Finding Angles for Quantum Signal Processing with Machine Precision

TL;DR

This paper introduces a new algorithm for quantum signal processing that efficiently finds large sequences of angles using a halving method and capitalization, enabling practical applications like Hamiltonian simulation with standard hardware.

Contribution

The paper presents a novel algorithm with halving and capitalization techniques for finding angle sequences in quantum signal processing, achieving high efficiency and precision.

Findings

Able to find over 3000 angles within 5 minutes

Operates effectively in standard double precision arithmetic

Demonstrates strong performance in Hamiltonian simulation applications

Abstract

We describe an algorithm for finding angle sequences in quantum signal processing, with a novel component we call halving based on a new algebraic uniqueness theorem, and another we call capitalization. We present both theoretical and experimental results that demonstrate the performance of the new algorithm. In particular, these two algorithmic ideas allow us to find sequences of more than 3000 angles within 5 minutes for important applications such as Hamiltonian simulation, all in standard double precision arithmetic. This is native to almost all hardware.