GRAPPA reconstruction using quantum computing

Girish Babu Reddy

Published Jan 1, 2024• 0 citations

Abstract

The prolonged time required for Magnetic Resonance Imaging (MRI) procedures often causes stress and anxiety in patients. Patients' elongated exposure to a narrow bore of a scanner increases healthcare costs. Additionally, long scan times increase patient discomfort and cause motion artifacts in images. As a clinical MRI method, Generalized Autocalibrating Partially Parallel Acquisition (GRAPPA) is a parallel imaging technique that shortens data acquisition time and increases spatial resolution by employing multiple phased-array coils. Missing data are reconstructed by solving a linear time-invariant (LTI) system. When a large size of an interpolation kernel is used, the number of equations of the LTI system is significantly increased and the reconstruction time is delayed. Both software-based and hardware-based approaches have been proposed to accelerate the GRAPPA reconstruction. Dimension reduction is often used as the software-based approach which generates virtual coils and reduces the actual number of physical coils, so the total number of LTI equations is decreased. Field-programmable gate array (FPGA) was employed as a hardware-based approach to solve the LTI system. In this research, a quantum computing method was proposed to accelerate GRAPPA reconstruction. Different from the dimension reduction and FPGA techniques, quantum computing is an emerging computing paradigm that can accelerate computing speed with quantum bits (qubits) rather than classical bits. We decomposed GRAPPA reconstruction into two components: calibration and synthesis, and then applied the D-Wave quantum computing service to accelerate the calibration process. A few calibration coefficients are estimated through solving an LTI system on the D-Wave quantum computer. Then, those calibrated coefficients are used to synthesize missing data in under sampled k-space to meet the requirements of the Nyquist sampling rate and avoid aliasing artifacts. Experimental results show that quantum computing can successfully solve the calibration problem in GRAPPA MRI. The calibrated coefficients and reconstruction results are the same as the outcomes completed on a local computer which has the classical von Neumann architecture. Quantum computing speeds have been quantitatively analyzed and it is promising to accelerate GRAPPA. One drawback of the current implementation is that the D-Wave quantum computing service cannot accept over 30 variables of an LTI system, and this may be caused by the limited qubits which can be used on the quantum computing service now.

DOI: 10.62791/20366

Related papers

Quantum Computing for Data Calibration in Parallel Magnetic Resonance Imaging Reconstruction

Girish Babu Reddy, Gulfam Saju, Yi Liu +1 more

Parallel imaging techniques, such as GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) play an important role in Magnetic Resonance Imaging (MRI) by significantly reducing scan times and enhancing patient comfort without compromising image quality. GRAPPA's algorithmic framework involving calibration and synthesis stages is critical in reconstructing high-quality images. However, the computational load of the calibration stage, especially with large convolutional kernel sizes or an increased number of receiver coils, poses a significant bottleneck and limits its efficiency and applicability in clinical settings. In this paper, we introduce an approach by proposing a hybrid software architecture that integrates quantum computing into the GRAPPA reconstruction process. Our method exploits the computational capabilities of quantum computing to accelerate the calibration phase, thereby enabling real-time processing speeds. Through experimentation, we demonstrate that the quantum-enhanced approach can expedite the calibration process to around 10–20 milliseconds of Quantum Processing Unit (QPU) programming time for each Linear Time-Invariant (LTI) system solved. The method maintains the integrity of calibration outcomes, achieving results on par with conventional central processing unit (CPU)-based processes. The result represents the progress towards real-time MRI reconstruction by reducing clinical MRI workflows times, improving patient throughput, and potentially enabling new diagnostic capabilities. Solving LTI system with more attributes on D-Wave quantum computer will be studied to show advantages of QPU to CPU in the future work.

