We present an algorithmic framework for quantum-inspired classical algorithms on close-to-
low-rank matrices, generalizing the series of results started by Tang's breakthrough quantum …

Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of
high-dimensional data as it automatically extracts sparse and meaningful features from a set …

We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst-case
running time n 1/2 m 1/2 s 2 poly (log (n), log (m), R, r, 1/δ), with n and s the dimension and …

We give two quantum algorithms for solving semidefinite programs (SDPs) providing
quantum speed-ups. We consider SDP instances with $ m $ constraint matrices, each of …

Identifying the underlying structure of a data set and extracting meaningful information is a
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …

We study planted problems-finding hidden structures in random noisy inputs-through the
lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of …

A popular method in combinatorial optimization is to express polytopes P, which may
potentially have exponentially many facets, as solutions of linear programs that use few …

From the winner of the Turing Award and the Abel Prize, an introduction to computational
complexity theory, its connections and interactions with mathematics, and its central role in …

It is well-known that any sum of squares (SOS) program can be cast as a semidefinite
program (SDP) of a particular structure and that therein lies the computational bottleneck for …

Following the first paper on quantum algorithms for SDP-solving by Brand\~ ao and Svore in
2016, rapid developments has been made on quantum optimization algorithms. Recently …