Year: 2025
Type: article
Abstract: Permutation puzzles, such as the Rubik's Cube and the 15 puzzle, are enjoyed by the general public and mathematicians alike. Here we introduce quantum versions of permutation puzzles where the pieces of the puzzles are replaced with indistinguishable quantum particles. The moves in the puzzle are achieved by swapping or permuting the particles. We show that simply permuting the particles can be mapped to a classical permutation puzzle, even though the identical particles are entangled. However, we obtain a genuine quantum puzzle by adding a quantum move: the square root of swap. The resulting puzzle cannot be mapped to a classical permutation puzzle. We focus predominately on the quantization of the $2\ifmmode\times\else\texttimes\fi{}2$ slide puzzle and briefly treat the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}1$ Rubik's Cube.
Source: Physical Review A
Institutions: University of Colorado Boulder, The University of Melbourne
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: University of Colorado Boulder
OpenAlex ID: W4409412206