Robust black-box quantum-state preparation via quantum signal processing

TL;DR

This paper introduces a new quantum algorithm for black-box quantum-state preparation using quantum signal processing, which avoids coherent arithmetic and achieves results comparable to existing methods.

Contribution

The paper develops a QSVT-based algorithm for quantum-state preparation that simplifies implementation and matches current state-of-the-art performance.

Findings

QSVT-based approach achieves comparable accuracy to existing algorithms.

The method avoids the need for coherent arithmetic in state preparation.

The algorithm is robust and applicable to states with simple classical descriptions.

Abstract

Black-box quantum-state preparation is a variant of quantum-state preparation where we want to construct an $n$-qubit state $|\psi_c\rangle \propto \sum_x c(x) |x\rangle$ with the amplitudes $c(x)$ given as a (quantum) oracle. This variant is particularly useful when the quantum state has a short and simple classical description. We use recent techniques, namely quantum signal processing (QSP) and quantum singular value transform (QSVT), to construct a new algorithm that prepares $|\psi_c\rangle$ without the need to carry out coherent arithmetic. We then compare our result with current state-of-the-art algorithms, showing that a QSVT-based approach achieves comparable results.