Nematic bits and logic gates*

Topological field structures in nematic liquid crystals are known to share analogies with superconducting quantum mater. While the experimental control of orientation and dynamics of nematic structures has been developed, little is known how such structures could be used for information storage and computation. We introduce nematic bits [1] by using a quaternionic mapping [2,3] from nematic defects to a Bloch sphere. By using electric fields, we show in theory and simulation how logic gates could be applied to nematic bits, analogous to Pauli, Hadamard and other quantum gates. We also show Bell-like correlations and nematic discord in two nematic bit ensambles, opening a pathway towards non-classical computational strategies in topological soft matter systems.

[1] Z. Kos and J. Dunkel, Nematic bits and logic gates, arXiv:2008.13094 (2020).
[2] S. Copar and S. Zumer, Quaternions and hybrid nematic disclinations, Proc. R. Soc. A 469, 20130204 (2013).
[3] J. Binysh, Z. Kos, S. Copar, M. Ravnik, and G. P. Alexander, Three-dimensional Active Defect Loops, Phys. Rev. Lett. 124, 257 (2020).