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This Concept Map, created with IHMC CmapTools, has information related to: Biosystem as topological quantum computer, BIOSYSTEM AS TOPOLOGICAL QUANTUM COMPUTER 2. 2-braids and genera- lization of TQC. a) Orbits of magnetic flux tubes in 4-D space- time are idealizable as string world sheets and can get 2-knotted and 2-braided. b) 2-braiding makes possible more general topological quantum computation (TQC). c) For 1-braiding basic gate corresponds to exchange of strands: strand a can go over b or below b. This defines a bit. d) For 2-braiding one has besides this vertex also reconnection: the strands can reconnect or not. This defines se- cond bit so that "cross- ing" is characterized by 2 bits. e) This allows genera- lized TQC based on ze- ro energy ontology (ZEO): basic structure is space-time surface, whose ends correspond to 3-surfaces defining braided flux tubes giving rise to 1-braids., BIOSYSTEM AS TOPOLOGICAL QUANTUM COMPUTER 3. DNA-cell membrane system as topological quantum computer. a) Several variants of TGD in question depending on whether the particles are quarks and antiquarks or electrons. b) Magnetic flux tubes representing braid strands connect DNA nucleotides to lipids of cell membrane. c) At the ends electrons or quarks and antiquarks. This could make sense in TGD since scaled variants of ordinary quarks are possible and might be im- portant in living matter. d) Time-like braiding cor- responds to the flow of 2-D liquid formed by lipids in liquid-crystal state. This flow could be induced by nerve pulse patterns. e) The space-like braiding is induced by the same flow since the ends of flux tubes at DNA nucleotides are fixed like threads connecting dancers to the wall., BIOSYSTEM AS TOPOLOGICAL QUANTUM COMPUTER 4. DNA-cell membrane TQC represents only one example. a) The proposal that flux tubes connect biomolecules to a kind of "Indra's net" means that the TQC could be automatically occurring at various hierarchy levels of the system. b) It could automatical- ly form memory repre- sentations about the mo- tion of system inducing space-like braidings. c) For instance, in the case of microtubules this procedure might be used for computational purposes. Now 2-braiding could define TQC. d) Flux tubes could form kind of 3-D coordinate grid with three tubes meeting at given node. This defines three planes and 2-D grid in each plane define time- like TQC. In each node 3 pairs of bits are needed what happens to the strands. This gives 6 bits: something do with the 6 bits of DNA codon?, BIOSYSTEM AS TOPOLOGICAL QUANTUM COMPUTER 1. e) Braiding statistics. The exchange operation for Dɮ corresponds to ± sign (Bose/Fermi sta- tistics). For Abelian anyons possible in D=2 because punctured pla- ne has non-trivial first homotopy group, braid statistics can corre- spond to a more general phase, and for non-Abe- lian anyons to matrix operation. f) TQC program corre- sponds to a unitary S- matrix constructed in terms of basic gate characterizing the basic braiding operation ex- changing the two braid strands. g) The unitary matrix defining TQC program defines time-like entang- lement in ZEO giving rise to density matrix which is proportional to unit matrix. The entangle- ment in question is ne- gentropic. h) In order to realize uni- tary S- matrix one must assign particles to the braid ends. Typically fer- mions belonging to the unitary representations of the group., BIOSYSTEM AS TOPOLOGICAL QUANTUM COMPUTER 1. Background concepts and ideas: a) The notion of mag- netic body consisting of flux tubes and sheets and carrying dark mat- ter as phases with large h_eff=n×h making pos- sible macroscopic quan- tum coherence. b) Knotting, linking and braiding of magnetic flux tubes in 3-space ideali- zable as strings. c) Dance metaphor. Dancers on 2-D parquet- te define time-like brai- ding in 3-D space-time. Each braiding pattern defines a TQC program. d) Imagine that the feet of dancers are fixed to a wall by threads. During dance the threads are geometrically enangled and define a representa- tion of the dance as spa- ce-like braiding in 3-space. Fundamental mechanism for memory representations.
