Quantum Implementation Circuits of Quantum Signal Representation and Type Conversion

Abstract

Quantum signal processing offers a possible solution to store and process massive signals efficiently. As the foundation of quantum signal processing, quantum signal representation (QSR) that stores color information using basis states, is convenient to retrieve accurately signals from quantum systems. But the existing QSRs are only focus on integer signals (i.e., images) and are difficult to be directly operated by quantum Fourier transform (QFT) and quantum wavelet transform (QWT). Thus, we propose four models of QSR for integer, real, and complex signals. Furthermore, we design quantum implementation circuits of type conversions of QSR with complexity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O$ </tex-math></inline-formula> (1). Type conversions of QSR are illustrated by general processes of QFT and Haar QWT, and demonstrate that the proposed QSRs are suitable for QFT and QWT.