QML

Quantum Machine Learning (QML) algorithms are a family of hybrid quantum–classical frameworks. A number of key QML algorithms are implemented, demonstrating how parameterized quantum circuits can be integrated with classical optimization and deep-learning tools to perform classification, generative modeling, and data compression tasks. Each implementation highlights both the algorithmic principles and the practical workflow, including state preparation, circuit design, training procedures, and performance evaluation.

• Hybrid Quantum Neural Networks (QNN) A hybrid quantum-classical algorithm, incorporating quantum layers into the structure of a classical neural network. A state preparation maps classical states in the quantum Hilbert state, following quantum layers are implemented by parameterized quantum circuits, providing different expressibility relative to the classical networks. Considering a specific example function we construct, train, and verify the hybrid classical-quantum neural network, building upon the deep-learning PyTorch module.
• Quantum Generative Adversarial Networks (GANs) - A quantum analogue of a classical learning algorithm that generates new data which mimics the training set data. The original model is trained by an adversarial optimization in a two-player minmax game, utilizing a gradient-based learning. In the quantum algorithm, the classical neural networks are replaced by quantum neural networks, which are parameterized quantum circuits.
• Quantum Support Vector Machine (QSVM) - Quantum version of the classical machine learning algorithm, classifying data points between into two distinct categories. Employing the dual problem formulation, the classification is dictated by a defined feature map and the kernel matrix. In the quantum algorithm, the feature map is implemented by a quantum circuit and the elements of the kernel matrix are evaluated by quantum measurements. The performance of various quantum feature maps are analyzed, for both a simplex and complex data sets.
• Quantum autoencoder - A quantum program is trained to reduce the memory required to encode data with a given structure. The example demonstrates how to use the encoder for anomaly detection. Two training approaches for the quantum autoencoder are presented, leveraging Classiq’s integration with PyTorch.