  Objective: Despite recent advancements in quantum computing, the limited
number of available qubits has hindered progress in CT reconstruction. This
study investigates the feasibility of utilizing quantum annealing-based
computed tomography (QACT) with current quantum bit levels. Approach: The QACT
algorithm aims to precisely solve quadratic unconstrained binary optimization
(QUBO) problems. Furthermore, a novel approach is proposed to reconstruct
images by approximating real numbers using the variational method. This
approach allows for accurate CT image reconstruction using a small number of
qubits. The study examines the impact of projection data quantity and noise on
various image sizes ranging from 4x4 to 24x24 pixels. The reconstructed results
are compared against conventional reconstruction algorithms, namely maximum
likelihood expectation maximization (MLEM) and filtered back projection (FBP).
Main result: By employing the variational approach and utilizing two qubits for
each pixel of the image, accurate reconstruction was achieved with an adequate
number of projections. Under conditions of abundant projections and lower noise
levels, the image quality in QACT outperformed that of MLEM and FBP. However,
in situations with limited projection data and in the presence of noise, the
image quality in QACT was inferior to that in MLEM. Significance: This study
developed the QACT reconstruction algorithm using the variational approach for
real-number reconstruction. Remarkably, only 2 qubits were required for each
pixel representation, demonstrating their sufficiency for accurate
reconstruction.
