Optimal normalization in quantum-classical hybrid models for anti-cancer drug response prediction

TL;DR

The paper tackles instability in quantum-classical hybrid models for anti-cancer drug response prediction caused by rotation-angle encoding at the neural–quantum interface. It proposes a generalized tanh normalization $\\boldsymbol{\\phi'} = r \\cdot \\tanh(\\boldsymbol{\\phi}/a)$ to stabilize training and mitigate $2\\pi$-periodicity effects. Evaluated on the GDSC gene-expression dataset across five drugs, the proposed normalization yields higher cross-validated AUC than both a classical baseline and other normalization schemes, demonstrating robust performance improvements. The work contributes a practical interface normalization strategy for hybrid quantum-classical learning in biomedical prediction and suggests possible extensions to other high-dimensional domains and real quantum devices. Overall, this study highlights the critical role of encoding normalization in enabling reliable quantum-assisted learning for complex biomedical tasks.

Abstract

Quantum-classical Hybrid Machine Learning (QHML) models are recognized for their robust performance and high generalization ability even for relatively small datasets. These qualities offer unique advantages for anti-cancer drug response prediction, where the number of available samples is typically small. However, such hybrid models appear to be very sensitive to the data encoding used at the interface of a neural network and a quantum circuit, with suboptimal choices leading to stability issues. To address this problem, we propose a novel strategy that uses a normalization function based on a moderated gradient version of the $\tanh$. This method transforms the outputs of the neural networks without concentrating them at the extreme value ranges. Our idea was evaluated on a dataset of gene expression and drug response measurements for various cancer cell lines, where we compared the prediction performance of a classical deep learning model and several QHML models. These results confirmed that QHML performed better than the classical models when data was optimally normalized. This study opens up new possibilities for biomedical data analysis using quantum computers.

Figures (8)

• Figure 1: Overview of the quantum-classical hybrid machine learning model. Our proposed normalization function normalizes features effectively for inputting to the quantum circuits.
• Figure 2: Parameterized quantum circuit architecture. (A) The parameterized quantum circuit consists of three parts and is characterized by 3 hyperparameters ($n_1$,$n_2$, and $n_3$). The measurement layer has two types described in Figure 2B. (B) We prepared two types of measurement layer. The difference is whether the integrations of values are done inside or outside of the quantum circuit.
• Figure 3: Distribution of values before and after normalization. The blue graph represents the features before normalization, and the orange graph represents the features after normalization. (A) Distribution of values before and after normalization of the model using the existing method described in Equation \ref{['eq:eq1']}. After normalization, values far from 0 are more densely distributed than before normalization. (B) Distribution of values before and after normalization of the model using the proposed method described in Equation \ref{['eq:eq2']}. ($a=20, r=\frac{\pi}{2}$). The shape of the original distribution remains preserved after normalization with a change in scale.
• Figure A1: Cetuximab
• Figure A3: Docetaxel