Abstract: Over the past ten years, the field of quantum machine learning (QML) has produced many polylogarithmic-time procedures for linear algebra routines, assuming certain "state preparation" assumptions. Though such algorithms are formally incomparable with classical computing, a recent line of work uses an analogous classical model of computation as an effective point of comparison to reveal speedups (or lack thereof) gained by QML. The resulting "dequantized" algorithms assume sampling access to input to speed up runtimes to polylogarithmic in input size.
In this talk, we will discuss the motivation behind this model and its relation to existing randomized linear algebra literature. Then, we will delve into an example quantum-inspired algorithm: Gilyen, Lloyd, and Tang's algorithm for low-rank matrix inversion. This dequantizes a variant of Harrow, Hassidim, and Lloyd's matrix inversion algorithm, a seminal work in QML. Finally, we will consider the implications of this work on exponential speedups in QML. No background of quantum computing is assumed for this talk.