arXiv:2410.22287quant-ph
Quantum permutation puzzles with indistinguishable particles
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 $2\times 2$ slide puzzle and briefly treat the $2\times 2 \times 1$ Rubik's Cube.
>> Unsurprisingly, the combined solver performed the best, solving the puzzle in an average of 4.77 moves. The quantum solver was next, with an average of 5.32 moves, while the classical solver came in last place with 5.88 moves on average. This effect is pretty neat. From the…
0hijinksView on HNParent context
In the paper [1] they do discuss generalizing to larger boards. Puzzle's like the 2D slide puzzle or 3D Rubick's cube are modeled by different permutation groups. So, their techniques will work for the Rubick's cube as well. They likely wrote the paper the way they did because…
abdullahkhalidsView on HNParent context