A State of the Art Report on the Physical Foundations of Quantum Information and Computing

From the Cybernetic Machine Specialist Group

"Let no one ignorant of geometry enter here."
The inscription to Plato's Academy

From Peter J. Marcer, chairman, dated 18/06/01

Introduction

The Group has been the Society's forum for the Physical Foundations of Computation since 1986.
In that year, David Deutsch gave the Group's inaugural lecture on the quantum theory of computation[1], published by him in the Royal Society Proceedings a year early. It says, as experiment has subsequently shown, that quantum physics provides new physical resources and means by which to compute. For example, qubits, the mapping of bits onto quanta of energy and angular momentum allows quantum parallelism. This ability of qubits to 'register' both 1 and 0 at the same time, would therefore (as has been shown theoretically) speed up a variety of computations thought impractical classically, including, Shor[2] showed, the factoring of very large numbers important in decryption. It may also even extend the very notion of what is computable (eg to topological (non-commutable) computation, since quantum theory concerns the physics of knots). The fact, that quantum computation, a physical theory, replaces the mathematical/Turing theory as the correct one, is one even now, which few scientists and computer practitioners have taken on board. The principle subject of the Group's annual programmes therefore concerns this fundamental paradigm change in science and computing.

The European Pathfinder Project

In 1998, the successful European Pathfinder Project, which the Group and the Society helped initiate, led to a substantial programme of EEC funding for academia for research into qubit quantum computing. The Group therefore decided that because members can now closely follow the developments in qubit computing in academia worldwide by connecting to the homepages of the Oxford University Centre for Quantum Computation,[www.qubit.org/], that it should concentrate its limited resources into the frontiers of computation, on what had become over the years its main interest. This is "Can quantum information processing explain how brains work?" For, as Perus[3], for example, has shown, the neural net and the quantum systems formalisms are epistemologically identical, except they concern mathematically real and complex quantities respectively. These formalisms therefore differ only in the fact that quantum theory explicitly concerns complex amplitudes defining a wave mechanics capable, in principle, of describing the holographic physical informational encoding/decoding of the 3 dimensional geometry of real objects. That is to say, geometrical, physical and not logical, mathematical representions, are proposed as the sine qua non of how brains really work; a proposal that would have been favoured for the last 2000 years since the time of Plato, until the rise, over the last fifty years, of digital computation. Is this therefore the nature of the paradigm change in science and information processing which Deutsch's quantum theory previews? The fact that geometry in quantum theory can, indeed, also be used to implement logic says yes [4] !

The Brain, a Quantum Physical Geometric Apparatus, the Living, Evolved Engineered Proof that Chemically Based Carbon Analogue Computation Does Work!

"So, fundamental theoretical chemistry is really (quantum) physics." Richard Feynman
Remarkably this Group interest also began in 1986 with the publication in the Royal Society Proceedings of another seminal paper, this time by the Noble Prize winning neurophysiologist, Sir John Eccles, who spoke to a joint meeting of the Group and the British Cybernetic Society at their Denis Gabor Memorial Lecture at King's College in 1989. In this paper [5], Sir John is prompted to hypothesize, on the basis of the experimental neurophysiological and neuropsychological evidence (described in his paper), "Do mental events cause neural events analogously to the probability fields of quantum mechanics?". It is a postulate in line with the belief held by many members of the Group, that human brains are vastly more versatile, competent, and efficient than the artificial intelligence of digital computers, and so are the role model for computation, and not vice verse. The leading question is therefore "Can quantum mechanics explain why the information processing geometry and dynamics of human brains and other biological systems are so different from any of the computing architectures we understand? [6]".

Deutsch's discovery and Eccles hypothesis could thus open up some of the most fundamental questions of our time, not only about how to compute, but of how brains work , of the nature of consciousness, mind and the self, of how these might be quantum mechanically engineered, etc; and just as remarkably about the nature of proof, itself. For from the viewpoint of physics, the brain is the living, engineered proof that chemically carbon-based analogue computation does work, and that consciousness and a science of consciousness exist! That is, the only valid proofs are now "physically quantum mechanically engineered solutions" ie actual apparatus, be they man-made or biologically evolved, which demonstrate the quantum physical process in question, as mathematically described. Such proofs therefore extend to include physical mechanisms like quantum teleportation [7], which concern information transfer protocols that no digital computer can employ.