IEEE High Performance Extreme Computing ConferenceSep 23, 20241 citation

A Comparative Analysis of Quantum Computational Paradigms in Medical Imaging and Diagnostics: A Comprehensive Review

Sushil Kami, Kavitha Rani N, N. Ragini

Abstract Quantum computing is set to revolutionize medical imaging and diagnostics by enhancing speed, accuracy, and the ability to process complex datasets, leading to improved patient outcomes. This review paper provides an extensive comparative study of how quantum-mechanical principles like superposition, entanglement, and interference can overcome the inherent limitations of classical binary computing in the medical field. We explore specific applications in MRI and CT scan reconstruction, the mathematical advantages of the Quantum Fourier Transform (QFT), the integration of Quantum Machine Learning (QML) for automated pathology detection, and the transformative potential of hybrid quantum-classical systems. The paper also addresses current hardware limitations such as qubit decoherence, evaluates materials science innovations in superconducting circuits, and provides a strategic roadmap for the future of quantum-enhanced healthcare. Keywords: Quantum Computing, Medical Imaging, MRI Reconstruction, Qubits, Quantum Machine Learning, Diagnostics, Materials Science Introduction The field of medical imaging has undergone significant transformations over the last few decades, progressing from simple analog X-ray plates to complex digital 3D reconstructions and functional metabolic imaging. However, as the medical community moves toward "Precision Medicine," the demand for ultra-high-resolution data and real-time diagnostic feedback is growing at an exponential rate. Classical computing systems, governed by Moore’s Law, are reaching a physical and algorithmic bottleneck. The sheer volume of data generated by modern 7-Tesla MRI, Dual-Energy CT scans, and high-resolution PET-CT systems is becoming increasingly difficult to process with traditional von Neumann architectures. In modern clinical settings, a single high-resolution volumetric scan can generate several gigabytes of raw data. This data requires intensive signal processing—often taking minutes or even hours—to reconstruct into a format that a radiologist can interpret. In emergency medicine, specifically for stroke or trauma patients, the latency of classical reconstruction algorithms can be the difference between recovery and permanent disability. Quantum computing introduces a fundamental paradigm shift. By leveraging quantum bits (qubits), which utilize the subatomic properties of superposition and entanglement, quantum computers can theoretically perform massive parallel computations that are mathematically impossible for classical binary systems. This paper provides a comprehensive review of these quantum paradigms, comparing their efficiency to classical methods and outlining the path toward clinical implementation. Theoretical Framework: The Physics of Quantum Advantage Classical computers operate on bits, representing a deterministic state of either 0 or 1. In medical imaging, this means algorithms must process pixels or voxels sequentially. Quantum computing utilizes the unique properties of quantum mechanics to alter the fundamental complexity classes of imaging tasks. 2.1 Superposition and Parallelism Unlike a bit, a qubit can exist in a state |⟩=|0⟩+|1⟩, where and are complex probability amplitudes such that ||2+||2=1. This allows n qubits to represent 2n states simultaneously. For a medical image consisting of 10241024 voxels, a quantum system can map the entire state space into a vastly smaller number of physical qubits (approximately 20 qubits for a million voxels). This allows for "Global Optimization," where the computer evaluates all possible image configurations at once to find the one with the least noise. 2.2 Entanglement and Non-Locality Entanglement allows qubits to be correlated in a way that exceeds classical physics. In image processing, this property is being researched to create "Quantum Sensors." These sensors use entangled photons or atoms to detect minute magnetic field variations in MRI far exceeding the sensitivity of classical induction coils. This could lead to MRI machines that do not require massive, expensive superconducting magnets, making them portable and more accessible. 