Quantum Machine Learning Models Based on Amplitude Encoding for Delay Forecasting: A Comparative Analysis of QSVR and QNN Models

Abstract

This paper presents a comparative analysis of two quantum machine learning models based on amplitude encoding Quantum Support Vector Regression (QSVR) and Quantum Neural Network (QNN) applied to the problem of delay (demand/replenishment lag) prediction in inventory management systems. The study uses a dataset comprising 52 months of sales history for 51 product categories. Classical feature vectors are mapped into quantum states via amplitude encoding, which embeds a d-dimensional vector into $\mathbf{n}=\left\lceil\log _{2} \mathbf{d}\right\rceil$ qubits with exponential space efficiency. The QSVR model employs a quantum kernel while the QNN model uses a data re-uploading variational circuit (4 qubits, 2 layers, R_Y rotation gates with CNOT entangling gates) trained with the COBYLA optimizer (200 iterations). Experimental results show that the QNN model achieved a slightly higher coefficient of determination $\left(\mathrm{R}^{2} \text{QNN}=0.8371\right.$ vs. $\left.\mathrm{R}^{2} \text{QSVR}=0.8185\right)$, whereas the QSVR model achieved a lower mean absolute error (MAE=0.4145 vs. 0.4630 for QNN), while in terms of RMSE the QNN model outperformed QSVR (0.4916 vs. 0.7270), indicating fewer large prediction errors. All experiments were simulated in Python using the IBM Qiskit quantum computing framework. The findings suggest that quantum machine learning models are a promising direction for practical inventory replenishment and delay-forecasting tasks.