A bit in two minds

Julian Barbour

Anirban Pathak

It is well known that most of the frequently used reversible logic gates (e.g., NOT, CNOT, SWAP, Toffoli, Fredkin) are self-inverse and are represented by square matrices that are unitary and Hermitian. However, with a simple minded argument, it is established that the most of the allowed reversible gates are non-self-inverse (unitary but non-Hermitian) in nature. It is also shown that the % of non-Hermitian gates increases with the dimension. For example, 58.33% of the 2-bit gates, 98.10% of the 3-bit gates and 99.99% of the 4-bit gates are non-Hermitian. As classical reversible gates are essentially permutation gates, above statistics is strictly valid for classical reversible gates, but the argument can be easily extended to include quantum gates and to establish that the majority of the quantum gates are also non-self-inverse. Further, the % of genuinely 2-bit reversible gates (i.e., 2-bit gates that cannot be decomposed as a product of two single bit gates) among all possible gates has been computed as 83.3%, and the applicability of this analysis in the optimization of circuit cost is discussed.

Navjot Singh Gadda

The Extended Mind Thesis holds that mental states are realized in extended physical systems and are not identical with processes occurring inside the brain. A central question raised by this hypothesis is how to model cognition within this extended framework. Here I propose that classical computation can't explain this extension and one rather needs a quantum mechanical description of cognition to help solve the Extended Minds Problem. I develop a computational model of the relationship between quantum information processing and cognition. In particular, I focus on a ramification of Quantum Cognition representing probabilistic relationships amongst information processing units associated directly through reversible local operations performed on data bits. Based on this, I formulate three classes of memory storage incorporating arbitrary permutations allowed during reversible computations which occur both locally as well as nonlocally and act upon inputted data bits and encode initial correlations amongst separate memory elements existing before computation occurred. In conclusion, I dicuss various implications of my work.

Sultan Tarlacı

The spin-mediated consciousness theory is a theory that says quantum spin is the seat of consciousness and the linchpin between mind and the brain, that is, spin is the mind-pixel. According to this theory, consciousness is intrinsically connected to the spin process and emerges from the self-referential collapses of spin states and the unity of mind is achieved by entanglement of these mind-pixels. This theory was initially proposed by biophysicist Huping Hu with his collaborator Maoxin Wu. It is a tentative hypothesis as are all current hypotheses about consciousness. The starting point is the fact that spin is basic quantum bit (qubit) for encoding information and, on the other hand, neural membranes and proteins are saturated with nuclear spin carrying nuclei and form the matrice of brain electrical activities. Indeed, spin is embedded in the microscopic structure of spacetime.