  Quantum image computing draws a lot of attention due to storing and
processing image data faster than classical. With increasing the image size,
the number of connections also increases, leading to the circuit complex.
Therefore, efficient quantum image representation and compression issues are
still challenging. The encoding of images for representation and compression in
quantum systems is different from classical ones. In quantum, encoding of
position is more concerned which is the major difference from the classical. In
this paper, a novel zero-discarded state connection novel enhance quantum
representation (ZSCNEQR) approach is introduced to reduce complexity further by
discarding '0' in the location representation information. In the control
operational gate, only input '1' contribute to its output thus, discarding zero
makes the proposed ZSCNEQR circuit more efficient. The proposed ZSCNEQR
approach significantly reduced the required bit for both representation and
compression. The proposed method requires 11.76\% less qubits compared to the
recent existing method. The results show that the proposed approach is highly
effective for representing and compressing images compared to the two relevant
existing methods in terms of rate-distortion performance.
