Cynthia Robot

1. Generate a circuit:

A new Quantum Circuit can be built using the Quasi simulator. Run the Quark2.Quark command inside the Quasi folder. (The main program in the Quark class). Two windows will open up. In the left window, click on Circuit>New tab and create a new circuit. Save the circuit (Let us assume you saved it as MyCircuit.xml).

2. Load the input sequence to the circuit:

To load the input sequence, run the following command in the folder where the program is saved. Ø java CrlAnalysis MyCrlFile.crl MyCircuit.xml This will calculate the input sequence from the MyCrlFile.crl and will load it into MyCircuit.xml

Simulation steps

Simulation steps:3. Simulate the circuit:

In the left window of the Quasi program, click circuit>load and load the MyCircuit.xml file. Then click run to finish button. This will simulate the circuit and the outputs are displayed in the second window. The data is stored in the xml format into the file called QuantumOutput.xml file.

4. Generate new CRL file:

Now, the QuantumOutput.xml file contains the results of the circuit along with their probabilities alpha2 and beta2. To generate the new CRL file, we need to run the following command. Ø java ReadWriteCrl MyCrlFile.crl QuantumOutput.xml The new CRL file with the name TestOutput.crl file is created.

This file can be used on the robots and the behavior can be observed.

Defining the Quantum ComputerYou don't have to go back too far to find the origins of quantum computing. While computers have been around for the majority of the 20th century, quantum computing was first theorized just 20 years ago, by a physicist at the Argonne National Laboratory. Paul Benioff is credited with first applying quantum theory to computers in 1981. Benioff theorized about creating a quantum Turing machine. Most digital computers, like the one you are using to read this article, are based on the Turing Theory. The Turing machine, developed by Alan Turing in the 1930s, consists of tape of unlimited length that is divided into little squares. Each square can either hold a symbol (1 or 0) or be left blank. A read-write device reads these symbols and blanks, which gives the machine its instructions to perform a certain program. Does this sound familiar? Well, in a quantum Turing machine, the difference is that the tape exists in a quantum state, as does the read-write head. This means that the symbols on the tape can be either 0 or 1 or a superposition of 0 and 1. While a normal Turing machine can only perform one calculation at a time, a quantum Turing machine can perform many calculations at once. Today's computers, like a Turing machine, work by manipulating bits that exist in one of two states: a 0 or a 1. Quantum computers aren't limited to two states; they encode information as quantum bits, or qubits. A qubit can be a 1 or a 0, or it can exist in a superposition that is simultaneously both 1 and 0 or somewhere in between. Qubits represent atoms that are working together to act as computer memory and a processor. Because a quantum computer can contain these multiple states simultaneously, it has the potential to be millions of times more powerful than today's most powerful supercomputers. This superposition of qubits is what gives quantum computers their inherent parallelism. According to physicist David Deutsch, this parallelism allows a quantum computer to work on a million computations at once, while your desktop PC works on one. A 30-qubit quantum computer would equal the processing power of a conventional computer that could run at 10 teraflops (trillions of floating-point operations per second). Today's typical desktop computers run at speeds measured in gigaflops (billions of floating-point operations per second). Quantum computers also utilize another aspect of quantum mechanics known as entanglement. One problem with the idea of quantum computers is that if you try to look at the subatomic particles, you could bump them, and thereby change their value. But in quantum physics, if you apply an outside force to two atoms, it can cause them to become entangled, and the second atom can take on the properties of the first atom. So if left alone, an atom will spin in all directions; but the instant it is disturbed it chooses one spin, or one value; and at the same time, the second entangled atom will choose an opposite spin, or value. This allows scientists to know the value of the qubits without actually looking at them, which would collapse them back into 1's or 0's.

Gerald Edelman's Work

Topobiology; An Introduction to Molecular Embryology

Neural Darwinism; The Theory of Neuronal Group Selection

The Remembered Present: A Biological Theory of Consciousness

Bright Air, Brilliant Fire: On the Matter of the Mind

Once one has committed oneself to looking at groups, the next step is to ask how these groups are organized. A map, in Edelman's terminology, is a connected set of groups with the property that when one of the inter-group connections in the map is active, others will often tend to be active as well. Maps are not fixed over the life of an organism. They may be formed and destroyed in a very simple way: the connection between two neuronal groups may be "strengthened" by increasing the weights of the neurons connecting the one group with the other, and "weakened" by decreasing the weights of the neurons connecting the two groups.

