Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution

Physicists and mathematicians were interested in the strange properties of quantum Latin squares. Ion Nechita and Jordi Pillet created a quantum version of Sudoku. The rows, columns, and subsquares have nine parallel lines instead of the usual 0 through 9.

Adam Burchardt, a researcher at Jagiellonian University in Poland, and his colleagues reexamined the old puzzle about the 36 officers. They wondered if the officers of Euler were made quantum.

Each entry is an officer with a well-defined rank. It is helpful to think of the 36 officers as colorful chess pieces, whose rank can be king, queen, rook, bishop, knight, or pawn, and whose regiment is represented by red, orange, yellow, green, blue, or purple. In the quantum version, officers are formed from the positions of ranks and armies. An officer could be a red king and an orange queen.

There is a correlation between different entities when it comes to the quantum states that compose these officers. If the king is red and the queen is orange, you should know immediately that the queen is orange. It is because of the peculiar nature ofentanglement that officers along each line can be in a straight line.

To prove the theory worked, the authors had to build an array filled with quantum officers. They had to rely on the computer for help with a lot of configurations. The researchers plugged in a classical near-solution that had 36 classical officers with only a few repeats of ranks and columns in a row or column. The solution to a Rubik's cube can be solved with brute force, where you fix the first row, then the first column, and so on. The puzzle array was closer to being a true solution when they repeated the algorithm over and over. The researchers were able to see the pattern and fill in the few remaining entries by hand.

In the 18th century, he couldn't have known about the possibility of quantum officers.

Nechita said that they close the book on the problem. I like the way they get it.

One surprising feature of their solution was that officer ranks are only entangled with adjacent ranks, and not with the adjacent infantry. The entries of the quantum Latin square have coefficients. The coefficients are numbers that tell you how much weight to give a term. The golden ratio is the ratio of coefficients that the algorithm landed on.