Efficient representations of digital images on quantum computers

Quantum image processing is the use of quantum computing to store, transmit, and process digital images on quantum computers. This paper introduces two enhanced quantum image representations to store quantum images. The first enhanced quantum representation based on the flexible representation for quantum images (EFRQI) is an amplitude representation that uses the partial negation operator to store the values of the pixels of $$2^n \times 2^n$$ image in the amplitudes of the qubits. The second enhanced quantum representation based on the novel enhanced quantum representation of digital images (ENEQR) is a basis state representation that uses the CNOT gate to store the values of the pixels in a qubit sequence. The proposed methods have better time complexity and quantum cost when compared with related models in the literature.