Improved Quantum Power Method and Numerical Integration Using Quantum Singular Value Transformation

TL;DR

This paper enhances quantum algorithms by accelerating the quantum power method and integrating numerical techniques within the quantum singular value transformation framework, achieving significant speedups.

Contribution

It demonstrates how QSVT can be used to improve the efficiency of quantum power methods and numerical integration techniques.

Findings

Accelerated quantum power method using QSVT

Polynomial speedup in numerical integration tasks

Demonstrated potential of QSVT in various quantum algorithms

Abstract

Quantum singular value transformation (QSVT) is a framework that has been shown to unify many primitives in quantum algorithms. In this work, we leverage the QSVT framework in two directions. We first show that the QSVT framework can accelerate one recently introduced quantum power method, which substantially improves its running time. Additionally, we incorporate several elementary numerical integration techniques, such as the rectangular method, Monte Carlo method, and quadrature method, into the QSVT framework, which results in polynomial speedup with respect to the size or the number of points of the grid. Our results thus provide further examples to demonstrate the potential of the QSVT and how it may enhance quantum algorithmic tasks.