Benchmarking Quantum and Classical Machine Learning Models on Oncological Data

Technical Summary: Benchmarking Quantum and Classical Machine Learning Models on Oncological Data

Problem Statement
Machine learning is increasingly applied to oncological data for detection, diagnosis, and treatment. However, biological data presents unique challenges, including high dimensionality, limited sample diversity, and complex feature interactions (the "curse of dimensionality"). While quantum machine learning (QML) is theoretically proposed to offer advantages in handling such complex, high-dimensional data, there is a lack of rigorous empirical evaluation demonstrating practical quantum advantage. Existing studies often fail to disentangle whether performance limitations stem from optimization issues (e.g., barren plateaus, local minima), intrinsic model expressivity, or data encoding schemes. Furthermore, classical baselines in prior works are frequently trained with fixed hyperparameters, leaving open the question of whether their optimal performance has been realized.

Methodology
The authors developed a rigorous benchmarking framework to fairly compare QML and classical machine learning (CML) models across tabular, omics, and spatial oncological datasets. The study utilized the Red Cedar quantum machine learning framework and AutoML-optimized classical neural networks.

• Datasets: The study evaluated three categories of data:
  1. Tabular: The Wisconsin Diagnostic Breast Cancer (WDBC) dataset.
  2. Omics: Genomic mRNA expression data from The Cancer Genome Atlas (TCGA) for breast (BRCA), colon (COAD), and ovarian (OV) cancers.
  3. Spatial: Medical imaging datasets from MedMNIST (BreastMNIST, PathMNIST, DermaMNIST).
• Preprocessing: The authors tested various preprocessing strategies, including random forest feature selection for tabular/omics data and ResNet18 feature extraction for spatial data.
• Quantum Model:
  • Encoding: The study employed bit-bit encoding, a method that classically encodes samples into bits corresponding to qubit initialization and readout. This approach offers universal approximation properties, allowing the model to theoretically achieve 100% training accuracy without expressivity constraints.
  • Architecture: A layered bipartite architecture with parameterized entangling nodes between label and data qubits.
  • Training: Models were trained using the Red Cedar framework's sub-net initialization and exact coordinate updates. This incremental warm-start strategy avoids barren plateaus and eliminates the need for classical optimizers. Training continued until 100% training accuracy was reached or a five-day time limit was hit.
• Classical Baseline:
  • AutoML: The TPOT2 library was used to evolve optimal neural network architectures and hyperparameters, ensuring the classical baselines were not under-optimized.
  • Comparison Stages: Classical models were trained on raw data, preprocessed data, and bit-bit encoded data (both pre-discretized and discretized) to ensure a fair comparison across data representations.
• Resource Estimation: A theoretical metric, $Q_{dataset}(1.0)$, was calculated. This represents the number of qubits required to encode a dataset such that 100% training and test accuracy is theoretically possible (i.e., no collisions in the discretized space). A threshold of 50 qubits was used as a heuristic for potential quantum advantage, based on the plateau of classical simulation capabilities.

Key Results

• No Evidence of Quantum Advantage: Across all tested datasets (WDBC, TCGA omics, and MedMNIST spatial) and preprocessing methods, the quantum models did not outperform the AutoML-optimized classical neural networks. The test accuracies of both model classes were statistically indistinguishable within standard error margins.
• Training Performance: All quantum models successfully reached 100% training accuracy, confirming that the training methodology effectively avoided optimization pitfalls like barren plateaus. Consequently, the lack of quantum advantage was not attributed to training failures.
• Generalization: Both quantum and classical models failed to consistently reach the theoretical maximum test accuracy as the number of qubits increased, particularly on datasets with higher complexity.
• Resource Estimation Findings:
  • WDBC and Omics: The $Q_{dataset}(1.0)$ values for WDBC (14–15 qubits) and omics datasets (15–20 qubits) were well below the 50-qubit threshold, suggesting these datasets are unlikely candidates for quantum advantage.
  • Spatial Datasets: Some spatial datasets (e.g., flattened BreastMNIST) approached or exceeded the 50-qubit threshold, but results were inconsistent across preprocessing methods (e.g., ResNet18 vs. flattening) and often attributed to data processing artifacts rather than intrinsic complexity.
• Robustness to Preprocessing: The resource estimation framework proved robust to preprocessing; for omics data, random forest feature selection reduced features by 99.8%, yet the $Q_{dataset}(1.0)$ remained statistically insignificant between preprocessed and raw datasets.

Significance and Claims
The paper claims to establish a more rigorous framework for assessing quantum advantage by systematically analyzing performance scaling with model size and employing fair, AutoML-optimized classical baselines. The primary conclusion is that current benchmark datasets in the quantum machine learning literature do not exhibit evidence of quantum advantage for oncological classification.

The authors argue that the field must move beyond these existing benchmarks. They suggest that meaningful progress toward practical quantum advantage requires analyzing higher-dimensional, more biologically realistic datasets (e.g., multi-omics, multi-modal, or time-series data) that possess the representational power and higher-order interactions necessary to leverage quantum computational properties. The study highlights that the current lack of accessible, complex open-source biological data is a barrier to demonstrating quantum utility in the life sciences.