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- TL;DR Summary
- Never-Repeating Tiles Can Safeguard Quantum Information
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/
Never-repeating tiles, also known as aperiodic tiles, are a set of shapes that can cover a plane completely without creating a repeating pattern. These tiles are used to create non-repetitive structures that can have unique properties beneficial for various applications, including safeguarding quantum information.
Never-repeating tiles can create a highly ordered yet non-repetitive structure, which can help in reducing errors and decoherence in quantum systems. The unique arrangement of these tiles can protect quantum bits (qubits) from environmental noise and other disturbances, thereby preserving the integrity of the quantum information.
Traditional methods of safeguarding quantum information often rely on periodic structures, which can be more susceptible to systematic errors and environmental interference. Never-repeating tiles provide a more robust framework by creating a non-repetitive, quasi-crystalline structure that can better isolate qubits from external perturbations and reduce error rates.
While the concept of using never-repeating tiles to safeguard quantum information is still primarily in the research phase, there have been promising theoretical and experimental studies. Researchers are exploring various materials and configurations to implement these tiles in practical quantum computing systems, aiming to enhance qubit coherence times and overall system stability.
One of the main challenges is the precise fabrication and arrangement of never-repeating tiles at the nanoscale, which is necessary for practical quantum computing applications. Additionally, integrating these structures with existing quantum hardware and ensuring compatibility with various qubit types are significant hurdles. Ongoing research is focused on addressing these challenges to make the use of never-repeating tiles a viable option for quantum information protection.