Circuit Design based on Feature Similarity for Quantum Generative Modeling

Quantum generative models are among the most promising candidates for a practical application of near-term quantum devices. However, current approaches mostly rely on general-purpose circuits, such as the hardware efficient ansatz paired with a random initialization strategy, which are known to suffer from trainability issues such as barren plateaus. To address these issues, a tensor network pretraining framework that initializes a quantum circuit ansatz with a classically computed high-quality solution for a linear entanglement structure has been proposed in literature. In order to improve the classical solution, the quantum circuit needs to be extended, while it is still an open question how the extension affects trainability. In this work, we propose the metric-based extension heuristic to design an extended circuit based on a similarity metric measured between the dataset features. We evaluate this method on the bars and stripes dataset and carry out simulations on financial data. Our results provide an experimental basis for problem-informed circuit design and show that the metric-based extension heuristic offers the means to introduce inductive bias while designing a circuit under limited resources.