Formally, we may consider the set of neural groups as the vertices of a graph, and draw an edge between two vertices whenever a significant proportion of the neurons of the two corresponding groups directly interact. Then a map is a connected subgraph of this graph, and the maps A and B are connected if there is an edge between some element of A and some element of B. (If for "map" one reads "program," and for "neural group" one reads "subroutine," then we have a process dependency graph as drawn in theoretical computer science.)

This is the set-up, the context in which Edelman's theory works. The meat of the theory is the following hypothesis: the large-scale dynamics of the brain is dominated by the natural selection of maps. Those maps which are active when good results are obtained are strengthened, those maps which are active when bad results are obtained are weakened. And maps are continually mutated by the natural chaos of neural dynamics, thus providing new fodder for the selection process. By use of computer simulations, Edelman and his colleage Reeke have shown that formal neural networks obeying this rule can carry out fairly complicated acts of perception.

This thumbnail sketch, it must be emphasized, does not do justice to Edelman's ideas. In Neural Darwinism Edelman presents neuronal group selection as a collection of precise biological hypotheses, and presents evidence in favor of a number of these hypotheses.

However, I consider that the basic concept of neuronal group selection is largelyindependent of the biological particularities in terms of which Edelman has phrased it. As argued in (Goertzel, 1993), I suspect that the mutation and selection of "transformations" or "maps" is a necessary component of the dynamics of any intelligent system.

Edelman's theory provides half of the argument that the brain is an EQC: it provides evidence that the brain is an evolving system. Edelman uses nonlinear differential equations on finite-dimensional spaces to model the dynamics of neuronal groups; he does not consider these groups as quantum systems. There is much evidence, however, that the brain is not as "classical" a system as Edelman and other more conventional neural net theorists would have it.

Will we ever have the amount of computing power we need, or want? If, as Moore's Law states, the number of transistors on a microprocessor continues to double every 18 months, the year 2020 or 2030 will find the circuits on a microprocessor measured on an atomic scale. And the logical next step will be to create quantum computers, which will harness the power of atoms and molecules to perform memory and processing tasks. Quantum computers have the potential to perform certain calculations billions of times faster than any silicon-based computer

How Quantum Computers Will Work

by Kevin Bonsor

I find Jibu and Yasue's perspective quite appealing. Rather than throwing out all we have learned about neural networks, in this view, we must merely accept that there are parallel quantum systems, working together with neural networks to create thought. In terms of Edelman's theory, we need not reject the idea of Neural Darwinism -- we must merely accept that these populations of neuronal maps have a quantum aspect as well as a classical aspect. In other words, the brain is an evolving population of quantum neural networks, selected and mutated based on their functionality in regard to their interaction with perceptual and motor systems, as determined by needs of the organism. Edelman, plus Jibu and Yasue, equals the brain as an EQC.

But what is EQC all about? The idea is a very, very simple one. Instead of programming a quantum computer, set up an ensemble of quantum computers, and allow them to evolve. Create criteria for judging QC's, and then, in the manner of natural selection, allow successful QC's to survive and (probabilistically) mutate and combine to form new candidate QC's, whereas unsuccessful QC's perish. The result is that one has quantum computers fulfilling desired functions via unknown means.

The neural wave function enfolds superposed possibilities, and then consciousness chooses one classical branch and annihilates the others. The choice is "unruly," Stapp (1993, p.32) says, "not individually controlled by any known law of physics." So the heart of consciousness is random on Stapp's view. He hopes that some future physics will find a law (1993, p.216), but it certainly looks like barring an enormous revolution in quantum physics, Stapp has installed chance deep in his theoretical framework, where the quantum choices associated with conscious events take place:

Yasue's Quantum Brain Dynamics3.1 The brain is remarkable in that it provides a variety of substrates for quantum fields. Different brain substrates for quantum fields have different functions. The sensory quantum field, for example, supervenes on oscillating biomolecules of high dipole moment in the neuronal membrane. When the pumping rate reaches a critical value, Froehlich condensation occurs with macroscopic coherence of quanta (Froehlich, 1968).

