Quantum-Inspired Algorithms from Randomized Numerical Linear Algebra

TL;DR

This paper develops classical algorithms inspired by quantum techniques for recommender systems and regression, achieving sharper bounds and leveraging randomized linear algebra methods, with practical effectiveness demonstrated on real data.

Contribution

It reveals that quantum-inspired algorithms are essentially leverage score sampling, enabling the use of classical linear algebra techniques for improved efficiency.

Findings

Sharper bounds for classical algorithms compared to quantum analogues

Algorithms are simpler and faster due to leverage score sampling

Experimental results show good performance on real-world datasets

Abstract

We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of attention in recent years; we obtain sharper bounds for these problems. More significantly, we achieve these improvements by arguing that the previous quantum-inspired algorithms for these problems are doing leverage or ridge-leverage score sampling in disguise; these are powerful and standard techniques in randomized numerical linear algebra. With this recognition, we are able to employ the large body of work in numerical linear algebra to obtain algorithms for these problems that are simpler or faster (or both) than existing approaches. Our experiments demonstrate that the proposed data structures also work well on real-world datasets.