Quantum signal processing without angle finding

TL;DR

This paper introduces a new quantum signal processing method that eliminates the classical angle-finding step, simplifying circuit design and enhancing scalability for implementing functions of Hermitian matrices.

Contribution

It presents a novel QSP approach that bypasses classical preprocessing, enabling more efficient and scalable quantum function implementation.

Findings

Reduces classical computational overhead in QSP.

Enables nearly optimal implementation of functions of Hermitian matrices.

Simplifies quantum circuit design for function implementation.

Abstract

Quantum signal processing (QSP) has emerged as a unifying subroutine in quantum algorithms. In QSP, we are given a function $f$ and a unitary black-box $U$, and the goal is to construct a quantum circuit for implementing $f(U)$ to a given precision. The existing approaches to performing QSP require a classical preprocessing step to compute rotation angle parameters for quantum circuits that implement $f$ approximately. However, this classical computation often becomes a bottleneck, limiting the scalability and practicality of QSP. In this work, we propose a novel approach to QSP that bypasses the computationally intensive angle-finding step. Our method leverages a quantum circuit for implementing a diagonal operator that encodes $f$, which can be constructed from a classical circuit for evaluating $f$. This approach to QSP simplifies the circuit design significantly while enabling nearly optimal implementation of functions of block-encoded Hermitian matrices for black-box functions. Our circuit closely resembles the phase estimation-based circuit for function implementation, challenging conventional skepticism about its efficiency. By reducing classical overhead, our work significantly broadens the applicability of QSP in quantum computing.