CQ CNN: A Hybrid Classical Quantum Convolutional Neural Network for Alzheimer's Disease Detection Using Diffusion Generated and U Net Segmented 3D MRI

TL;DR

This paper proposes an end to end hybrid classical quantum convolutional neural network (CQ CNN) for AD detection using clinically formatted 3D MRI data and concludes that CQCNN architecture like models could become a viable option and even a potential alternative to classical models for AD detection, especially in data limited and resource constrained clinical settings.

Abstract

The detection of Alzheimer disease (AD) from clinical MRI data is an active area of research in medical imaging. Recent advances in quantum computing, particularly the integration of parameterized quantum circuits (PQCs) with classical machine learning architectures, offer new opportunities to develop models that may outperform traditional methods. However, quantum machine learning (QML) remains in its early stages and requires further experimental analysis to better understand its behavior and limitations. In this paper, we propose an end to end hybrid classical quantum convolutional neural network (CQ CNN) for AD detection using clinically formatted 3D MRI data. Our approach involves developing a framework to make 3D MRI data usable for machine learning, designing and training a brain tissue segmentation model (Skull Net), and training a diffusion model to generate synthetic images for the minority class. Our converged models exhibit potential quantum advantages, achieving higher accuracy in fewer epochs than classical models. The proposed beta8 3 qubit model achieves an accuracy of 97.50%, surpassing state of the art (SOTA) models while requiring significantly fewer computational resources. In particular, the architecture employs only 13K parameters (0.48 MB), reducing the parameter count by more than 99.99% compared to current SOTA models. Furthermore, the diffusion-generated data used to train our quantum models, in conjunction with real samples, preserve clinical structural standards, representing a notable first in the field of QML. We conclude that CQCNN architecture like models, with further improvements in gradient optimization techniques, could become a viable option and even a potential alternative to classical models for AD detection, especially in data limited and resource constrained clinical settings.

Figures (10)

• Figure 1: Subfigure (a) illustrates the 3D MRI volume in a three-dimensional coordinate system, where the brain is represented as a collection of voxels, forming the full anatomical structure. Subfigure (b) shows example 2D slices extracted from the 3D volume, one from each of the three primary anatomical planes: axial (horizontal cross-section), coronal (vertical front-to-back cross-section), and sagittal (side view). Subfigure (c) presents MRI images of the axial, coronal, and sagittal views, along with corresponding brain masks that isolate the brain tissue from surrounding structures.
• Figure 2: The illustration depicts the diffusion process applied to a sagittal plane of an MRI image sample. The forward process starts with a clean image $x_0$ and progressively adds Gaussian noise over $T$ timesteps. At each timestep, the image is modified according to the conditional distribution $q(x_t | x_{t-1})$. As $t$ increases, the image becomes progressively more corrupted, ultimately resulting in pure noise at $x_T$. In the reverse process, the model learns to recover the original clean image $x_0$ starting from pure noise $x_T$ by learning the conditional distribution $p(x_{t-1} | x_t)$ at each timestep using a U-Net.
• Figure 3: The illustration depicts the architecture of a U-Net, which has four main components: the encoder, bottleneck, decoder, and skip connections. The encoder consists of five convolutional blocks (C1 to C5), progressively reducing spatial dimensions from 128×128 to 8×8 while increasing the feature channels from 32 to 512. Each block uses convolutional operations (blue) with 3×3 kernels, ReLU activations, and "same" padding (purple), followed by max-pooling layers (red arrows) for downsampling. The bottleneck operates at the lowest resolution (8×8) with the highest abstraction level (512 channels). The decoder upscales feature maps back to 128×128 using transposed convolutions (green arrows) and convolutional blocks (C6 to C9) while reducing feature channels. Skip connections (gray arrows) link corresponding layers of the encoder and decoder, ensuring that fine-grained spatial details are preserved. Finally, a 1×1 convolution (yellow) generates the output segmentation map (128×128×1).
• Figure 4: Schematic depiction of a classical neural network (a) and a quantum neural network (b) for binary classification. In Subfigure (a), $x_1, x_2, \dots, x_m$ denote the $m$ input neurons representing the input features. The hidden layer consists of $n$ neurons represented as $h_{1}^{[1]}, h_{2}^{[1]}, \dots, h_{n}^{[1]}$, where the superscript $[1]$ indicates the first hidden layer, and the subscript identifies the specific neuron within that layer (e.g., $h_{1}^{[1]}$ is the first neuron in the first hidden layer). The output layer neurons, representing the predicted probabilities for each class given the input features, are denoted by $y_1$ and $y_2$. In Subfigure (b), the input and output layers are similar to those in Subfigure (a). However, the classical hidden layers are replaced by a 3-qubit PQC. The classical features are first reduced to match the number of qubits, represented as $q_1, q_2, q_3$, with three black dots indicating the qubits. These features are then encoded into quantum states through data encoding. A parameterized ansatz is applied to capture complex relationships using quantum operations. Afterward, quantum measurements are performed, and the PQC outputs a classical probability. This probability passes through an intermediate linear layer, denoted as $o_1$. Finally, $o_1$ is mapped to the output probability using Equation \ref{['eq:12']}.
• Figure 5: The schematic depicts a PQC using ZZFeatureMap encoding, with subfigure (a) showing a 2-qubit circuit and subfigure (b) showing a 3-qubit circuit. Each qubit is initialized with a Hadamard gate $H$, followed by phase rotations $P(2 \cdot x[i])$ to encode classical data into a quantum state. Entanglement is then introduced through controlled-Z (CZ) gates, which create correlations between qubits by applying phase shifts based on their classical values. A phase rotation $P(2.0(\pi - x[i])(\pi - x[i]))$ is applied to introduce further phase shifts based on the classical values. The ansatz circuit applies trainable single-qubit rotations $R_y(\theta_i)$ to further refine the quantum state.