  Our goal is to reconstruct tomographic images with few measurements and a low
signal-to-noise ratio. In clinical imaging, this helps to improve patient
comfort and reduce radiation exposure. As quantum computing advances, we
propose to use an adiabatic quantum computer and associated hybrid methods to
solve the reconstruction problem. Tomographic reconstruction is an ill-posed
inverse problem. We test our reconstruction technique for image size, noise
content, and underdetermination of the measured projection data. We then
present the reconstructed binary and integer-valued images of up to 32 by 32
pixels. The demonstrated method competes with traditional reconstruction
algorithms and is superior in terms of robustness to noise and reconstructions
from few projections. We postulate that hybrid quantum computing will soon
reach maturity for real applications in tomographic reconstruction. Finally, we
point out the current limitations regarding the problem size and
interpretability of the algorithm.
