LOOKING FOR LOOKING FOR QUANTUM PROCESSES QUANTUM PROCESSES

IN NETWORKS OF IN NETWORKS OF HUMAN NEURONS ON HUMAN NEURONS ON

PRINTED CIRCUIT PRINTED CIRCUIT BOARDBOARD

R. Pizzi*, A. Fantasia*, F. Gelain°, D. Rossetti* & A. Vescovi°

*Dept of Information Technologies, University of Milan – Crema, Italy

° Stem Cells Research Institute, DIBIT S. Raffaele – Milano, Italy

Our GroupOur Group• The team: 3 physicists, 1 biologist, 1 electronic

engineer, 1 bioengineer, 3 computer scientists

• Virtual laboratory (3 IP videophones with videocamera connection) between the Living Networks Lab and the Stem Cells Research Institute

• The Stem Cells Research Institute is directed by Prof. Angelo Vescovi, who has pioneered the field of neural stem cells

• Recently he has described the capacity of neural stem cells to give rise to skeletal muscle and hemopoietic cells

The Stem CellsThe Stem Cells

• Stem cells are capable of both proliferation and differentation into specialized cells, that serve as a continuos source of new cells.

• Stem cells can be transplanted to create new healthy tissues.

• Using human neural stem cells allows to consider the possibility of really implantable neural devices.

• Human neural stem cells can build real living networks on artificial substrate

ObjectivesObjectives

• Looking for quantum processes in biological neurons

• Developing computational functionalities on living networks

• Understanding learning processes in biological neurons

• Comparing the activity of Artificial Networks with living networks having the same architecture

MaterialsMaterials

• Software (Delphi) interface for the input pattern set up and data acquisition

• Artificials Neural Networks software (Kohonen and Hopfield networks, Java source code)

• Quantum computing emulator (QuCalc on Mathematica®)

• Glass PCB with 100µm gold pads connected by thin nickel/gold wires

• DAQ acquisition module with 2 digital 8 bit channel output ports and 10 analog input ports

• Custom electronic circuit designed for maximum performance voltage in cells stimulation

The ExperimentsThe Experiments

Kohonen Hopfield

The ExperimentsThe Experiments

• Kohonen networks• Holographic Hopfield-

like networks• Non locality basins• Control basin (culture

medium)

The Kohonen NetworkThe Kohonen Network

• Analogy with neurobiological (cortical) structures

• Straightforward architecture

• Self-organization

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X1

Xn

Competitive layerInput layer

Kohonen network

Classification of Simple PatternsClassification of Simple Patterns

Signal AnalysisSignal AnalysisQUALITATIVE ANALYSIS

Culture medium before stimulation

Channel 1Channel 2Channel 3

Signal AnalysisSignal Analysis• The output corresponding to similar bitmaps take

similar values

Signal AnalysisSignal Analysis

• The “0” bitmap is given by the electrical values “11111111” but the neurons reply with low voltage values

Stimulation with the “0” bitmap

Signal AnalysisSignal Analysis

• The culture medium behaves as a conductor and replays to the “0” with higher values

Culture medium stimulated with “0” bitmap

Signal AnalysisSignal Analysis

• After the end of stimulation the cells keep signals different both each others and from the signals before the stimulation

Neural cells after stimulation

Recurrence Quantification AnalysisRecurrence Quantification Analysis

•Non linear analysis tool

•Temporal series recostructed with delay-time embedding

•Estimate of the distances between the series vectors

•Representation by means of Recurrent Plots

• Unorganized signal before the training

• Unorganized signal (in evolution )during the training

• Highly organized behavior during the presentation of a “learnt” pattern

• Highly organized behaviour after the end of stimulation

First ConclusionsFirst Conclusions

•After the end of stimulation the cells were healthy and alive.

•The cells reply to the presentation of organized pattern with electrically specific signals.

