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Quantum Machine Learning Quantum Simulation

Permutation Superposition Oracles for Quantum Query Lower Bounds

arXiv
Authors: Christian Majenz, Giulio Malavolta, Michael Walter

Year

2024

Paper ID

65441

Status

Preprint

Abstract Read

~2 min

Abstract Words

108

Citations

N/A

Abstract

We propose a generalization of Zhandry's compressed oracle method to random permutations, where an algorithm can query both the permutation and its inverse. We show how to use the resulting oracle simulation to bound the success probability of an algorithm for any predicate on input-output pairs, a key feature of Zhandry's technique that had hitherto resisted attempts at generalization to random permutations. One key technical ingredient is to use strictly monotone factorizations to represent the permutation in the oracle's database. As an application of our framework, we show that the one-round sponge construction is unconditionally preimage resistant in the random permutation model. This proves a conjecture by Unruh.

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  • This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
  • It adds a 2024 reference point for readers tracking recent quantum research.
  • We propose a generalization of Zhandry's compressed oracle method to random permutations, where an algorithm can query both the permutation and its inverse.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2407.09655 [2] arXiv https://arxiv.org/abs/2407.09655 [3] Publisher https://arxiv.org/abs/2407.09655

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