# Quantum Neural Networks Approach for Water Discharge Forecast
## 1 Introduction  
Water resources are essential for human life; throughout history, rivers have been the nuclei of the places where civilizations were born. Floods are among the hazards that produce significant life losses annually [1, 2]. Therefore, the analysis and modeling of river discharge is essential for limiting the negative impact of such hazards and taking prevention measures, among which plans in the case of disasters are essential [3, 4, 5, 6, 7]. Various techniques have been employed to describe the pattern of the river flow, for example, statistics-based approaches, including Box-Jenkins models [8, 9, 10, 11, 12], Generalized Linear Models (GLMs) [13], Generalized Additive Models (GAMs) [14], Generalized Additive Mixed Models (GAMMs) [15, 16], and Weighted Regression [17]. Utilizing Artificial Intelligence (AI) techniques [18, 19, 20, 21] in forecasting the river flow increased the models' accuracy, given the ability of machine learning (ML) techniques to capture the high variability of the various data series, such as in medicine, cybersecurity, engineering, environmental sciences, decision making, economics, etc. [22, 23, 24, 25, 26, 27, 28, 29]. Hybrid algorithms overperform in many cases compared to the single AI ones [30, 31] in terms of the forecast. However, in most cases, the extremes are not well captured, impacting the neighboring values' prediction. The rapid development of quantum computing hardware has led to the parallel advancement of multiple technological approaches. Among these, superconducting circuits and ion trap technologies have demonstrated significant advantages and currently holda leading position in the field [32; 33]. Ion trap technology has exhibited remarkable performance in high-precision quantum gate operations, providing strong support for constructing large-scale and stable quantum computers. By confining single or multiple ions and precisely controlling their states using laser techniques, ion trap technology effectively reduces external interference. It also maintains qubit coherence, thereby enabling high-fidelity quantum logic gate operations [32; 33]. In quantum simulation, quantum computers can simulate intricate quantum systems beyond the capabilities of classical computers. This enables in-depth studies of quantum many-body physics and quantum chemistry, facilitating research into high-temperature superconductivity mechanisms, novel drug design, and material discovery [33; 34]. The quantum algorithms integrate the strengths of quantum and classical computing, leveraging quantum trials to achieve superior approximations compared to classical methods, with practical applications in logistics scheduling and financial risk management [33; 35; 36]. Quantum neural networks (QNNs) represent a fusion of quantum computing and neural networks, aiming to enhance neural network performance by harnessing quantum properties. The fundamental principle of QNNs involves using qubits to represent neuron states and employing quantum gate operations to facilitate information processing and transmission between neurons [37]. QNNs exploit quantum superposition and entanglement to enable more complex and efficient information processing. For instance, in a simple QNN model, the input quantum state undergoes a series of quantum gate transformations to produce an output state analogous to the computational process of neurons in classical networks [38]. In practical applications, QNNs exhibit unique advantages. QNNs outperform classical neural networks in image recognition tasks by effectively capturing intricate features within image data [39]. The superposition states of qubits allow simultaneous representation of multiple states, enabling QNNs to process high-dimensional data more comprehensively and improve recognition accuracy [40]. Applications of QNNs can be seen in chemistry [40], materials informatics [41], hardware security [42], times series forecasting [43; 44], and weather prediction [45]. A review of the recent applications of QNNs is presented in [46].