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Quantum Latin circles were enthusiastically received by a team of astronomers and mathematicians who were interested in what was unusual. Last year, French mathematicians Ion Nechita by Jordi Pillet created the quantum version of Sudoku-SudoQ. Instead of using numbers 0 to 9, in SudoQ each row, rows, and subsquares have nine vectors.
This progress led Adam Burchardta post-doctoral researcher at Jagiellonian University in Poland, and colleagues to review Euler’s old portrait of 36 police officers.
In the old problem books, every entry is by a police officer with a clear role and a team. It is useful to take between 36 officers as beautiful pieces of chess, whose role may be king, queen, rook, bishop, knight, or pawn, and their group is represented by red, orange, yellow, green, blue, or brown. But in the quantum type, officers are made up of higher classes and groups. A soldier can be the top of the red king and the orange queen, for example.
In short, the multiplicity states that the authors of these offices have a special relationship called entanglement, which affects the interaction between different organizations. If the red king is captured by the orange queen, for example, then even the king and queen are both in large groups of several groups, seeing that the king is red tells you immediately that the queen is orange. It is because of the unusual nature of the closure that officers on each line can be perpendicular.
The theory seemed to work, but to prove it, the authors had to form a 6-by-6 team filled with quantum officers. The number of possible changes and constraints means that they depend on computer support. The researchers linked an old-fashioned answer (a system of 36 officers who repeated it several times in a row or line) and used an algorithm that modified the system to find the exact answer for quantity. The algorithm works like eliminating the Rubik’s Cube with a dynamic force, where you create the first line, then the first part, the second part and so on. By repeating the algorithm over and over, the graphics team moves very close to becoming a real solution. Eventually, the researchers reached a point where they could see the form and fill in the few notes left by hand.
In a sense, Euler was guilty – though he had no idea, in the 18th century, of the potential of quantum officers.
Nechita says: “They close the book on this problem, which is so good. “It’s a very good result, and I love the way they get it.”
One surprising aspect of their response, according to co-author Suhail, on the other hand, an astronomer at the Indian Institute of Technology Madras in Chennai, was that government officials were attracted to neighboring positions (kings with queens, traveling companions and bishops). , fighters) and groups. and neighboring regiments. Another surprise was the coefficients that appear in quantum Latin square literature. These coefficients are numbers that tell you, in particular, how much weight to give different words in the superposition. Surprisingly, the number of coefficients reached by this trend was Φ, or 1.618…, a notable value of gold.
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