3.2 Another quantum field-supporting biosubstrate is a dense nanolevel web of protein molecules which penetrates neuronal and neuroglial membrane boundaries. I call this filamentous web the "nanolevel neuropil." Inside the neuron the nanolevel neuropil consists not only of microtubules but also neurofibrils and other structures which connect via protein strands to proteins floating in the cell membrane. Outside the neuron in the synaptic cleft is the extracellular matrix of collagen and glyco-conjugates, which are also connected to membrane proteins, so that a pervasive web is formed.

3.3 There are quasi-crystalline water molecules within the microtubules and associated with hydrophylic regions on the web

of protein fila- ments. This ordered water is yet another brain biosubstrate for a quantum field which supports super-radiance and self-induced trans- parency within the microtubules (Jibu et al, 1994).

3.4 Jibu and Yasue (1992, 1993) have proposed, following some earlier suggestions by Umezawa (e.g. Ricciardi & Umezawa, 1967), that vacuum states of this water rotational field record memory. I have suggested that the function of the nanolevel neuropil is cognitive (Globus, 1995).

3.5 There is a fourth quantum field substrate where an interaction takes place between the sensory quantum field and the cognition/memory quantum field. This is a plasma of charged particles interacting with the electromagnetic field. The structure of this bio-plasma is peculiar: it is divided into two very thin layers separated by a permeable membrane. Membrane channels open and close, and ions rush back and forth between the two layers down electrical and chemical gradients. It is in this perimembranous bioplasma, whose state is given by the ionic density distribution, that sensory and cognition/memory quantum fields interact. In this interaction of quantum fields, classical orders may be formed (as when the multiplication of complex conjugates gives a real number).

An evolutionary quantum computer (EQC) is a physical system that maintains an internal ensemble of macroscopic "quantum subsystems" manifesting significant quantum indeterminacy, with the property that the of quantum subsystems is continually changing in such a way as to optimize some measure of the emergent patterns between the system and its environment. It seems probable that the brain is an EQC, and that electronic EQC dissimilar to the brain can also be constructed; a speculative design in this regard is described, called QELA (Quantum Evolving Logic Array), involving Superconducting Quantum Interference Devices interfacing with re-configurable Field Programmable Logic Arrays. EQC has interesting implications for a quantum pan psychic view of consciousness: it provides an explanation of why, if everything is conscious to some extent, the human brain is so much more conscious than most other systems. The explanation is that, via EQC, the brain is able to maintain significant quantum randomness ("raw awareness") in a way that is correlated with its structure and behavior. Only EQC provides this kind of correlation, because only EQC allows uncollapsed quantum systems to interact significantly with the wave-function-collapsed, classical everyday world. In many- worlds-terms, EQC allows systems with a broad span over the range of possible universes to interact significantly with systems existing in narrow regions of universe-space.

4. U/Y v. H/S

4.1 The conception of the brain is far richer in U/Y than H/S; for U/Y, the brain generates second order quantum fields. A Geiger counter or Schroedinger's cat box has a quantum field description (as a Bogoliubov transformation of the quantized field) but such ordinary measurement devices do not sustain quantum fields like the brain does. So reality is described by wave functions, both microscopic and macroscopic, and among those macroscopic realities are well- developed human brains which themselves sustain quantum fields and their interactions.

4.2 We should not think of these second order quantum fields as making measurements but as offering possibilities to the match. Both sensory input and cognition/memory participate in the evolution of the state variable by offering possibilities to the match, but the latter is far richer than the former. I have previously called this rich quantum plenum of superposed possibilities the "holoworld" (Globus, 1987) and suggested that the probabilities of the various possibilities are tuned (Globus, 1995). The more limited possibilities of sensory input continually interact with the tuned holoworld, and a classical order continually unfolds in the perimembranous bioplasma.

4.3 So instead of a measurement collapsing the wave function of a quantum field to a classical order, we have a match between quantum cognition/memory and quantum reality, a match in which classical order is unfolded.

Surprisingly enough, one can argue that this is a viable model of brain dynamics. Edelman, with his theory of neuronal group selection, has already made a strong case for the brain as an evolutionary system. And Jibu and Yasue have made a good case for the brain as a macroscopic quantum system. Putting these two together, we obtain a strikingly solid case for the brain as an EQC. The EQC explanation of why the human brain is so acutely conscious then fits right in.

In order to see that is the inversion about average,

consider what happens when acts on an arbitrary

vector . Expressing D as , it follows that:

. By the discussion

above, each component of the vector is A where A is

the average of all components of the vector . Therefore

the ith component of the vector is given by

which can be written as

which is precisely the inversion about averag