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

Abstract

Black-box quantum-state preparation is a variant of quantum-state preparation where we want to construct an $n$-qubit state $|{\psi }_c⟩\propto {\sum }_{x}c(x)|x⟩$ 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 $|{\psi }_c⟩$ 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.

8 pages, 3 figures, comments are welcome