Exploring Quantum Neural Networks for Demand Forecasting

TL;DR

An approach for training demand prediction models using quantum neural networks to overcome the limitations of traditional machine learning approaches in training predictive models for complex market dynamics is presented.

Abstract

Forecasting demand for assets and services can be addressed in various markets, providing a competitive advantage when the predictive models used demonstrate high accuracy. However, the training of machine learning models incurs high computational costs, which may limit the training of prediction models based on available computational capacity. In this context, this paper presents an approach for training demand prediction models using quantum neural networks. For this purpose, a quantum neural network was used to forecast demand for vehicle financing. A classical recurrent neural network was used to compare the results, and they show a similar predictive capacity between the classical and quantum models, with the advantage of using a lower number of training parameters and also converging in fewer steps. Utilizing quantum computing techniques offers a promising solution to overcome the limitations of traditional machine learning approaches in training predictive models for complex market dynamics.

Figures (13)

• Figure 1: A two-layered ansatz applied to four qubits. Each layer is defined by a variational circuit $V_j$ dependent on some parameters $\boldsymbol{\theta}_j$. The circuits $Ent$ are used to entangle the qubits, and the state $\ket{\psi}^{\otimes n}$ denotes the output of the feature map.
• Figure 2: Cumulative variance of the data. The x-axis represents the component index, while the y-axis represents the variance. The sets used in this article were marked in black (4 features), green (8 features), and red (19 features, the complete dataset). The bars represent the individual variance of each component, while the blue line represents the cumulative variance.
• Figure 3: Variational Quantum Circuit. Hadamard gates layer prepares the qubits in uniform superposition, Ry gates (red) encode the data in qubits, variational layer, or ansatz (blue) entangle the qubits and applies parametrized rotations, where $\theta_i$, $\phi_i$ and $\omega_i$ represent, respectively, the rotation angles in the x, y, and z axes in each qubit $i$, and are the trainable parameters of the model. Measurement layer (green) collapse the qubits, generating the outputs 2023Ogur.
• Figure 4: Entanglement Layers used in variational circuit (Figure \ref{['fig:rede_usada']}). In (a), here named "entanglement layer 1", the qubits are entangled in pairs, and these pairs are subsequently tied together. In (b), here named "entanglement layer 2", the qubits are entangled in a cascade. Adapted from 2023Ogur.
• Figure 5: Predictions for quantum models with 4 features. Figure (a) shows the quantum experiment 1 with 1 layer, figure (b) quantum experiment 2 with 1 layer, figure (c) quantum experiment 1 with 3 layers, figure (d) quantum experiment 2 with 3 layers, figure (e) quantum experiment 1 with 5 layers and (f) quantum experiment 2 with 5 layers. The x-axis shows the model's training months, while the y-axis represents average daily financing. The distributions obtained from 10 experiments are shown in the colored violin graphs, while the actual values are shown in the black line.