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

2026-06-23

AI Summary

This work addresses the limitations of grayscale CT image reconstruction within the QUBO (Quadratic Unconstrained Binary Optimization) framework, where fixed binary variable budgets constrain representation fidelity—global bit-plane encoding leads to explosive problem size and coupling complexity, while low-bit encoding incurs significant quantization error. To overcome this, the authors propose a dynamic local grayscale interval encoding scheme that adaptively encodes only the active pixels within the neighborhood of the current estimate in each iteration, guided by a boundary-hit strategy to dynamically alternate between search expansion and local refinement. The QUBO formulation further integrates a balance between projection data consistency and an edge-preserving quadratic prior. This approach transcends fixed bit-width constraints, substantially enhancing grayscale expressiveness and optimization stability. Experiments demonstrate superior reconstruction quality over multiple classical and learning-based baselines under sparse-view and limited-angle fan-beam CT settings, with successful deployment on the D-Wave hybrid quantum-classical solver.

Abstract

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.

Problem

• quantum computed tomography
• grayscale reconstruction
• QUBO
• binary encoding
• quantization error

Innovation

• dynamic interval encoding
• prior-balanced QUBO
• quantum computed tomography
• gray-level representation
• hybrid quantum-classical solver