2.3 Quantum Interference and Phase Estimation Quantum interference is used to bias the probability of measuring the correct answer in an algorithm. In image denoising and deconvolution, interference patterns can be engineered to amplify the signal (the anatomical structure) while canceling out the noise (electronic artifacts or motion blur). This process, known as Quantum Phase Estimation (QPE), is a core component of many imaging algorithms that provide a "Quantum Speedup." Applications in Medical Modalities 3.1 Accelerated MRI Reconstruction via Quantum Fourier Transform (QFT) MRI relies on the Fast Fourier Transform (FFT) to convert raw signals from the frequency domain (k-space) into the spatial domain. The classical FFT has a complexity of O(NlogN). In contrast, the Quantum Fourier Transform (QFT) operates with a complexity of O(log2N). This exponential speedup has several critical clinical implications: Real-time Guided Surgery: Surgeons currently rely on static images. QFT could allow for "Live MRI," providing updated feedback during neurosurgery as brain tissue shifts. Pediatric and Geriatric Care: Reducing scan times from 45 minutes to 45 seconds would eliminate the need for anesthesia in children who cannot remain still. Low-Field Imaging: Higher computational power can compensate for lower-quality raw signals, allowing for high-quality images from smaller, less expensive MRI units in rural areas. 3.2 CT and PET Optimization: The Radon Transform CT scans utilize the Radon transform to reconstruct 3D volumes from 2D projections. Classical iterative reconstruction (IR) is computationally expensive and often results in "staircase artifacts." Quantum algorithms, such as the HHL (Harrow-Hassidim-Lloyd) algorithm for linear systems of equations, can solve the massive matrices required for CT reconstruction with logarithmic scaling. This allows for higher resolution while simultaneously reducing the radiation dose required for the patient. 3.3 Comparative Analysis: A Detailed Quantitative Review Table 1: Comparative Analysis: Classical vs. Quantum Computing in Medical Imaging Feature Classical Computing (Binary) Quantum Computing (Qubit) Clinical Impact & Consequences Basic Data Unit Bits (0 or 1) Qubits (Superposition) Exponentially higher data density and state representation. Logic Gates Boolean Logic (AND, OR, NOT) Unitary Gates (Hadamard, CNOT) Ability to explore multiple logical paths simultaneously. Processing Power Sequential or Vectorized (CPU/GPU) Massively Parallel (Global) Enables real-time diagnostic feedback during surgical procedures. MRI Scaling O (N log N) Complexity O (log2 N) Complexity Theoretical 100x speedup in image reconstruction times. Algorithmic Aim Gradient Descent (Local Minima) Quantum Annealing (Global Minima) Superior noise reduction and image clarity by finding the "true" global optimum. Storage & Memory Linear Growth Exponential Growth (2n) Efficient management of high-dimensional datasets like whole-genome sequencing. Radiation Safety Higher Dose (to maintain SNR) Lower Dose (Q-enhanced SNR) Significant reduction in long-term radiation exposure for chronic patients. Biomarker Detection Limited by pixel resolution/noise Enhanced via Quantum Interference Early-stage detection of micro-metastases and neurodegenerative markers. Hardware State Mature (Silicon CMOS) Emerging (NISQ Era) Shift toward hybrid architectures in the immediate clinical future. The transition from classical to quantum paradigms represents a shift from linear deterministic processing to exponential probabilistic optimization. While classical systems are robust and reliable for standard data management, quantum systems address the "computational bottleneck" inherent in high-resolution volumetric imaging (7T MRI, 4D-CT). The primary clinical advantage identified is the acceleration of the Radon and Fourier transforms, which reduces patient wait times and allows for lower-dose diagnostic protocols without sacrificing image quality. Integration with Artificial Intelligence (AI) and Machine Learning The synergy between Quantum Science and Artificial Intelligence Quantum Machine Learning (QML) is a primary focus for current research at institutions like eminent University. 4.1 Quantum Neural Networks (QNN) and Feature Spaces In classical AI, deep learning models often struggle with the "curse of dimensionality" when analyzing 4D imaging datasets. QNNs utilize "Quantum Feature Maps" to project data into a high-dimensional Hilbert space where classes of data (e.g., malignant vs. benign) become linearly separable. This leads to significantly higher sensitivity in automated mammography and lung cancer screening. 4.2 Automated Segmentation and Pathology Detection Automated segmentation involves the computer outlining the boundaries of an organ or a tumor. Classical AI requires thousands of labeled images to learn these boundaries. Preliminary studies suggest that QML algorithms can achieve higher accuracy with 70% less training data because the quantum kernels are inherently better at recognizing complex geometric patterns in biological tissue. Materials Science and Hardware Implementation The transition from theory to clinical practice is a challenge of Materials Science. The qubits must be isolated from all external interference to prevent "decoherence." Superconducting Qubits: Currently favored by IBM and Google, these use Josephson junctions made of superconducting materials like Niobium. They require dilution refrigerators to reach temperatures colder than deep space (15 mK). Trapped Ion Qubits: Utilize individual atoms (li

