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 \((H \times W)\). 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.