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

arXiv: https://arxiv.org/abs/2606.24561 · HTML: https://mlsanity.com/paper/2606.24561/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [3DGR-CT: Sparse-View CT Reconstruction with a 3D Gaussian Representation](https://mlsanity.com/paper/2312.15676/) (2023)
- [Discretized Gaussian Representation for Tomographic Reconstruction](https://mlsanity.com/paper/2411.04844/) (2024)
- [Quantum Medical Imaging Algorithms](https://mlsanity.com/paper/2004.02036/) (2020)
- [Highly accurate quantum optimization algorithm for CT image reconstructions based on sinogram patterns](https://mlsanity.com/paper/2207.02448/) (2022)
- [Quantum optimization algorithms for CT image segmentation from X-ray data](https://mlsanity.com/paper/2306.05522/) (2023)
- [Unsupervised Self-Prior Embedding Neural Representation for Iterative Sparse-View CT Reconstruction](https://mlsanity.com/paper/2502.05445/) (2025)
- [Hybrid adiabatic quantum computing for tomographic image reconstruction -- opportunities and limitations](https://mlsanity.com/paper/2212.01312/) (2022)

## Abstract (arXiv)

Quadratic unconstrained binary optimization (QUBO)-based quantum computed tomography (CT) casts reconstruction as a binary quadratic problem for quantum annealing and hybrid quantum--classical solvers. For grayscale CT, however, image encoding is constrained by the binary-variable budget: fixed global bit-plane encodings increase QUBO size and coupling complexity as gray-level precision improves, whereas low-bit encodings introduce quantization error. We propose a QUBO-based grayscale CT reconstruction framework that combines dynamic interval encoding with prior-balanced optimization. Each refinement round encodes active pixels only within local gray-level intervals around the current estimate, and a boundary-hit-guided update rule adaptively switches between search expansion and local refinement. To improve optimization stability, the method balances projection-domain data consistency and an edge-preserving quadratic prior before forming the final QUBO. Sparse-view and limited-angle fan-beam CT experiments show that the proposed method recovers structures and gray-level distributions more faithfully than the evaluated analytic, iterative, variational, and representation-based baselines. Expressivity analysis and ablation studies further indicate that the improvement mainly arises from effective gray-level representation through dynamic local encoding and more stable data-fidelity--prior coupling. Experiments on the D-Wave hybrid binary quadratic model (BQM) solver further demonstrate that the formulation is executable on a hardware-backed hybrid quantum--classical backend.