A surprising new solution to the famous “36 officers puzzle” offers a novel way of encoding quantum information.
. Instead of using the integers 0 through 9, in SudoQ the rows, columns, and subsquares each have nine perpendicular vectors., a postdoctoral researcher at Jagiellonian University in Poland, and his colleagues to reexamine Euler’s old puzzle about the 36 officers. What if, they wondered, Euler’s officers were made quantum?
The theory seemed to work, but to prove it, the authors had to construct a 6-by-6 array filled with quantum officers. A vast number of possible configurations and entanglements meant they had to rely on computer help. The researchers plugged in a classical near-solution and applied an algorithm that tweaked the arrangement toward a true quantum solution.
One surprising feature of their solution, according to coauthor Suhail Rather, a physicist at the Indian Institute of Technology Madras in Chennai, was that officer ranks are entangled only with adjacent ranks and regiments with adjacent regiments. Another surprise was the coefficients that appear in the entries of the quantum Latin square. These coefficients are numbers that tell you, essentially, how much weight to give different terms in a superposition.
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