Quantum permutation puzzles with indistinguishable particles Article Swipe

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Noah Lordi , Maedée Trank-Greene , Akira Kyle , Joshua Combes ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2410.22287

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.

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Permutation (music) Computer science Mathematics Physics Acoustics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2410.22287
PDF: https://arxiv.org/pdf/2410.22287
OA Status: green
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2410.22287

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Title: Quantum permutation puzzles with indistinguishable particles

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-10-29

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Authors: Noah Lordi, Maedée Trank-Greene, Akira Kyle, Joshua Combes

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Landing page: https://arxiv.org/abs/2410.22287

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PDF URL: https://arxiv.org/pdf/2410.22287

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Concepts: Permutation (music), Computer science, Mathematics, Physics, Acoustics

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