A Classical Quadratic Speedup for Planted $k$XOR

• URL: http://arxiv.org/abs/2508.09422v1
• Date: Wed, 13 Aug 2025 01:45:47 GMT
• Title: A Classical Quadratic Speedup for Planted $k$XOR
• Authors: Meghal Gupta, William He, Ryan O'Donnell, Noah G. Singer,
• Abstract summary: A recent work of Schmidhuber et al exhibited a quantum algorithm for the noisy planted $k$XOR problem running quartically faster than all known classical algorithms.<n>We design a new classical algorithm that is quadratically faster than the best previous one, in the case of large constant $k$.
• Score: 1.593690982728631
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A recent work of Schmidhuber et al (QIP, SODA, & Phys. Rev. X 2025) exhibited a quantum algorithm for the noisy planted $k$XOR problem running quartically faster than all known classical algorithms. In this work, we design a new classical algorithm that is quadratically faster than the best previous one, in the case of large constant $k$. Thus for such $k$, the quantum speedup of Schmidhuber et al. becomes only quadratic (though it retains a space advantage). Our algorithm, which also works in the semirandom case, combines tools from sublinear-time algorithms (essentially, the birthday paradox) and polynomial anticoncentration.

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