It is therefore on this biological frontier of information processing, that the Group is now concentrating its investigations and programme, the success of which is regularly reported in its homepages. These investigations show

(a) that while qubit computing research concentrates on the discrete/particle observable properties of quantum mechanical systems, usually taken to concern the eigenvalues of quantum mechanical operators, (b) that (i) quantum (rather than thermodynamically) optimally controlled chemistry[8,9] likely appropriate to the brain/organism's chemically based computation, and (ii) quantum mechanical neural information processing in brains are both much more likely to involve observable gauge invariant phases of the quantum state vector, known as the Berry/geometric phase [10], and therefore some quantum mechanical formulation of holography, where phase is the essential quantity of physical significance.

Indeed effective technology from the ANDcorporation (www.ANDcorporation.com), for example, for face pattern recognition, based on one such phase formulation is already being marketed. It employs digital technology simulating phase (rather the bit) gates. Another is Schempp's quantum holography[11,12] based on the 3 dimensional Heisenberg Lie group, the topological mathematical foundations of which describe the realisable quantum mechanical controls in production use in medical diagnosic systems, such as provide magnetic resonance imaging (MRI) of 2D brain/body slices and 3D microscopy, see http://www.civm.mc.duke.edu. These medical tools are a culmination of the discovery in magnetic resonance spectroscopy, of the possibility of quantum mechanical control by Erwin Hahn some 50 years ago[12]! Such control is thus a factual possibility intuitively in conflict apparently with the usual physics community's lay presentations of quantum mechanics based on Heisenberg's so-called Uncertainty Principle. But one resolved in Schempp's quantum holography describing MRI, which has also been shown to explain the principle features of the brain's information processing geometry and dynamics[6]. In this quantum holographic model of the brain, such controls relate to the fact, in respect to any kind of illumination arriving at the senses, that the sensory data consists of both local phase and amplitude information. Such data is therefore, this generalised holography shows, sufficient to the immediate full 3D spatial wavefront reconstruction (and subsequent filtering) of the whole of the 3D object images carried in the illumination (following that illumination's incidence with those objects). Thus it makes no evolutionary sense, whatsoever, for a biological sensory apparatus (working in a 3D spatial environment) not to use every aspect of the sensory data including these local amplitudes and phases for the immediate 3D reconstruction of images, be these visual, acoustic, or whatsoever. For if it's brain (including such sensory apparatus) did not do so, it would, by throwing away essential information on which its fitness for survival depends, put its organism at risk. And, as MRI proves, this is no less true in quantum holography than it is in classical holography; - a concept pioneered in quantum mechanics as early as 1934, by Haldane, who before the discovery of holography, intuited that the full-fledged de Broglie wave (with frequency, wavelength, amplitude and phase) was involved in all phenomena in the universe! The details of such approaches can be found in the number and content of the papers presented at the BCSCMsG International Symposium held now annually in Liege, Belguim as part of the International Conference on Computing Anticipatory Systems CASYS, and which papers are published in either the American Insitute of Physics Conference Proceedings, or the International Journal of Computing Anticipatory Systems. Such holographic models, (first conceptualised and developed, on the basis of his experimental findings by the well known Stanford neurophysiologist Karl Pribram [13]) now include those of DNA[14], of the prokaryote cell[15], as well as of the brain/mind system[16] and of the full neuron structure[16]. The latter includes the dendrites, axon, and the synaptic bouton with its hexagonal presynaptic vesicular grid which, on neural firing, releases a single synaptic vesicle probabilistically across the synaptic cleft to provide the synaptic gain [5,6,11]; an incredible evolutionary feature of the working of the human neuron, which helped lead Eccles to his hypothesis, and one which quantum holography predicts[6]! Furthermore, quantum holography describes the mathematical lattice rescaling procedure fundamental to Wilson's renormalization group methodology [17] for the calculation of material phase transitions, such as those between liquid and solid etc, which govern all the properties of matter.

This universal methodology for the calculation of stable and unstable critical fixed points (ie attractors) for which Wilson was awarded the 1982 Nobel Prize, therefore not only shows that quantum mechanical effects at atomic scales in upto 4 dimensions [17] govern the macroscopic properties of all materials, ie their nomena and qualia, in the neighbourhood of these calculable critical fixed points, but to the fact that under these circumstances:-

(a) that Tegmark's recent well publized calculations [18] supposedly proving that the quantum mechanical effects only concern atomic scales, are false under the special circumstances Wilson's theory supposes, and
(b) that a wholly quantum mechanical cosmos [19]evolving by symmetry breaking [17] through the set of critical unstable time reversal symmetric fixed points (now being actively researched[20]) can be postulated.

