Analyzing Images of Blood Cells with Quantum Machine Learning Methods: Equilibrium Propagation and Variational Quantum Circuits to Detect Acute Myeloid Leukemia

Technical Summary: Analyzing Images of Blood Cells with Quantum Machine Learning Methods

Problem Statement
The paper addresses the feasibility of applying Quantum Machine Learning (QML) to real-world medical imaging, specifically the automated detection of Acute Myeloid Leukemia (AML) from blood cell microscopy images. While classical deep convolutional networks (CNNs) have demonstrated high accuracy in this domain, they rely on backpropagation, a method fundamentally incompatible with quantum systems. Backpropagation requires intermediate measurements to compute gradients, which collapse quantum states and destroy the superposition and entanglement necessary for quantum advantage. Furthermore, classical methods often demand substantial computational resources and large annotated datasets, which are costly to acquire in medical contexts. The study aims to evaluate whether QML algorithms can achieve competitive performance under severe constraints, including limited qubit resources, reduced image resolution, and the absence of backpropagation.

Methodology
The authors utilized the AML-Cytomorphology dataset, comprising 18,365 expert-annotated single-cell blood smear images (100 AML patients, 100 healthy controls). To ensure fair comparison across all methods and align with practical quantum constraints, images were resized to 64×64 pixels.

The study evaluated two distinct approaches against classical baselines (CNN and Dense Neural Networks):

1. Variational Quantum Circuits (VQC):

   • Architecture: A 4-qubit classifier implemented via classical simulation using IBM's Qiskit.
   • Input Processing: Raw images were converted to grayscale, and 20 engineered scalar features (covering intensity statistics, GLCM textures, morphology, edge metrics, and FFT frequency) were extracted. These were reduced to 4 dimensions via Principal Component Analysis (PCA) and rescaled to match rotation gate domains.
   • Circuit Design: The circuit employed a ZZFeatureMap for data encoding to create entanglement and a shallow RealAmplitudes ansatz (2 layers, 8 trainable parameters, depth 12) optimized for Noisy Intermediate-Scale Quantum (NISQ) devices.
   • Training: A hybrid classical-quantum loop was used. The quantum circuit acted as a black box; a classical optimizer (COBYLA, gradient-free) iteratively adjusted parameters to minimize the mean squared error between the expectation value of the first qubit ($\langle Z_0 \rangle$) and target labels. This avoided the need for quantum gradient computation.

2. Equilibrium Propagation (EP):

   • Concept: A quantum-inspired, energy-based learning method implemented on Hopfield-like neural networks with symmetric weights.
   • Mechanism: EP avoids backpropagation entirely. It trains the network through two phases: a "Free Phase" where the network settles to an equilibrium state based on input, and a "Nudged Phase" where output neurons are weakly adjusted toward target labels. Weight updates are derived from the difference between these two equilibrium states.
   • Architecture: A layered network (256–128–64 hidden units with tanh activations) trained using momentum SGD and early stopping.

Experimental Protocol
To assess data efficiency, the authors constructed balanced subsets of the dataset containing 50, 100, 200, and 250 samples per class. All models were evaluated using stratified 80/20 train-test splits. The VQC and EP models were compared against classical CNN and Dense NN baselines under identical experimental conditions.

Key Results

• Performance on Full Subsets (250 samples/class):
  • Classical CNN: Achieved 98.4% accuracy (training time: 745s).
  • Equilibrium Propagation (EP): Achieved 86.4% accuracy (training time: 89.4s), representing a gap of only 12% from the CNN without using backpropagation.
  • Variational Quantum Circuit (VQC): Achieved 83.0% accuracy (training time: 180s).
• Data Efficiency:
  • The VQC demonstrated remarkable stability, maintaining 83% accuracy even with only 50 samples per class.
  • In contrast, the Classical CNN required 250 samples per class (5× more data) to reach its peak performance of 98.4%; at 50 samples, CNN accuracy dropped to 92%.
  • This suggests that quantum methods may be more data-efficient, a critical advantage for medical domains where expert annotations are scarce.

Significance and Claims
The paper posits that these results establish reproducible baselines for QML in healthcare, validating the feasibility of these methods in the NISQ era. Key claims include:

1. Feasibility without Backpropagation: The success of EP demonstrates that energy-based learning can serve as a viable, quantum-compatible alternative to backpropagation for training neural networks on real clinical data.
2. Data Efficiency as a Quantum Advantage: While classical CNNs currently hold higher absolute accuracy, the VQC's ability to maintain robust performance with minimal training data (50 samples) highlights a potential advantage for rare disease research where large datasets are unavailable.
3. NISQ Compatibility: The shallow 12-depth circuit design is explicitly optimized for current hardware constraints (e.g., IBM Quantum systems with ~100 qubits and limited coherence times), suggesting that near-term experimental validation is possible.
4. Resource-Constrained Deployment: The authors note that EP, with its low inference time (0.13s) and lack of backpropagation, is particularly suitable for edge deployment on neuromorphic hardware, potentially enabling battery-powered point-of-care diagnostics.

The authors maintain a modest tone, acknowledging that current results rely on ideal statevector simulations (which do not account for shot noise or gate errors) and that feature engineering limits representational capacity compared to end-to-end CNNs. They conclude that while classical methods currently outperform quantum ones in absolute accuracy, quantum methods offer competitive performance when data availability is the limiting resource rather than model capacity.