Porter, Topological Quantum Computation

Topological Quantum Computation/Error Correction In Microtubules

 

Mitchell Porter
Visiting Research Scholar
Quantum Consciousness Group
Center for Consciousness Studies
The University of Arizona
mjporter@u.arizona.edu
www.u.arizona.edu/~mjporter

 

Quantum approaches can explain enigmatic features of consciousness, but face an apparent obstacle. Quantum superpositions must be sustained for time intervals approaching neurophysiology (e.g. tens to hundreds of milliseconds) in the face of apparent rapid decoherence at brain temperature. Technological quantum computing schemes avoid decoherence because of low temperatures and the use of quantum error correction. Evolution may have provided a natural form of quantum error correction in microtubules.

 

Quantum error correction may be facilitated by topologies -- for instance, toroidal surfaces (e.g. Kitaev, http://xxx.lanl.gov/abs/quant-ph/9707021; -- in which global, topological degrees of freedom are protected from local errors and decoherence. Topological quantum computation and error correction have been suggested in microtubules by Mitchell Porter. (see www.u.arizona.edu/~mjporter)

 

Figure 1: A microtubule topological qu-tetrit. Four vibrational patterns in the microtubule lattice (top), which correlate with functional attachment patterns of microtubule-associated proteins are the eigenstates of a quantum superposition of all fours states (bottom). Quantum computation in the superposition phase reduces to one particular eigenstate pattern. The topological patterns are resistant to decoherence at the level of any particular subunit.

 

 

The microtubule lattice features a series of helical winding patterns which repeat on longitudinal protofilaments at 3, 5, 8, 13, 21 and higher numbers of subunit dimers (tubulins). These particular winding patterns (whose repeat intervals match the Fibonacci series) define attachment sites of the microtubule-associated proteins (MAPs), and are found in simulations of self-localized phonon excitations in microtubules (Samsonovich, 1992: These suggest topological global states in microtubules which may be resistant to local decoherence. Penrose has suggested the Fibonacci patterns on microtubules may be optimal for error correction.