References

1. Deutsch D. 1985, Quantum Theory, The Church-Turing principle and the universal quantum computer, Proceedings Royal Society of London, A400, 97-117.
2. Shor P. 1994, Proceedings of the 35th Annual Conference on Foundations of Computer Science, Goldwasser S.editor, IEEE Computer Society, Los Alamitos, CA, 124-134.
3. Perus M.1996, Neuro-Quantum Parallelism in Brain-Mind and Computers, Informatica 20, 173-183.
4. Lloyd. S. 2001, Computation from Geometry, Science 292, 1st June, 1669.
5. Eccles J. 1986 Do Mental Events Cause Neural Events Analogously To The Probability Fields Of Quantum Mechanics? Proceedings Royal Society London, B227, 411-428. see also, 1989, The Evolution of the Brain, and the Creation of the Self, Springer Verlag, London.
6. Marcer P. and Mitchell E, 2001, What is Consciousness? The Physical Nature of Consciousness, Van Loocke P. editor, John Benjamins, Amsterdam.
7. Sudbery T.,1997, The Fastest Way from A to B., Nature, 390, 11th December,551-552; also Binz E., Schempp W. 1999, Quantum Teleportation and Spin Echo, Unitary Symplectic Spinor Approach. In. Aspects of Complex Analysis, Differential Geometry, Mathematical Physics and Applications, Dimiev S. Sekigawa K. editors, World Scientific, 314-365.
8. Rice S.A. 1992, New Ideas for Guiding the Evolution of a Quantum System, Science, 258, 16th October, 4 12-413.
9. Leichtle C. and Schleich W.P., Averbukh I.Sh. and Shapiro M. 1998, Quantum State Holography, Physics Review Letters 80, 7, 1418-1421.
10. Resta R., 1997, Polarization as a Berry Phase,(The Berry Phase), Europhysics News, 28,19; also
Berry M. V., 1989, The Geometric Phase, Scientific American, December, 26-32.
11. Schempp W. 1992, Quantum holography and Neurocomputer Architectures, J. of Mathematical Imaging and Vision, 2, 279-326.
12. Binz E. Schempp W. 2000, Creating Magnetic Resonance Images, Proceedings CASYS '99, International Journal of Computing Anticipatory Systems, 7, 223-232; also, Schempp W. 1998, Magnetic Resonance Imaging, Mathematical Foundations and Applications, John Wiley, New York; (and Schempp W. 1986, Harmonic Analysis on the Heisenberg Group with Applications in Signal Theory, Pitman Notes in Mathematics Series, 14, Longman Scientific and Technical, London).
13. Pribram K.H. 1991, Brain and Perception; Holonomy and Structure in Figural Processing, Lawrence Eribaum Associates, New Jersey.
14. The DNA-wave Biocomputer, 2002, Gariaev P.et al. CASYS 2001 Proceedings, The International Journal of Computing Anticipatory Systems, Dubois D., editor. (in press); also Marcer P. and Schempp W., 1996, A Mathematically Specified Template For DNA And The Genetic Code, In Terms Of The Physically Realizable Processes Of Quantum Holography, Proceedings of the Greenwich Symposium on Living Computers, editors Fedorec A. and Marcer P., 45-62.
15. Marcer P. and Schempp W. 1998, The Model of the Prokaryote Cell as an Anticipatory System Working By Quantum Holography, Proceedings of the 1st International Conference CASYS' 97 On Computing Anticipatory Systems, Liege, Belgium, August 11-15, International Journal of Computing Anticipatory Systems, editor Dubois D. vol 2, 307-313.
16. Marcer P. and Schempp W. 1997, The Model of the Neuron Working by Quantum Holography, Informatica 21, 519-534; also Marcer P., Schempp W. 1998, The Brain as a Conscious System, International Journal of General Systems, 27, 1/3, 231-248.
17. Wilson G.K. 1982, The Nobel Prize in Physics, Science,218,19th November,763-764; also 1983, The Renormalization Group and Critical Phenomena, Reviews of Modern Physics, 55, 3, July, 583-599.
18. Tegmark M. 2000, The Importance of Quantum Decoherence in Brain Processes, Physics Review, E 61,4194-4208.
19. Marcer P, Quantum Millenium, Quantum Universe, Quantum Biosphere, Quantum Man, or What Physicists can Teach Biologists and Biology, Physics, Proceedings CASYS 2000, Vice-Presidential Introductory Preface, International Journal of Computing Anticipatory Systems, Dubois D.editor, (in press)
20. Marcer P. et al, Self-reference, the Dimensionality and Scale of Quantum Mechanical Effects, Critical Phenomena and Qualia ,to be presented at the BCSCMsG Symposium at CASYS 2001in Liege, 12-18th August.