Reproduce “Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra” on OpenResearch
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About this paper
Nadiia Chepurko, Kenneth L. Clarkson, Lior Horesh, Honghao Lin, David P. Woodruff
Researchers at MIT, IBM Research, and Carnegie Mellon University refined quantum-inspired algorithms by establishing their implicit connection to Randomized Numerical Linear Algebra (RNLA). This allowed for the development of classical algorithms for dynamic ridge regression and low-rank approximation with significantly sharper theoretical bounds and up to 40x speedups over exact solutions in empirical tests.
Key insights
- Quantum-inspired algorithms that use $l_2$-sampling are implicitly performing leverage score or ridge leverage score sampling, providing a unifying framework and enabling the direct application of RNLA tools.
- Leveraging RNLA techniques substantially reduces the high-degree polynomial dependencies on problem parameters, yielding significantly sharper theoretical bounds for classical algorithms.
- Efficient dynamic data structures, based on binary trees, enable rapid updates and weighted random sampling, which is crucial for achieving sublinear performance in dynamic settings.
Summary by alphaXiv.
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