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Title | Einsteins (the Tiles) Meet Error Correction for Quantum Superposition | |

Date | Monday March 25, @06:07PM | |

Author | Fnord666 | |

Topic | ||

from the Aperiodic-indistinguishability dept. |

Never-Repeating Patterns of 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.

At the heart of the correspondence is a simple observation: In both aperiodic tilings and quantum error-correcting codes, learning about a small part of a large system reveals nothing about the system as a whole.

...in 1995, the applied mathematician Peter Shor discovered a clever way to store quantum information. His encoding had two key properties. First, it could tolerate errors that only affected individual qubits. Second, it came with a procedure for correcting errors as they occurred, preventing them from piling up and derailing a computation. Shor's discovery was the first example of a quantum error-correcting code, and its two key properties are the defining features of all such codes.

...An infinite two-dimensional plane covered with Penrose tiles, like a grid of qubits, can be described using the mathematical framework of quantum physics: The quantum states are specific tilings instead of 0s and 1s. An error simply deletes a single patch of the tiling pattern, the way certain errors in qubit arrays wipe out the state of every qubit in a small cluster.

The next step was to identify tiling configurations that wouldn't be affected by localized errors, like the virtual qubit states in ordinary quantum error-correcting codes. The solution, as in an ordinary code, was to use superpositions. A carefully chosen superposition of Penrose tilings is akin to a bathroom tile arrangement proposed by the world's most indecisive interior decorator. Even if a piece of that jumbled blueprint is missing, it won't betray any information about the overall floor plan.

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I wonder... does the Penrose / Einstein principle of non-repetition preclude cylindrical, or even donut surface topology full tilings? If not, that could solve the infinite plane mapping into a physically realizable quantum computer problem. I do wonder, but not enough to give up all my other work and hobbies to pursue deeply theoretical mathematics being heavily studied by thousands of PhD mathematicians less than half my age...

**Related**:

Hobbyist Finds Math's Elusive 'Einstein' Tile

How Space and Time Could Be a Quantum Error-Correcting Code

How Quantum Computers Will Correct Their Errors

Links |

- "JoeMerchant" - https://soylentnews.org/~JoeMerchant/
- "Never-Repeating Patterns of Tiles Can Safeguard Quantum Information" - https://www.quantamagazine.org/never-repeating-tiles-can-safeguard-quantum-information-20240223/
- "discovered a connection" - https://www.quantamagazine.org/never-repeating-tiles-can-safeguard-quantum-information-20240223/
- "discovered" - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.52.R2493
- "Hobbyist Finds Math's Elusive 'Einstein' Tile" - https://www.quantamagazine.org/hobbyist-finds-maths-elusive-einstein-tile-20230404/
- "How Space and Time Could Be a Quantum Error-Correcting Code" - https://www.quantamagazine.org/how-space-and-time-could-be-a-quantum-error-correcting-code-20190103/
- "How Quantum Computers Will Correct Their Errors" - https://www.quantamagazine.org/how-quantum-computers-will-correct-their-errors-20211116/
- "Original Submission" - https://soylentnews.org/submit.pl?op=viewsub&subid=62393

printed from SoylentNews, Einsteins (the Tiles) Meet Error Correction for Quantum Superposition on 2024-06-22 16:39:16