# Optimization Strategies in Quantum Machine Learning: A Performance Analysis
## 2 Literature Review and Background
### Quantum Neural Networks (QNNs)  
Quantum machine learning (QML) represents a synergistic fusion of principles from quantum computing and classical machine learning, intended for the development of novel methodologies that enhance computational efficiency and performance. A key innovation in this domain is the Quantum Neural Network (QNN), a machine learning model that exploits quantum phenomena such as entanglement and superposition to perform computations. QNNs are inspired by the principles of quantum physics and quantum computing, where neurons are represented as quantum states, and transitions between these states are governed by operations derived from quantum logic gates [14]. QNNs hold significant potential to outperform classical neural networks in various applications. Several models and frameworks for designing and implementing QNNs have been proposed, showcasing their ability to leverage quantum computing principles for superior data processing. Compared to classical neural networks, QNNs exhibit enhanced efficiency in recognizing patterns and performing classification tasks. They also require fewer parameters and reduced training times thanks to the parallelism inherent in quantum computing. Furthermore, the use of linear functions in QNN training can mitigate overfitting and improve the generalization capabilities of the network [15; 16; 17; 18]. [PERSON] and [PERSON] [19] have extensively discussed the advantages of QNNs over classical artificial neural networks (ANNs). The key benefits include quantum parallelism, exponentially increased memory capacity, faster learning rates, improved performance with fewer hidden neurons, the ability to solve linearly inseparable problems using single-layer networks, and high-speed information processing. These attributes position QNNs as a promising tool for addressing challenges that are computationally infeasible for classical systems. Despite these advantages, the development of QNNs faces several challenges. Much of the research in this field has focused on mapping classical neural network components to their quantum counterparts. However, this is not always straightforward due to the absence of direct quantum analogs for certain classical components, such as non-linear activation functions. Additionally, all operations in quantum algorithms must be reversible,  
Figure 1: General VQA architecture. imposing constraints on the design of the QNN architecture. As a result, there is no unified consensus on the precise definition of QNNs within the academic community [10; 20; 21]. Nevertheless, ongoing research continues to explore innovative approaches to overcome these limitations and unlock the full potential of QNNs. Optimization algorithms are integral to the training of QNNs as they iteratively adjust quantum circuit parameters to minimize the cost function. Among the available approaches, gradient-free optimization methods are particularly notable. These techniques circumvent the need for gradient calculations during backpropagation, making them well suited for noisy or computationally complex quantum algorithms [22]. A prominent example is the COBYLA (Constrained Optimization by Linear Approximation) optimizer, which has demonstrated exceptional performance in various studies. For instance, in [23], COBYLA outperformed two other optimizers--SPSA and SLSQP--highlighting its efficacy. Furthermore, COBYLA was successfully implemented in the QNN framework presented by [PERSON] et al. [23]. In contrast, gradient-based optimizers rely on the computation of gradients within the QNN. While these methods typically demand more computational time compared to gradient-free approaches, they provide the benefit of convergence guarantees, making them a robust choice for certain applications [22]. One widely recognized gradient-based algorithm is ADAM (Adaptive Moment Estimation), which has been effectively utilized in QNN contexts. For example, in a study by [PERSON] et al., the ADAM optimizer enabled a QNN to achieve optimal performance [24].