In the classical version of the problem, each entry is an officer with a well-defined rank and regiment. What if, they wondered, Euler’s officers were made quantum? These advances led Adam Burchardt, a postdoctoral researcher at Jagiellonian University in Poland, and his colleagues to reexamine Euler’s old puzzle about the 36 officers. Instead of using the integers 0 through 9, in SudoQ the rows, columns and subsquares each have nine perpendicular vectors. Last year, the French mathematical physicists Ion Nechita and Jordi Pillet created a quantum version of Sudoku - SudoQ. Quantum Latin squares were quickly adopted by a community of theoretical physicists and mathematicians interested in their unusual properties. Analogous to the requirement that symbols along each row and column of a Latin square not repeat, the quantum states along each row or column of a quantum Latin square must correspond to vectors that are perpendicular to one another. A superposition is the arrow formed by combining multiple vectors. Mathematically, a quantum state is represented by a vector, which has a length and direction, like an arrow. (Quantum objects stay in this limbo until they are measured, at which point they settle on one state.) Entries of quantum Latin squares are also quantum states that can be in quantum superpositions. In quantum mechanics, objects such as electrons can be in a “superposition” of multiple possible states: here and there, for example, or magnetically oriented both up and down. The new era of quantum puzzling began in 2016, when Jamie Vicary of the University of Cambridge and his then-student Ben Musto had the idea that the entries appearing in Latin squares could be made quantum. And not only that, but you can feel throughout the paper their love for the problem.” “There’s a lot of quantum magic in there. “I think their paper is very beautiful,” said Gemma De las Cuevas, a quantum physicist at the University of Innsbruck who was not involved with the work. The result is the latest in a line of work developing quantum versions of magic square and Latin square puzzles, which is not just fun and games, but has applications for quantum communication and quantum computing. In a paper posted online and submitted to Physical Review Letters, a group of quantum physicists in India and Poland demonstrates that it is possible to arrange 36 officers in a way that fulfills Euler’s criteria - so long as the officers can have a quantum mixture of ranks and regiments. Euler’s 36 officers puzzle asks for an “orthogonal Latin square,” in which two sets of properties, such as ranks and regiments, both satisfy the rules of the Latin square simultaneously.īut whereas Euler thought no such 6-by-6 square exists, recently the game has changed. One popular Latin square - Sudoku - has subsquares that also lack repeating symbols. These squares have been used in art and urban planning, and just for fun. Cultures around the world have made “magic squares,” arrays of numbers that add to the same sum along each row and column, and “Latin squares” filled with symbols that each appear once per row and column.

Similar puzzles have entranced people for more than 2,000 years. In 1960, mathematicians used computers to prove that solutions exist for any number of regiments and ranks greater than two, except, curiously, six. But after searching in vain for a solution for the case of 36 officers, Euler concluded that “such an arrangement is impossible, though we can’t give a rigorous demonstration of this.” More than a century later, the French mathematician Gaston Tarry proved that, indeed, there was no way to arrange Euler’s 36 officers in a 6-by-6 square without repetition. The puzzle is easily solved when there are five ranks and five regiments, or seven ranks and seven regiments. Can the 36 officers be arranged in a 6-by-6 square so that no row or column repeats a rank or regiment? Labs supporting Ukrainian Scientists is an expansive list of labs and PIs offering support at this time.In 1779, the Swiss mathematician Leonhard Euler posed a puzzle that has since become famous: Six army regiments each have six officers of six different ranks.

Science for Ukraine provides an overview of labs offering a place for researchers and students who are affected to work from, as well as offers of employment, funding, and accommodation:.

Personally, I have found the messages of support from scientists everywhere to be truly heartfelt, and I would like to highlight some of the community initiatives I’ve seen here: We also want to use our platform to highlight the response from the scientific community.

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