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Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problem
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 $c^*$.
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.
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.
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.
