Corpus ID: 221703259

An improved quantum-inspired algorithm for linear regression

@article{Gilyen2020AnIQ,
  title={An improved quantum-inspired algorithm for linear regression},
  author={Andr'as Gily'en and Zhao Song and Ewin Tang},
  journal={ArXiv},
  year={2020},
  volume={abs/2009.07268}
}
We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09] for low-rank matrices [Wossnig et al., Physical Review Letters'18], when the input matrix $A$ is stored in a data structure applicable for QRAM-based state preparation. Namely, given an $A \in \mathbb{C}^{m\times n}$ with minimum singular value $\sigma$ and which supports certain efficient $\ell_2$-norm importance sampling queries… Expand
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