Quantum CT via Dynamic Interval Encoding and Prior-Balanced QUBO Reconstruction

In quantum computed tomography (CT), reconstruction is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem. A major challenge in this domain is the "binary-variable budget": fixed global bit-plane encodings require an impractical number of binary variables to achieve high gray-level precision. This paper addresses how to achieve high-fidelity grayscale reconstruction while keeping the QUBO instance size compact enough for current hybrid quantum-classical solvers.

The authors propose a dynamic interval encoding framework. Instead of assigning a fixed global bit-depth to every pixel, the method uses a local, low-bit representation that focuses on a narrow gray-level interval around the current pixel estimate. This interval is updated iteratively: if the solver's output hits the boundary of the current interval, the search range expands; otherwise, it contracts to refine the local precision. To ensure stability, the authors also introduce a prior-balanced optimization strategy that normalizes the data-fidelity and edge-preserving prior terms before constructing the final QUBO objective.

Experiments on sparse-view and limited-angle fan-beam CT data demonstrate that the proposed method recovers structural details and gray-level distributions more accurately than standard analytic, iterative, and variational baselines. Ablation studies confirm that the improvement stems from the effective gray-level representation provided by the dynamic local encoding and the increased stability of the balanced data-prior coupling. Furthermore, the authors successfully executed their formulation on a D-Wave hybrid binary quadratic model (BQM) solver, proving its viability on hardware-backed quantum-classical systems.