Sun. May 29th, 2022

Quantum Latin squares were quickly adopted by a community of theoretical physicists and mathematicians interested in their unusual properties. Last year, the French mathematical physicist Ayon Nechita And Jordi Pilates has created a quantum version of Sudoku.Sudoku. Instead of using integers from 0 to 9, SudoQ has nine perpendicular vectors in each of the rows, columns, and subscores.

This led to progress Adam Barchard, A postdoctoral researcher at the Jagilonian University in Poland and his colleagues to re-examine Euler’s old puzzle about 36 officers. If they are surprised, are Euler’s officers quantum?

In the classical version of the problem, each entry is an officer with a well-defined rank and regiment. It is helpful to imagine 36 officers as colorful chess pieces, whose rank may be King, Queen, Rook, Bishop, Knight or Pan, and whose regiments are represented by red, orange, yellow, green, blue or purple. But in the Quantum version, officers are made up of ranks and regiments’ superpositions. For example, an officer could be a superposition of a red king and an orange queen.

Critically, Quantum says that the composition of these officials has a special relationship called entanglement, which involves interrelationships between different entities. For example, if a red king is involved with an orange queen, even if both the king and the queen are in superposition of multiple regiments, if the king observes red, he will immediately tell you that the queen is orange. It is because of the strange nature of the entanglement that officers can be perpendicular to each line.

The theory seemed to work, but to prove it, the authors had to create a 6-by-6 array filled with quantum officers. The huge number of potential configurations and complexities meant they had to rely on computer help. Researchers have plugged a classical near-solution (a system of 36 classical officers with only a few repetitions of ranks and regiments in a row or column) and applied an algorithm that tweaked the system towards a true quantum solution. The algorithm works a bit like solving a Rubik’s cube with brute force, where you fix the first row, then the first column, the second column, and so on. When they repeatedly repeat the algorithm, the puzzle array moves closer and closer to becoming a true solution. Eventually, the researchers reached a point where they could see the pattern and fill in some remaining entries by hand.

Euler, in a sense, was proved wrong যদিও although he did not know the possibility of a quantum officer in the 18th century.

“They close the book on this issue, which is already pretty good,” Nechita said. “It’s a beautiful result, and I like the way they got it.”

According to Suhail Rathar, a physicist and co-author at the Indian Institute of Technology Madras in Chennai, one of the amazing features of their solution was that officer positions were associated only with contiguous ranks (king with queens, rook with bishops, knights with pandas) and regiments. With adjoining regiments. The coefficients present at the entry of the Quantum Latin square were another surprise. These coefficients are numbers that tell you, basically, the weight of different positions in a superposition. Interestingly, the ratio of the coefficients of the algorithm is Φ, or 1.618…, the famous golden ratio.

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