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Quantum Machine Learning
Quantum algorithms for the Goldreich-Levin learning problem
arXiv
Authors: Hongwei Li
Year
2019
Paper ID
39497
Status
Preprint
Abstract Read
~2 min
Abstract Words
106
Citations
N/A
Abstract
The Goldreich-Levin algorithm was originally proposed for a cryptographic purpose and then applied to learning. The algorithm is to find some larger Walsh coefficients of an n variable Boolean function. Roughly speaking, it takes a poly\(n,frac{1}εlogfrac{1}δ\) time to output the vectors w with Walsh coefficients S(w)geqε with probability at least 1-δ. However, in this paper, a quantum algorithm for this problem is given with query complexity O\(frac{logfrac{1}δ}{ε4}\), which is independent of n. Furthermore, the quantum algorithm is generalized to apply for an n variable m output Boolean function F with query complexity O\(2mfrac{logfrac{1}δ}{ε4}\).
Why This Paper Matters
- This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
- It adds a 2019 reference point for readers tracking recent quantum research.
- The Goldreich-Levin algorithm was originally proposed for a cryptographic purpose and then applied to learning.
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