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Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning
Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gily\'en, Su, Low, and Wiebe [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions.
Quantum-inspired sublinear algorithm for solving low-rank semidefinite programming
In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank constraints; specifically, given an SDP with $m$ constraint matrices, each of dimension $n$ and rank $r$, our algorithm can compute any entry and efficient descriptions of the spectral decomposition of the solution matrix.
Quantum-inspired sublinear classical algorithms for solving low-rank linear systems
Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the quantum algorithm for recommendation systems.
