The paper introduces quantum redshift. By using the quantum structure of the electromagnetic waves, we can describe the redshift. Losing the quanta masses along the traveling in the space is the reason of the decreasing the frequency of the electromagnetic waves. Recursive quantum redshift predict distance of the objects by calculating the z parameter of the waves since they have emitted. Non-recursive quantum redshift is a fast and good approximation of the recursive quantum redshift. The distances in the quantum redshift is less than the distances in the accelerated expansion space theory. The paper provides z parameter of distances between zero and 12 billion light years.