Abstract
We present the first quantum version of the one-dimensional integer wavelet S-Transform (QIST). This version is based on a new Quantum Block Representation by Basis States (QBRBS) and the design of a quantum rounding operator. The QBRBS format facilitates storing and manipulating pairs of signal elements, decreasing the use of additional qubits and gates. Also, the quantum rounding operator exploits the features of the S-Transform to avoid nonlinearities. Complete quantum circuits for addition, subtraction, and halving operations were developed. The complexity analysis showed a polynomial quantum complexity, O(n), and a time complexity of O(1). The experiments performed on MATLAB and Qiskit verify the theoretical results coinciding with the results of the classical version. Finally, the new quantum transform’s feasibility and accuracy enable new quantum developments in information hiding, compression, and IoT applications.
Published Version
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