Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gily\'en et al. [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions.
The presented approach is a natural fit for distributional property testing both in the classical and the quantum case, demonstrating the first speed-ups for testing properties of density operators that can be accessed coherently rather than only via sampling; for classical distributions our algorithms significantly improve the precision dependence of some earlier results.
We also show that in a continuous phase-query model, our gradient computation algorithm has optimal query complexity up to poly-logarithmic factors, for a particular class of smooth functions.
Quantum Physics Computational Complexity