Quantum Neural Information Processing

Here the premise is that the brain is the role model for the computer, and not vice versa!

The criterion therefore concerns such alternative models as can be experimentally validated against the actual fact of, say, neurophysiology and cognition, so as to provide sound mathematical, physical, chemical, etc, explanations of why the morphology and dynamics, of brain, neuron, or biological system are the way they are.

Sharpening the Focus

A good starting point is therefore neural net models. These models are based on the successful concept, pioneered by Hebb, of the biological synapse/neuron as a weighting function. It is a concept which, since the work of Hopfield in the early eighties, has advanced the computational understanding of the learning process and of the means to solve NP complete problems (such as the travelling salesman), which, as far as is known, are no longer open to algorithmic solution as the size of the problem grows, because of their complexity, but might be, if a successful analogue neural net technology, such as exists in biological systems, were realized.

The Proposed Generalization

The effectiveness of quantum, as compared to digital algorithms, and evidence cited below, therefore suggests that spin as the continuous spectrum of values between zero and one, with the alternative interpretation of a weighting function appropriate to neural nets, should become the Cybernetic Machine Group's principal focus for 1999. For the behaviour of spin relative to a reference spin, as quantum entanglement, implies quantum parallelism, ie a superposition of all weighting possibilities simultaneously, generalizing the concept of the artificial neural net. It can thus be postulated, that if such quantum neural network models as learning systems, can be devised providing an understanding of their actual physics, then the key to new technology, by means of which NP complete problems can be solved, will be to hand.
The Evidence for such a Generalization

Such a generalization of a neural network, is, in principle, as Perus¹ has shown, a highly valid concept, since the two formalisms can be set down in identical ways so as to express their properties, except that the neural net formalism concerns real quantities, while the quantum systems formalism concerns complex quantities. Weights, taking values from 0 to 1, the key to understanding traditional neural nets, therefore become complex quantities, expressible through unit vectors(spins) in terms of phase. Wave properties and considerations of phase, could therefore contribute additional structure and understanding, both to how neural net parallelism works, and to an explanation of the basis of the technology by means of which this can be achieved. One can then ask, do such considerations provide a better explanation of actual neuron dynamics and morphology, and if so, attempt experimental validation advancing biological understanding.

What therefore is the evidence?

1. It is well known that even simple animals with very few neurons, like nematode worms, exhibit complex behaviours, showing that actual neurons have much more complex information processing capabilities, than their current artificial neural net counterparts,



2. The weighting strategies, successfully applied in existing neural nets, are often based on actual physical mechanisms; for example, simulated annealing, the Sherrington - Kirkpatrick model² of interacting spins, the Cooper/Nestor Corporation model³ of Coulomb energy interaction of charges, etc, ie classical physical behaviours. These suggest the possibility of various nanotechnological and nanobiological analogue mechanisms for neural nets, extendable to their quantum mechanical counterparts.



3. Extended models of neurons postulating such additional information processing capabilities and mechanisms by means of which components of neurons, such as dendrites, the principal dendrite, the neuron surface, entropic holes(Maxwell demons) in the surface of the neuron, the neural body, the axon and the synapse and the synaptic interior could all function, already exist^4,5,6,7,8



4. These extended models imply that actual individual neurons, might, for example, use an actual configuration of interacting spins (as described in the Sherrington- Kirkpatrick model of a neural net); or charges (as in the Cooper/Nestor Corporation model); or a matrix of ions/occupation states as a quantum computational net as described by Deutsch⁹ (so as, for example, to emulate non-procedural programming using matrices and decision tables⁷) etc. Such hidden mechanism common to neural nodes, utilizing individual particles at the nanolevel to realize known successful weighting strategies, could explain, how an actual neuron combines many thousands of dendrite inputs at its neural node, and why actual synapses have a common generic morphology and dynamics to produce the synaptic gain across the synaptic cleft, so discriminating between neural node and synaptic functioning.



5. Such a neuron, and brain or network of such neurons (in relation to a particular weighting strategy or model) would therefore behave respectively as a) a neural net, and b) as what Rosen¹⁰ defines as an anticipatory system, containing a model of itself with a view to computing its present state, as a function of the prediction of the model, which Dubois¹¹ has shown is a methodology which facilitates the rapid interation of such a learning/adaptive system to the desired problem solution,



6. One such model of the neuron⁶ providing an explanation of all the basic physiological features of actual neurons listed in III above, is based on quantum holography⁵. Here, phase is not only the essential parameter of physical significance, as in the postulated model of quantum neural information processing, but the essential means by which holograms ie the 3 dimensional representations of objects maybe encoded, decoded or transmitted.
   The model⁶ describes the preparation and quantum measurement of a Quantum Hall system. Here, signal processing (described as a rotation in the ray space) takes place in a resonant cavity (the neuron body) as a consequence of the "squeezing" input signal pump action (of the principal dendrite). This results in advanced and retarded signals (in the axon) to an hexangonal lattice (the presynaptic vesicular grid), so that a single quantum (vesicle) is output probabilistically to provide the (synaptic) output gain, as quite remarkably happens in actual synapses across the synaptic cleft. Such an apparatus would be a multiple input, single output, phase gate/filter with memory, employing experimental techniques (current and proposed) for quantum information processing :-
   
   
   1. where the preparation (of the neuron) concerns the first stage of holographic encoding, so that wavelet mixing on the hologram plane (the neuron surface) between input radiation (from the active dentrites) and reference radiation (from the neuron body) produces a hologram, which manifests itself as a configuration of ions, and Maxwell demons. The entropic radiation (from the Maxwell demons) may also produce stochastic cooling during measurement, and
   
   
   
   2. where measurement, taking place by the radiative "squeezing" action of a second reference and pump beam(the principal dendrite), acts so as to :-
   
   
   
   1. complete the second stage of holographic encoding, and the inverse process of decoding on the surface. This takes the form of a multiplexing reference beam write and a demultiplexing reference beam read , updating the neuron memory (the dendrites), while
   
   
   
   2. in the resonant cavity (neuron body), all the signals from the memory (the dendrites) are simultaneously attentuated, except the closest to the new (dendritic) input. This is amplified and output (through the axon) to another resonant cavity (the synapse).
   
