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Quantum symmetrization is the task of transforming a non-strictly increasing list of $n$ integers into an equal superposition of all permutations of the list (or more generally, performing this operation coherently on a superposition of such lists).
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We are aware of concurrent work that also gives an algorithm for preparing Dicke states with polylogarithmic depth but uses only polylogarithmically many ancillas [ 37 ] . The approaches are very different: while we use sorting networks, the other approach applies a simple sequence of collective rotations and parity measurements. Our approach solves a more general symmetrization problem, while the other approach is simpler, likely performs better in practice, and can perform better when the Hamming weight is lower
Cited in the paper.
2024
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P. Mukhopadhyay, T. F. Stetina, and N. Wiebe, PRX Quantum 5
2024
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T. Kuwahara, T. V. Vu, and K. Saito, Nature Communications 15
2024
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L. Piroli, G. Styliaris, and J. I. Cirac, arXiv preprint arXiv:2403.07604 (2024)
2024
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C.-J. Lin, Z.-W. Liu, V. V. Albert, and A. V. Gorshkov, arXiv preprint arXiv:2409.20561 (2024)
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