Quantum Operations on Sequence and Image with EHands and QCrank: Implementations for NISQ Device

We report practical implementations of quantum algorithms on noisy intermediate-scale quantum (NISQ) hardware for core signal and image processing tasks, including convolution of real-valued functions, discrete-time Fourier transform (DTFT) of time series, squared gradient computation, and edge detection in grayscale images. Input data are encoded using QCrank, a protocol that enables efficient quantum representation of sequences of classical real values through parallel, uniformly controlled rotation gates. Quantum transformations are performed via the EHands protocol, which offers a universal framework for elementary quantum arithmetic operations—multiplication, addition, and negation—facilitating the construction of  multivariate polynomial transformations required by these algorithms.

Experimental evaluations on IBM quantum processors demonstrate that accurate and interpretable results can be achieved for several target operations despite inherent hardware noise. These results establish the viability of specialized quantum circuit architectures for nontrivial real-world data processing on NISQ devices and underscore the potential of polynomial-based quantum transformations in bridging the gap between current quantum capabilities and practical computational applications.