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This research establishes a tight N^(1/4) quantum lower bound for collision finding by introducing a novel matrix-discrepancy method, effectively closing the gap between theoretical limits and classical birthday-paradox intuition. By proving that no more efficient one-way quantum protocol exists in this regime, the study provides a definitive benchmark for assessing the inherent hardness of search problems critical to cryptography and large-scale data analysis.
USC Researchers Sharpen The Quantum Limit For Collision Search
USC's Guangxu Yang and colleagues prove a tight quantum lower bound for collision finding, lifting it from N^1/12 to N^1/4 with a new matrix-discrepancy method.
A team of computer scientists has established a far stronger limit on how efficiently quantum computers can solve collision finding, one of the workhorse problems behind cryptography and large-scale data analysis. In a paper posted to arXiv on 9 July 2026, they prove a one-way quantum communication lower bound of N to the power of one-fourth, sharpening the previous best bound of N to the power of one-twelfth. The jump closes…
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