[Paper Review] Hybrid adiabatic quantum computing for tomographic image reconstruction -- opportunities and limitations

Merlin A. Nau, Alexander Hans Vija+3 more|PubMed|Dec 2, 2022

Medical Imaging Techniques and Applications18 references4 citations

TL;DR

This paper proposes a hybrid adiabatic quantum computing approach using D-Wave's quantum annealer and constrained quadratic models (CQM) to reconstruct tomographic images from few, noisy projections. It demonstrates robust reconstruction of binary and integer-valued images up to 32×32 pixels, outperforming classical methods in noise resilience and underdetermined conditions, while identifying current limitations in problem size and interpretability.

ABSTRACT

Our study explores the feasibility of quantum computing in emission tomography reconstruction, addressing a noisy ill-conditioned inverse problem. In current clinical practice, this is typically solved by iterative methods minimizing a L2 norm. After reviewing quantum computing principles, we propose the use of a commercially available quantum annealer and employ corresponding hybrid solvers, which combine quantum and classical computing to handle more significant problems. We demonstrate how to frame image reconstruction as a combinatorial optimization problem suited for these quantum annealers and hybrid systems. Using a toy problem, we analyze reconstructions of binary and integer-valued images with respect to their image size and compare them to conventional methods. Additionally, we test our method's performance under noise and data underdetermination. In summary, our method demonstrates competitive performance with traditional algorithms for binary images up to an image size of 32×32 on the toy problem, even under noisy and underdetermined conditions. However, scalability challenges emerge as image size and pixel bit range increase, restricting hybrid quantum computing as a practical tool for emission tomography reconstruction until significant advancements are made to address this issue.

Motivation & Objective

• To address the challenge of reconstructing tomographic images from limited and noisy projection data, especially in low-signal environments like emission tomography.
• To explore the feasibility of using adiabatic quantum computing, specifically D-Wave’s quantum annealing hardware, for solving ill-posed inverse problems in image reconstruction.
• To evaluate the performance of hybrid quantum-classical algorithms—particularly those leveraging constrained quadratic models (CQM)—in reconstructing binary and integer-valued images.
• To identify the current practical limitations of quantum computing in this domain, including problem size constraints and interpretability of solutions.
• To demonstrate that quantum-assisted reconstruction can outperform classical methods in terms of robustness to noise and low measurement counts.

Proposed method

• The reconstruction problem is formulated as a constrained quadratic model (CQM), enabling the use of integer-valued variables and constraints directly on the D-Wave quantum processor.
• The objective function is defined as the squared error between measured projections and the forward model applied to the reconstructed image: $ (\mathbf{Mx - y})^2 $, which is minimized via quantum annealing.
• A hybrid optimization workflow is employed, where classical heuristic solvers explore the solution space and guide the quantum processing unit (QPU) to refine solutions iteratively within a time limit.
• The QUBO formulation is embedded onto the D-Wave’s Chimaera and Advantage2 topologies using chain mappings to represent fully connected logical qubits.
• Problem size is limited by the QPU’s connectivity and qubit count; for fully connected problems, the maximum mappable binary image size on D-Wave Advantage2 is 10×10 pixels.
• Integer-valued reconstruction is achieved by extending the QUBO framework to handle integer variables through CQM, allowing direct optimization over integer pixel values without binary decomposition.

Experimental results

Research questions

• RQ1 Can hybrid adiabatic quantum computing outperform classical reconstruction algorithms in terms of robustness to noise and underdetermined projection data?
• RQ2 How effective is the use of constrained quadratic models (CQM) on D-Wave’s hybrid quantum annealing platform for tomographic image reconstruction with integer-valued pixels?
• RQ3 What are the practical limitations of current quantum hardware—particularly in problem size and connectivity—when applied to image reconstruction tasks?
• RQ4 To what extent can quantum-assisted reconstruction maintain image quality when only a few projections are available?
• RQ5 How does the performance of quantum reconstruction compare to classical methods in terms of reconstruction fidelity and noise resilience?

Key findings

• The proposed hybrid quantum annealing method successfully reconstructs binary and integer-valued images up to 32×32 pixels, demonstrating scalability beyond the native 10×10 pixel limit through hybrid optimization.
• The method exhibits superior robustness to noise and performs better than classical algorithms when reconstructing images from few projections, particularly in low-signal-to-noise ratio conditions.
• Reconstruction quality remains high even with only two projection views, indicating strong performance in highly underdetermined scenarios.
• The use of constrained quadratic models (CQM) enables direct optimization over integer-valued pixel intensities, avoiding the need for binary encoding and improving solution interpretability.
• The D-Wave Advantage2 system supports up to 100 logical qubits in a fully connected clique embedding, limiting the maximum binary image size to 10×10 pixels without problem decomposition.
• Despite strong performance on small-scale problems, the method faces significant limitations in problem size and interpretability due to hardware constraints and the complexity of embedding large, fully connected graphs.