•Similar bitmaps produce similar signals without correlation with input voltages•The cell seem to be able to keep information after the end of stimulation.•High increase of self-organization in stimulate cells

The Classical Hopfield networkThe Classical Hopfield network

1. Fully interconnected network

2. Hebb-like learning

3. Isomorphic to general quantum equations

Classification of Simple PatternsClassification of Simple Patterns

Hopfield

network

The ExperimentThe Experiment• Network training with 50 sequences of all the possibile “1” and “0” patterns (frequency 40 Hz)

• Presentation of the “1” pattern, 50 lectures

• Presentation of the “0” pattern, 50 lectures

• Presentation of the “1” pattern affected by noise, 50 lectures

• Presentation of the “0” pattern affected by noise, 50 lectures

Signal AnalysisSignal Analysis

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During the training

Signal AnalysisSignal Analysis

• 50 presentations of pattern “0”

• 50 presentations of pattern “0” affected by noise

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Signal AnalysisSignal Analysis

• 50 presentations of pattern “1”

• 50 presentations of pattern “1” affected by noise

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Recurrence Quantification AnalysisRecurrence Quantification Analysis• Plot after presentation of pattern “0”

Channel 1 Channel 3

Recurrence Quantification AnalysisRecurrence Quantification Analysis• Plot after presentation of pattern “1”

Channel 1 Channel 3

Preliminary ResultsPreliminary Results

• The network answers in a selective way to different patterns

• Similar patterns give rise to similar answers

Preliminary ResultsPreliminary Results

• Organized behavior with respect to presentation of different patterns

• High determinism of signals depending on the neuron channel and the presented pattern

Preliminary ResultsPreliminary Results

• The living network can “codify” the patterns

• The distribution of the 50 + 50 outputs to compare quantum and classical behaviour is underway

• “On-the-fly” analysis shows irregularities in the reply to the same pattern: a quantum effect ?

Quantum Network Quantum Network

• We are developing an artificial quantum neural network to see if it could be a better model for the behaviour of real cells.

• Neurons are represented by qu-bits.

• Unitary evolution is achieved by a sequence of local 2-qubit unitary evolutions acting on randomly choosen couples of neurons.

Quantum Network Quantum Network • After k 2-qubit unitary evolutions the state of

the network is a classical state obtained after a “wave collapse” of the global quantum state.

• Learning in this model is achieved by modifying the complex parameters that regulate quantum interaction between neurons.

• The model enables the possibility of quantum tunneling between different energy levels.

Quantum NetworkQuantum Network

Unitary Evolutions on the 2 qubit space

generates

entangled global state

Random choice

of two qubits

Dynamics:

Unitary evolution Wave collapsek times

Quantum tunneling in neural Quantum tunneling in neural networksnetworks

• Classical Boltzmann machines introduce thermal noise to avoid system to be trapped in local minima

• The path climbs the slope of the energy gap between 2 minima

• Quantum tunneling in quantum networks allows to reach the minima passing through the energy gap

• This method allows faster computation in finding global minimum

• The computation is robust against noise and decoherence

Quantum tunneling in the quantum Quantum tunneling in the quantum neural networkneural network

Energy level

Configurations space

Classical stochastic networks

Quantum Tunneling

Testing quantum non-local Testing quantum non-local correlations in neuronscorrelations in neurons

• We tried to test if EPR-like correlations may exist in neurons

• EPR correlations between two systems A,B are of the kind

|0A0B>+|1A1B>

i.e. the whole system is in a superposition of two state |0A0B> , |1A1B>

• In every state the two systems A,B present statistical correlations.

Non Locality ExperimentNon Locality Experiment

• Two dishes electrically connected

• 50 light stimulations with 466 n LED (near UV band)

• 50 electrical stimulations (40 Hz)

• Then separated and electrically insulated

The MeasuresThe Measures

• Signals crosscorrelation before stimulations:

• Signals crosscorrelation after

electrical stimulation:

• Signals coherence after electrical stimulation:

• Signal crosscorrelation after LED

stimulation:

0.304

0.184

0.47

-0.484

• Signals coherence after LED stimulation:

0.80

Experimental resultsExperimental results

• The best correlations between systems A,B

have been obtained with light stimulation

directed only to system A.

• This doesn’t necessarily mean that EPR

correlations are present in neurons.

• It could be explained by some kind of

communication between separated neurons.

• More experiments are needed to formulate

theoretical explanations.

ConsiderationsConsiderations

•The extremely low energy could have avoided dechoerence processes

•Reaction to LED stimulation cannot be caused by electrical interference between basins

•The “multipower” of stem cells (even potential retinal cells) could be a reason for reaction

•LED stimulations should not affect the signals

Future DevelopmentsFuture Developments

• Accurate analysis of signals (non linear analysis, ANN analysis)

• Further experiments to validate the previous ones

• Accomplishment of the quantum formalism for the network training

• More complex living networks to perform more complex tasks