Estimating QSVT angles for matrix inversion with large condition numbers

TL;DR

This paper introduces a numerical method to efficiently estimate QSVT angles for matrix inversion problems with large condition numbers, enabling better handling of ill-conditioned matrices in quantum algorithms.

Contribution

A novel numerical technique for estimating QSVT angles that reduces computational complexity for ill-conditioned matrices in quantum computing.

Findings

Enables efficient estimation of QSVT angles for large condition numbers

Reduces the need for expensive numerical computations

Facilitates simulation of QSVT circuits for ill-conditioned problems

Abstract

Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition number grows. Computing QSVT angles for ill-conditioned problems is a numerically challenging task. We propose a numerical technique for estimating QSVT angles for large condition numbers. This technique allows one to avoid expensive numerical computations of QSVT angles and to emulate QSVT circuits for solving ill-conditioned problems.