DNA as a topological quantum computerFor years ago I developed a model of topological quantum computation combining TGD based view about spacetime with basic ideas about topological quantum computation and ended up with the proposal that DNA might act as a topological quantum computer. The first guess (see this) was that parallel DNA or RNA strands could form braids. The problem is that the number of braid strands is limited and the computations are restricted within single cell nucleus. The need to establish the hardware for each computation separately can be also seen as a restriction. One can imagine also other manners in which DNA or RNA could act as a topological quantum computer and it good to try to state clearly what one wants.
1. The recent progress in quantum TGD and TGD inspired quantum biology After the advent of the first model for topological quantum computation in TGD Universe (see this), the mathematical and physical understanding of TGD has developed dramatically and the earlier quite speculative picture can be replaced with a framework which leads to a rather unique view about topological quantum computations by DNA. 1.1 Universe as a topological quantum computer One can say that the recent formulation of quantum TGD states that the entire Universe behaves like a topological quantum computer. This notion of topological quantum computer differs however from the standard one in many respects.
The evolution of ideas related to quantum biology provides also new valuable insights. In particular, the notion of magnetic body leads to a model of living system in which dark matter at magnetic flux quanta of the field body of biological system uses biological body as a motor instrument and sensory receptor (see this). Quantum control would be naturally via the genome and sensory input would be from cell membrane containing all kinds of receptors. This would suggest that magnetic flux sheets traverse through DNA strands and cell membranes. The quantization of magnetic flux with unit defined by Planck constant having arbitrarily large values leads naturally to the notions of supergenome and hypergenome (see this). Supergenome would consists of DNA strands of separate nuclei belonging to single magnetic flux sheet and these sequences of genomes would be like lines of text at the page of book. Supergenomes in turn can combine to form text lines at the pages of a bigger book, I have used the term hypergenome. This hierarchy of genomes would give rise to a collective gene expression at the level of organs, individuals of a species, and at the collective level consisting of populations containing several species. Even biosphere could express itself coherently via all the genomes of the biosphere. The model of topological quantum computation performed by DNA should be consistent with this general picture. 2. Model for DNA based topological quantum computation The most promising model of DNA as topological quantum computer relies on the hierarchy of genomes. The flux sheets or collections of parallel flux tubes assignable to a magnetic body would traverse the DNA strands of several nuclei so that strands would be analogous to lines of text on the page of a book. DNA strands would define the intersections of magnetic or number theoretic braids with plane and braiding would be associated with with the magnetic field lines or flux tubes transversal to DNA. The Mmatrix defining topological quantum computation would act on quantum states assignable to nucleotides. 2.1 The interpretation of nucleotides The interpretation of the A,T,C,G degree of freedom is not obvious and one can consider several options. 1) The quantum numbers entangled by braids having nothing to do with (A,T,C,G) assignable to nucleotides and the braiding does not affect nucleotides. 2) The nucleotides (A,T,C,G) correspond to four different colors (a,t,c,g) for braid strands with conjugate nucleotides defining conjugate colors. The subgroup of allowed braidings would preserve the color patterns. The minimal assumption is that braid strands connect only identical nucleotides. A stronger  probably unrealistic  assumption is that braiding permutes nucleotides physically. 3) The entangled quantum numbers are in 11 correspondence with states A, T, C, G of nucleotide. In zero energy ontology this would be possible without breaking of fundamental conservation laws. One can even consider the possibility that A,T,C,G are these quantum numbers. Topological quantum computation in time direction would thus make it possible to replace the DNA strands with new ones and provide a purely quantal mechanism of genetic evolution. Only introns could be involved with topological quantum computations in this sense since they would not induce mutations visible at the level of aminoacids. The intronic portions of genome would not be evolutionary invariants: whether or not this is the case should be easily testable. 4) The combination of options 2) and 3) might make sense for topological quantum computations in time like direction. One would have superposition of topological quantum computations associated with various color patterns and the halting of the computation would mean in general the occurrence of a mutation. The option 2) with braid strands connecting only identical nucleotides is rather attractive since it explains several facts about genome (as do also options 3) and 4)).
One can imagine two basic realizations of topological quantum computation like processes or to be more precise  entanglement by braiding. In TGD framework this entanglement could be interpreted in terms of Connes tensor product. 1. Spacelike entanglement The first realization would rely spacelike braids. Braid strands would connect identical lines of text at the page of book defined by sequences of genomes of different nuclei. Inside nucleus the strands would connect DNA and its conjugate. The braiding operation would take place between lines. In this case it would be perhaps more appropriate to speak about quantum memory storage of a function realized as entanglement. These functions could represent various rules about the behavior of and survival in the physical world. For this option A,T,C,G cannot correspond to entangled quantum numbers and the interpretation as braid colors is natural. Braiding cannot correspond to a physical braiding of nucleotides so that (A,T,C,G) could correspond to braid color (strands would connect only identical nucleotides). Strands would not connect strand and its conjugate like hydrogen bonds do but would be like long flux lines of dipole field starting from nucleotide and ending to its conjugate so that braiding would emerge naturally. Color magnetic flux tube structures of almost atom size appear in the TGD based model of nucleus and have light quarks and antiquarks at their ends (see this). This could be the case also now since quarks and antiquarks appear also in the model of high T_{c} superconductivity which should be present also in living matter (see this). 2. Lightlike entanglement Second realization would rely on lightlike braids at the boundaries of lightlike 3surfaces connecting 2surfaces assignable to single genome at different moments of time. Braiding would be dynamical and dance metaphor would apply. The lightlike surface could intersect genomes only at initial and final moments and strands would connect only identical nucleotides. Lightlikeness in the induced metric of course allows the partonic 3surface to look static at the level of imbedding space. The fundamental number theoretic braids defined by the minima of the Higgs like field associated with the modified Dirac operator would be very natural in this case. Genes would define only the hardware unless they code for the magnetic body of DNA too, which looks implausible. The presence of quantum memory and quantum programs would mean a breakdown of genetic determinism since the braidings representing memories and programs would develop quantum jump by quantum jump and distinguish between individuals with the same genome. Also the personal development of individual would take place at this level. It would be these programs (that is magnetic bodies) which would differentiate between us and our cousins with almost identical genome. 3. Biological evolution as an evolution of topological quantum computation This framework allows to understand biological evolution as an evolution of topological quantum computation like processes in which already existing programs become building blocks of more complex programs.