Apr 29, 20260 citations

A New Approach to Quantum Computing Multi-Qubit Generation and Development of Quantum Computing Platform with Magnetic Resonance Imaging Techniques

Zang‐Hee Cho, Young‐Don Son, Hyejin Jeong +4 more

Explosive increase of interest in quantum computing has resulted in various proposals for generation of quantum bits or qubits, the basic quantum computing unit. The superconducting qubits of Josephson Junction are the most widely accepted and currently used, while the Ion-trap and a similar molecule-based qubits have been proposed more recently. In these methods, each qubit is generated individually with great effort. Here we proposed a new technique using magnetic resonance imaging (MRI)-based qubit generation, by which multiple qubits can be generated. Simultaneously this provides a complete qubit platform for quantum computing. Central to the proposed method is the simultaneous generation of multiple qubits using the 'gradient' concept together with multiple radiofrequency coils, one for all qubits, and others for individual qubits with each small Q-coil. Another key concept is the time-encoded probability amplitude (TEPA) technique, using individual Q-coils together with the spin-echo series in each qubit incorporating readout gating for time-encoding. This MRI-based qubit-generation and qubit-encoding technique allowed us to develop an entirely new class of quantum computing platform. Our newly proposed MRI-based qubits are well-suited to currently available electronics, superconducting and semiconductor technologies, as well as nuclear magnetic resonance and MRI physics and technology.

arXiv:2206.05932Jun 13, 20223 citations

Pursuit and Review of Magnetic Resonance Imaging (MRI) based Quantum Computing -- Qubit Generation, Spin Purification, Tailored RF Pulses and MRI Sequences for Quantum Computing

Z. H. Cho, Jihye Han, Dae‐Hwan Suk +5 more

We propose a novel MRI (Magnetic Resonance Imaging) technique based quantum bit (qubit) generation with water proton NMR (1H-NMR), distinct from previously proposed NMR chemical shift or spectroscopic techniques based qubit generation. We briefly review prior NMR-based techniques in the context of quantum computing, focusing on MRI-related methods. The proposed technique utilizes MRI-based gradient methods combined with set of local reverse gradients to generate multiple qubits. This configuration enables the creation of multiple localized constant magnetic fields, each producing a qubit with highly homogeneous field, therefore, a unique single frequency. The RF electronics and signal processing techniques are analogous to those used in conventional MRI scanners, allowing operation at room temperature, with the exception of the main magnet, which remains identical to that of standard MRI systems. Additional advantages of this method include the ability to leverage the extensive pulse techniques and hardware developed for MRI scanners over the past 50 years. Furthermore, the wide array of MRI pulse sequences enables highly sophisticated signal processing for quantum computing applications, such as the spin purification.

arXiv:2505.12778May 19, 20250 citations

An FPGA-Based Quantum Computing Emulation Framework Based on Serial-Parallel Architecture

Y. H. Lee, Mohamed Khalil-Hani, Muhammad Nadzir Marsono

Hardware emulation of quantum systems can mimic more efficiently the parallel behaviour of quantum computations, thus allowing higher processing speed-up than software simulations. In this paper, an efficient hardware emulation method that employs a serial-parallel hardware architecture targeted for field programmable gate array (FPGA) is proposed. Quantum Fourier transform and Grover’s search are chosen as case studies in this work since they are the core of many useful quantum algorithms. Experimental work shows that, with the proposed emulation architecture, a linear reduction in resource utilization is attained against the pipeline implementations proposed in prior works. The proposed work contributes to the formulation of a proof-of-concept baseline FPGA emulation framework with optimization on datapath designs that can be extended to emulate practical large-scale quantum circuits.

International Journal of Reconfigurable ComputingJan 1, 201638 citations

Evaluation of quantum contouring algorithms for treatment planning on MR abdominal images

Rachel Glenn, Tucker Netherton, Adrian Celaya +4 more

Introduction: Quantum computing is increasingly being investigated for integration into medical radiology and healthcare applications worldwide. Given its potential to enhance clinical care and medical research, there is growing interest in evaluating its practical applications in clinical workflows. Methods: We developed an evaluation of quantum computing-based auto-contouring methods to introduce medical physicists to this emerging technology. We implemented existing quantum algorithms as prototypes tailored for specific quantum hardware, focusing on their application to auto-contouring in medical imaging. The evaluation was performed using a medical resonance imaging (MRI) abdominal dataset, comprising 102 patient scans. Results: The quantum algorithms were applied to the dataset and assessed for their potential in auto-contouring tasks. One of the quantum-based auto contouring methods demonstrated conceptual feasibility, practical performance is still limited by current available quantum hardware and scalability constraints. Discussion: Our findings suggest that while quantum computing for auto-contouring shows promise, it remains in its early stages. At present, artificial intelligence-based algorithms continue to be the preferred choice for auto-contouring in treatment planning due to their greater efficiency and accuracy. As quantum hardware and algorithms mature, their integration into clinical workflows may become more viable.

Frontiers in OncologyAug 6, 20250 citations