Two-Level Decomposition Significantly Reduces Quantum Circuit Complexity for Image Analysis

Quantum computing promises revolutionary advances in image processing, but current limitations in hardware present significant challenges. Emmanuel Billias and Nikos Chrisochoides, from Old Dominion University, along with their colleagues, are addressing this problem by developing a new approach to edge detection in medical images that can run on today’s quantum computers. Their research introduces a two-level decomposition strategy that dramatically reduces the computational demands of quantum algorithms, achieving over 62% reductions in circuit complexity and 93% fewer operations while maintaining high accuracy. This breakthrough demonstrates the potential for performing complex image analysis on near-term quantum devices and offers early evidence of a pathway towards utility-scale quantum computing, successfully applied to raw MRI data and large 2D and 3D datasets.

Quantum Image Processing for Medical Applications

Quantum computing offers immense potential for revolutionizing medical imaging, particularly in areas demanding real-time analysis, such as image-guided neurosurgery. Accurate and rapid edge detection is crucial for identifying critical anatomical structures during these procedures, but applying quantum algorithms to high-resolution medical images presents challenges due to limitations of current quantum hardware and the sheer volume of data involved. Researchers have developed a hybrid quantum-classical methodology centered around a two-level decomposition strategy. This approach optimizes how images are prepared for quantum processing by partitioning the input image into sub-images, each processed by a separate quantum circuit, effectively distributing the computational load and minimizing artifacts.

This process improves the quality of subsequent quantum processing and allows for scalability. The team focused on enhancing the Quantum Hadamard Edge Detection (QHED) algorithm by restructuring the circuit using a more efficient gate and employing circuit-cutting techniques. These improvements minimize circuit depth and mitigate the impact of noise, leading to substantial gains in fidelity and a significant reduction in the number of operations required. This two-level decomposition represents a significant step towards practical quantum image processing. To demonstrate scalability, the researchers implemented a distributed computing methodology and successfully applied their image-level decomposition to both 2D and 3D brain MRI images. Furthermore, they processed raw MRI data using an inverse quantum Fourier transform, potentially eliminating the need for costly classical data conversion. These results demonstrate the feasibility of performing high-fidelity QHED on current quantum hardware and pave the way for integrating quantum image processing into clinical workflows.

Distributed Quantum Image Processing with D-NISQ

This research presents a novel approach, D-NISQ (Distributed Near-term Intermediate-Scale Quantum Computing), to tackle the challenges of running quantum algorithms on current, limited-scale quantum hardware for medical image processing. The core idea is to decompose large images into smaller sub-images, process them individually on a distributed computing cluster simulating a quantum processing unit, and then reassemble the results, allowing for processing images that would be too large for current quantum computers. The D-NISQ approach divides large images into smaller sub-images with overlapping buffer pixels to maintain continuity and avoid artifacts. The research focuses on combining the Inverse Quantum Fourier Transform (IQFT) and a modified Quantum Hadamard Edge Detection (QHED) algorithm, with each sub-image processed by a quantum circuit on a distributed computing cluster.

A modified QHED circuit (QHEDM) is proposed to improve performance and reduce the number of quantum gates. The QHEDM circuit, combined with image decomposition and distributed processing, demonstrates significantly higher fidelity compared to the original QHED circuit, especially for larger images. The approach allows for processing images that are too large for current quantum computers, as demonstrated with 2D and 3D medical images. The QHEDM circuit reduces the number of quantum gates required, making it more suitable for current quantum hardware. The research relies heavily on simulations using IBM Qiskit and a high-performance computing cluster, evaluating performance based on fidelity, circuit depth, and the number of CNOT (CX) gates. Circuit optimization is essential for improving the performance of quantum algorithms on current quantum hardware, demonstrating the potential of quantum computing for medical image analysis.

Quantum Edge Detection on Noisy MRI Data

Results demonstrate the feasibility of performing high-fidelity Quantum Homomorphic Edge Detection (QHED) on current quantum hardware and provide early evidence of distributed utility-scale quantum computing. This is illustrated by processing raw k-space MRI data with an inverse quantum Fourier transform and a distributed simulation of the modified QHED on large 2D and 3D MRI datasets. The research focuses on Quantum Computing, Quantum Edge Detection, Algorithm development, and techniques including Circuit Cutting and Circuit Knitting, alongside Problem Decomposition strategies for achieving Quantum Utility-Scale computation in the field of Medical Image Computing.

Linear Scaling and Quantum Image Processing

This work demonstrates that a restructured gate yields a substantial fidelity enhancement in the QHED circuit by reducing circuit depth to linear scaling with respect to input size. When integrated with circuit cutting techniques, these optimizations yield further fidelity improvements, although they currently incur a classical overhead associated with post-processing required for stitching subcircuits. The feasibility of constructing a computational pipeline beginning with k-space data input, reducing computational complexity, and culminating in a distributed quantum edge detection algorithm has been shown, enabling image analysis and feature extraction with viable results. The approach has been validated for both two-dimensional (2D) pixel-based and three-dimensional (3D) voxel-based representations, demonstrating that utility-scale quantum hardware can be leveraged for medical image processing.

Future work will include a more thorough quantitative analysis of performance on 2D and 3D noise-based models. Reducing the width of the proposed quantum circuit achieves a decoupling of gate count and fidelity, although this currently incurs a classical overhead due to the necessary knitting step following circuit cutting. Another promising direction is the full distribution of the pipeline, starting from the inverse quantum Fourier transform (IQFT) circuit. While theoretically possible to reconstruct the original statevector from cut circuit statevectors, current software limitations prevent direct implementation.

The long-term objective is to synergistically combine quantum sensing’s ability to gather more precise raw data with quantum computing’s capacity to process intraoperative data rapidly, potentially transforming IGNS and general medical image computing. This research was supported in part by the Richard T. Cheng Endowment at Old Dominion University (ODU). The authors thank Min Dong at ITS in ODU for his help with the HPC cluster at ODU. This work was performed using computational facilities at ODU enabled by grants from the National Science Foundation and Virginia’s Commonwealth Technology Research Fund. Gemini and Grammarly were used to improve readability; the authors reviewed and take full responsibility for the final content.