   
   
   That is, the neuron/dendrite memory is described as a general purpose adaptive filter bank/ spectrum of holograms respectively. The model, which utilises Maxwell demons in the neuron surface to create and destroy particle/occupation states, concerns trapped cooled ions in entangled states, where rotations in the quantum mechanical ray space described by the fundamental spectral theorem of Hilbert and Von Neumann, determine the required weightings, and where each hologram, a spectral line, defines a perspective of a three dimensional image, which can be encoded and decoded by means of a hologram plane (the neuron surface). It also strongly suggests that the 3 dimensional perception and cognition taking place in the brain, utilises the cortices as hologram planes.


7. The specification of quantum holography as signal processing based on the nilpotent Heisenberg Lie Group, as defined by Schempp^5,12, provides the mathematical foundations of magnetic resonance imaging¹³. Here quantum holography, produced by spin echo techniques, describes the resonant coupling of electromagnetic fields with the nuclear quantum spin populations of soft body tissues, so as to output a hologram of the required body slice image as in the form of a diffraction pattern, as is actually the case. This pattern is then converted by fast Fourier transform action to yield the body slice image displayed.



8. Further evidence of the experimental validity of the significance of quantum holography, is provided by its ability to correctly describe the quantum teleportation experiments of di Martini and Zeilinger groups¹⁴, as well MNR quantum computation as performed by Jones, Mosca and Hansen¹⁵ and the Quantum Hall effect¹⁶.

The Proposed Cybernetic Machine Group Programme

A) To establish an on-line network and database of all the relevant workers in the sphere of the groups new focus, together with scientific papers past, and present and of research being undertaken,

B) To hold an international symposium in Liege as part of CASYS'99 in August at the invitation of its organisers, asbl CHAOS, Dr. Ir. Daniel Dubois, with the objective of making the case for a further Pathfinder exercise and the importance of establishing a structured programme in relation to the new narrowed CMG focus with respect to :-

1. models of quantum neural information processing, and anticipatory systems



2. building actual quantum neural information processing testbeds and technology



3. quantum holography and its applications with respect to:-
   
   
   1. describing current experimental testbeds, such as quantum teleportation, NMR computation, quantum Hall effect, etc., and
   
   
   
   2. functional magnetic resonance imaging tomography, so as experimentally validate/demonstrate the width of the theory's applicability,


4. to further the understanding of information processing in biological systems such as DNA, neurons, living cells, brains, organisms etc with a view to how such processes as reproduction, cognition, perception, thought, etc may take place, using (a), (b) and (c) as the basis for this new understanding, as already begun in the research programme, outlined in "Wider Perspectives - Nature, Cognition and Quantum Physics", which follows this article, also see17.

The objective is to collect further evidence in the form of a body of sound research in an attempt, as to justify a further Pathfinder exercise to establish the case for a Network of Excellence, and a Further Structured Programme, of which the Wider Perspectives programme could be a part.

References

1. Perus M. (1996) Neuro-Quantum Paralleism in Brain-Mind and Computers, Informatica 20, 173-183.
2. Sherrington D. (1990) Spin glasses, Report OUTP-90-01S, University of Oxford, Oxford.
3. Cooper L. and Reilly D.L. (1987) Learning system architectures composed of multiple learning modules, in Proceedings of the 1st IEEE International Conference on Neural Nets, San Diego, California.
4. Jibu M. and Yasue J. (1993) Intracellular Quantum Signal Transfer in Umezawa's Quantum Brain Dynamics, Intern. J. Cybernetics and Systems, 24, 1-7.
5. Schempp W. (1993) see Wider Perspectives reference list 13.
6. Marcer P. and Schempp W. (1997) see Wider Perspectives reference list 11.
7. Marcer P. (1992) The Neuron : a Computational Model Utilizing Quantum Devices, Nanobiology 1, 289-291.
8. Clement B.E.P.,et al. (in press) The Brain as a Huygens Machine, Informatica.
9. Deutsch D. (1989) Quantum Computational Networks, Proc. Roy. Soc. Lond. A425, 73-90.
10. Rosen R. (1985) Anticipatory Systems, Pergamon Press.
11. Dubois D. M. (1998) Introduction to Computing Anticipatory Systems, Intern. J. of Computing Anticipatory Systems, 1, vol.2, 3-14.
12. Schempp W. (1986) see Wider Perspectives reference list 14.
13. Schempp W. (1998) see Wider Perspectives reference list 7.
14. Bouwmeester D. et al. (1997) see Wider Perspectives reference list 5.
15. Jones J. A. et al. (1998) see Wider Perspectives reference list 25.
16. Schempp W.(1998) (private communication) The Quantum Hall Effect.
17. Marcer P. (1998) A Quantum Leap to Advances in Pattern Recognition, Proc. Intern. Conference on Advances in Pattern Recognition, ICAPR'98, 23-25 Nov. Plymouth, UK, ed. Singh S., 375-384.