(Roughly) Daily

… in the process of which, as Ben Brubaker explains, we learn some fascinating things…

If you want to tile a bathroom floor, square tiles are the simplest option — they fit together without any gaps in a grid pattern that can continue indefinitely. That square grid has a property shared by many other tilings: Shift the whole grid over by a fixed amount, and the resulting pattern is indistinguishable from the original. But to many mathematicians, such “periodic” tilings are boring. If you’ve seen one small patch, you’ve seen it all.

In the 1960s, mathematicians began to study “aperiodic” tile sets with far richer behavior. Perhaps the most famous is a pair of diamond-shaped tiles discovered in the 1970s by the polymathic physicist and future Nobel laureate Roger Penrose. Copies of these two tiles can form infinitely many different patterns that go on forever, called Penrose tilings. Yet no matter how you arrange the tiles, you’ll never get a periodic repeating pattern.

“These are tilings that shouldn’t really exist,” said Nikolas Breuckmann, a physicist at the University of Bristol.

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…

Fascinating: “Never-Repeating Tiles Can Safeguard Quantum Information,” from @benbenbrubaker in @QuantaMagazine.

Plus- bonus background on tiling.

* “We couldn’t build quantum computers unless the universe were quantum and computing. We can build such machines because the universe is storing and processing information in the quantum realm. When we build quantum computers, we’re hijacking that underlying computation in order to make it do things we want: little and/or/not calculations. We’re hacking into the universe.” –Seth Lloyd

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As we care for qubits, we might send carefully-calculated birthday greetings to Herman Hollerith; he was born on this date in 1860. A statistician and inventor, he was a seminal figure in the development of data processing: he invented (for the 1890 U.S. Census) an electromechanical tabulating machine for punched cards to assist in summarizing information (and, later, for use in accounting). His invention of the punched card tabulating machine, which he patented in 1884, marked the beginning of the era of mechanized binary code and semiautomatic data processing systems– and his approach dominated that landscape for nearly a century.

The company that Hollerith founded to exploit his invention was merged in 1911 with several other companies to form the Computing-Tabulating-Recording Company. In 1924, the company was renamed “International Business Machines” (or, as we know it, IBM).

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