An Improved Classical Singular Value Transformation for Quantum Machine Learning
Ainesh Bakshi, Ewin Tang
Abstract
The field of quantum machine learning (QML) produces many proposals for attaining quantum speedups for tasks in machine learning and data analysis. Such speedups can only manifest if classical algorithms for these tasks perform significantly slower than quantum ones. We study quantum-classical gaps in QML through the quantum singular value transformation (QSVT) framework. QSVT, introduced by Gilyén, Su, Low and Wiebe [GSLW19], unifies all major types of quantum speedup [MRTC21]; in particular, a wide variety of QML proposals are applications of QSVT on low-rank classical data. We challenge these proposals by providing a classical algorithm that matches the performance of QSVT in this regime up to a small polynomial overhead.