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Explore a groundbreaking research seminar that challenges previous claims of exponential quantum speedup in cryptographic problems. Learn about the Short-Integer-Solution (SIS^inf) problem, which involves finding solutions to linear equations over finite fields where each entry must be a small number under infinity norm. Discover how Chen, Liu, and Zhandry's 2021 quantum algorithm appeared to demonstrate exponential quantum advantage for SIS^inf in specific parameter regimes outside typical cryptographic ranges, using novel algorithmic techniques distinct from previous quantum speedup methods. Examine the speaker's collaborative work with Robin Kothari and Ryan O'Donnell that presents efficient classical algorithms for both SIS^inf and more general Constrained-Integer-Solution problems, effectively eliminating the claimed exponential quantum speedup. Understand the implications of this research for quantum computing's potential advantages in cryptographic applications and gain insights into the ongoing dialogue between quantum and classical algorithmic approaches to structured mathematical problems.
