Hybrid Phase-Based Representation of Quantum Images

We propose a novel and hybrid quantum-classical algorithm that requires only O(log HW) qubits and reduces the multi-qubit gate costs required to represent an image of dimension (H x W). In this algorithm, no qubit is needed to store the color information of the image. We represent the location information of an image with a superposition of mutually orthogonal vectors of an arbitrary basis and store the pixel information in the phases of the corresponding basis vectors without any extra qubit cost. We further present a classical algorithm to encode the phases and show that the inclusion of the classical algorithm significantly reduces the number of multi-qubit quantum gates required for image representation. Finally, we implement our algorithm on the classical simulator provided by IBM quantum as a proof of concept.