Good day! Quantum algorithms like quantum support vector machines (QSVMs) and quantum neural networks (QNNs) differ from their classical counterparts in several key ways. One major difference is in their computational power - quantum computers can perform certain computations much faster than classical computers, so QSVMs and QNNs have the potential to provide significant speedups. However, demonstrating practical quantum advantage is still an open challenge.

Another key difference is in how data is represented. Classical algorithms work with bits that are either 0 or 1, while quantum algorithms use qubits which can be in superposition states. This means QNNs can take quantum data as input, allowing them to potentially model quantum systems more naturally than classical neural networks.

The structure of QNNs is often similar to feedforward classical neural nets, with input passing through layers of qubits before reaching the output. But the operations at each layer leverage quantum effects. Some QNN designs even mimic aspects of classical neural nets, like convolutional networks, in a quantum circuit.

Training QNNs involves optimizing network parameters, just like classical neural net training. However, the noisy, error-prone nature of current quantum devices makes QNN training more challenging. Techniques like variational quantum circuits help make training more robust, and some approaches involve pre-training QNNs on classical simulators before deploying them on quantum hardware.

While classical SVMs and neural networks are quite general-purpose, QSVMs and QNNs may be particularly well-suited for certain applications like modeling quantum systems, working with quantum-enhanced feature spaces, and providing learning speedups for specific problems. But it's important to note that QNNs are not simply "quantum versions" of classical neural nets - they are fundamentally different and suited for different types of problems.

Overall, while QSVMs and QNNs have some conceptual similarities to their classical counterparts, they differ significantly in computational power, data representation, network structure, training process, and target applications due to being based on the principles of quantum mechanics. Further developments in quantum hardware, algorithms, and training techniques will be needed to fully realize their potential I think.