For over half a century, aperiodic tilings have fascinated mathematicians, hobbyists and researchers in many other fields. Now, two physicists have discovered a connection between aperiodic tilings and a seemingly unrelated branch of computer science: the study of how future quantum computers can encode information to shield it from errors. In a paper posted to the preprint server arxiv.org in November, the researchers showed how to transform Penrose tilings into an entirely new type of quantum error-correcting code. They also constructed similar codes based on two other kinds of aperiodic tiling.
Interesting. I haven't read the full article but in an interesting coincidence, I recently read a Scientific American article on tiles - Inside Mathematicians’ Search for the Mysterious ‘Einstein Tile’. While the Penrose tile is made up of two tiles that generate a non-repeatable pattern, an Einstein Tile consists of a single tile. I wonder if they've examined that one. I did see it listed in the Related Articles section of the quantamagazine link - Hobbyist Finds Math’s Elusive ‘Einstein’ Tile.jedishrfu said:TL;DR Summary: Never-Repeating Tiles Can Safeguard Quantum Information
https://www.quantamagazine.org/never-repeating-tiles-can-safeguard-quantum-information-20240223/