Possibility of High Performance Quantum Computation by using Evanescent Photons in Living Systems

Transcription

1 OnLine Journal of Biological Sciences 8 (1): 1-14, 8 ISSN Science Publications Possibility of Hig Performance Quantum Computation by using Evanescent Potons in Living Systems Takaaki Musa MRI, , Namiki, Kanazwa-ku, Yokoama 36-5 Japan Abstract: Penrose and Hameroff suggested tat microtubles in living systems functioned as quantum computers by utilizing evanescent potons. On te basis of te teorem tat te evanescent poton is a superluminal particle, te possibility of ig performance computation in living systems as been studied. From te teoretical analysis, it is sown tat te living system can acieve large quantum bits computation compared wit te conventional processors. Key words: Microtuble, Quantum computation, Tunneling poton INTRODUCTION Penrose and Hameroff suggested tat microtubles in living systems functioned as quantum computers, wit tublin proteins in macrotubles acting as quantum bits of computation [1]. Georgiev as supposed tat mind is a macroscopic quantum wave governing te dynamics of quantum coerent cytoskeletal protein system inside te cytoplasm of te brain cortical neurons []. Te cytoskeletal protein conformational states are entangled and condensation of evanescent (tunneling) potons emitted by te ordered water tat forms coerent domains in its interaction wit te local electromagnetic field. Georgiev pointed out tat created evanescent potons ave negative energy and are sown to be capable of realizing group velocity faster tan ligt velocity in vacuum. It was also proposed by [3-5] tat te conscious process in te brain is related wit te macroscopic condensates of massive evanescent potons generated by te Higgs mecanism. Tey claimed tat uman consciousness can be understand as arising from tose creation-anniilation dynamics of a finite number of evanescent potons in te brain. In tis article, te autor studies te possibility of muc iger performance of computation in microtubles of living systems, wic utilize evanescent potons compared wit solid state computer systems. Te possibility of faster-tan-ligt speed in te quantum region witin mictotubles: E. Recami claimed in is study [6] tat tunneling potons traveling in an evanescent mode can move wit superluminal group speed. Te evanescent poton generated in macroscopic domain of te dynamically ordered structure of water satisfies te following Klein-Goldon equation given by: 1 1 mc A(x,t) = c t (1) Tis equation as te solution for te poton traveling in an evanescent mode sown as: Et + px A(x, t) = exp - () wic corresponds to te superluminal elementary particle of an imaginary mass satisfying E = p c - m c 4. By te Faster-Tan-Ligt (FTL) property of evanescent potons, te iger capability of computation by living systems is sown as follows. Uncertainty principle for te superluminal elementary particle: From relativistic equations of energy and momentum of te moving particle, sown as: and mc E = (3) 1-v / c p = 1 v /c we obtain te relation given by p /v= E/c. From wic, we ave: (4) v p p v E = (5) v c

2 OnLine J. Biol. Sci., 8 (1): 1-14, 8 Supposing tat v/v, Eq. 5 can be simplified as: v p E (6) c Tis relation is valid for te superluminal particle, wic energy and te momentum can be sown respectively as: and E = mc (7) perform computation satisfy te relation E E, were E is a minimum averaged energy required to perform computation and E is an uncertainty of energy to perform computation. Ten we ave: E / t (11) were t is a operational time of an elementary logical operation. Instead of te logical gate using particles moving at subluminal speed including potons, energy required for te quantum tunneling poton logical gate becomes: p = (8) β ( β 1) t E (1) were m is an absolute value of te rest mass for te superluminal particle. According to M. Park and Y. Park, te uncertainty relation for te superluminal particle can be given by [7]. p t v v (9) were v and v are te velocities of a superluminal particle before and after te measurement and is te Plank constant divided by π. From Eq. 6 and 9 can be rewritten as: E t ββ ( 1) wen we let v = c, were β = v/c. (1) Energy cost for te quantum tunneling poton computation: R. Feynman discussed te possibility of a quantum computer tat computational energy cost versus speed is limited by energy dissipation during computation by taking an example of reversible computing [8]. According to is idea, te computational speed is limited by minimum energy required to transport a bit of information irreversibly between two devices. Benioff sowed tat te computational speed is close to te limit by te time-energy uncertainty principle [9]. Margolus and Levitin ave also sown tat te number of elementary operations tat a pysical system can perform per second is limited by E / π, were E is an averaged energy to perform computation [1]. From wic te minimum energy to 11 As an uncertainty in te momentum of tunneling potons moving at te superluminal speed can be given by: p = ω c (13) were m is an absolute value of te mass for te tunneling poton moving at superluminal speed and ω is an angular frequency of te poton, te velocity of te tunneling poton can be estimated as [11]. v c 1+ 1 ω t (14) If we let te tunneling distance be d, te time for a poton tunneling troug te barrier can be rougly estimated as by t = d/v. Ten te velocity of te tunneling poton can be given by: c c c v c ω d ω d 4 ω d (15) If T is te relaxation time of a single qubit and t is te operation time of a single logical gate, te figure of merit of te computation can be defined as R = T/ t, wic is te number of qubits times te number of gate operations. As a superposition state of te L-qubits system would decoerence approximately L times faster tan te superpotition state of one qubit [1], ten te relaxation time of te L-qubits system can be rougly estimated to be L times te relaxation time of a single

