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no code implementations • 14 Oct 2019 • Nai-Hui Chia, András Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, Chunhao Wang

Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gily\'en et al. [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions.

no code implementations • 10 Jan 2019 • Nai-Hui Chia, Tongyang Li, Han-Hsuan Lin, Chunhao Wang

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.

no code implementations • 12 Nov 2018 • Nai-Hui Chia, Han-Hsuan Lin, Chunhao Wang

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.

no code implementations • 25 Oct 2018 • Kai-Min Chung, Han-Hsuan Lin

In the problem of PAC learning quantum process, we want to learn an $\epsilon$-approximate of an unknown quantum process $c^*$ from a known finite concept class $C$ with probability $1-\delta$ using samples $\{(x_1, c^*(x_1)),(x_2, c^*(x_2)),\dots\}$, where $\{x_1, x_2, \dots\}$ are computational basis states sampled from an unknown distribution $D$ and $\{c^*(x_1), c^*(x_2),\dots\}$ are the (possibly mixed) quantum states outputted by $c^*$.

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