Solving problems on a quantum chessboard

phys.org | 5/3/2019 | Staff
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Physicists at the University of Innsbruck are proposing a new model that could demonstrate the supremacy of quantum computers over classical supercomputers in solving optimization problems. In a recent paper, they demonstrate that just a few quantum particles would be sufficient to solve the mathematically difficult N-queens problem in chess even for large chess boards.

The queen problem is a mathematical task, which already had the great mathematician Carl Friedrich Gauss occupied, but for which he surprisingly did not find the right solution. The challenge here is how to arrange eight queens on a classical chess board with 8 x 8 squares so that no two queens threaten each other. Mathematically, it is relatively easy to determine that there are 92 different ways to arrange the queens. On a chess board with 25 x 25 squares there are already more than 2 billion possibilities. The calculation of this number alone took a total of 53 years of CPU time.

Task - Queens - Field - Diagonals - Restrictions

The task becomes even more difficult if some queens are already on the field and certain diagonals may not be occupied. Recently it has been shown that with these additional restrictions the problem with 21 queens can no longer be solved by classical mathematical algorithms in a reasonable time. "I came across this topic by chance and thought that quantum physics really could play out its advantages here," says Wolfgang Lechner from the Department of Theoretical Physics at the University of Innsbruck and the Institute of Quantum Optics and Quantum Information at the Austrian Academy of Sciences. Together with Helmut Ritsch and Ph.D. students Valentin Torggler and Philipp Aumann, Lechner developed a quantum chessboard on which the queens puzzle could be solved experimentally with the help of quantum physics.

"An optical lattice of laser beams into which individual atoms are placed can be used...
(Excerpt) Read more at: phys.org
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