3 qubit computation. Tus te minimum energy required to perform quantum computation for te L-qubits system can be given from Eq. 11 as: OnLine J. Biol. Sci., 8 (1): 1-14, 8 ν L E T G L (16) were ν G is te number of gate operations. Similar to tis equation, te minimum energy required to perform quantum computation utilizing superluminal particle can be estimated from Eq. 1 as: ν L ββ ( 1)T G L E (17) Supposing tat E = E, an increase of qubit size to perform computation by superluminal evanescent poton compared wit te conventional computation can be given by: Fig. 1: Cytoskelton of biological cells, including neurons of te brain log [ ββ ( 1)] (18) + L 1 1/Llog wen satisfying L<L, were: 1 c c c β ω d ω d 4 ω d (19) Possibility of ig performance computation in te biological brain: Te cytoskelton of biological cells, including neurons of te brain, is made up of microtubles as sown in Fig. 1 [13]. Te uman brain contains about 1 18 tublins. Eac microtuble is a ollow cylindrical tube of tublin proteins, wic outer core diameter is 5 nm, as sown in Fig.. Hameroff and Tuszynski proposed tat microtuble subunit tublins undergo coerent excitations, wic leads to te automatic sequence were quantum coerence superposition is emerged in certain tublins and consciousness is occurred as sown in Fig. 3 [1]. According to teir ypotesis of quantum brain, microtuble quantum states link to tose of oter neurons by quantum coerent potons tunneling troug membranes in biological systems functioning in a way resembled as an ion trap computers. In te infra-red spectrum region, evanescent potons tey would propagate losslessly in a microtubule as sown in Fig. 4. From Eq. 18 and 19, an increase of qubit size to perform computation by te evanescent poton compared wit te conventional computation, wen Fig. : Hollow cylindrical tube of tublin proteins satisfying L<L, can be obtained as sown in Fig. 5 at te wavelengt in te infra-red region, wen we let d 15 nm, wic is of te same order as te extracellular space between te brain cells. From wic, it is seen tat te biological brain as te possibility to perform ig efficient computation up to qubits more tan conventional silicon processors for te infrared ligt, wic wavelengt is λ = 1µm, wit te same energy dissipation. 1

4 OnLine J. Biol. Sci., 8 (1): 1-14, 8 Hence it can be considered tat quantum states preserved in microtubules by te superluminal potons attain ig efficient computation compared wit te silicon processors. CONCLUSION Fig. 3: Scematic diagram of quantum computation conducted in a tuble On te basis of te teorem tat te evanescent poton is a superluminal particle, te possibility of ig performance computation in living systems as been studied. From te teoretical analysis, it is sown tat te biological brain as te possibility to acieve large quantum bits computation compared wit te conventional processors. Tus it is considered tat te uman brain as te possibility to attain ig efficient computation process compared wit silicon processors. REFERENCES (a) Structure of te centriole cylinder b) Waveguide of visible and infra-red ligt in te centriole cylinder Fig. 4: Structure of centriole cylinder comprised of nine microtuble triplets(a) and possible waveguide including visible and infra-red ligt (B) Fig. 5: Increase of quantum bits for quantum computation at te infrared spectrum region 1. Hameroff, S. and Penrose, R., Towards a Science of Consciousness - Te First Tucson Discussion and Debate, eds. Hameroff,S.R, Kaszniak, A.W. and Scott,A.C., MIT Press, Cambridge, MA: Georgiev, D.D., 3. On te dynamic timescale of mind-brain interaction, Proceedings of Quantum Mind II: Consciousness, Quantum Pysics and te Brain, Marc, Te Convention Center, Tucson, Arizona, ttp://cogprints.org/4463/. 3. Jibu, M. and K. Yasue, Wat is mind? Quantum field teory of evanescent potons in brain as quantum teory of consciousness. Informatica, 1: Jibu, M., K. Yasue and S. Agan, Evanescent (tunneling) poton and cellular vision. BioSystem, 4: Jibu, M., K.H. Pribram and K. Yasue, From conscious experience to memory storage and ritrieval: Te role of quantum brain dynamics and boson condensation of evanescent potons. Int. J. Modern Pys. B, 1: Recami, E., 1. A bird s-eye view of te experimental status-of-te-art for superluminal motions, Found. of Pys. 31: Park, M. and Y. Park, On te foundation of te relativistic dynamics wit te tacyon. Nuovo Cimento, 111: Feynman, R.P., Feynman Lectures on Computation. First edition, Penguin Books, London. 13

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