Quantum Modelling of Time Series: Expressivity vs. Trainability

As time series feature unstructured data and unique processing requirements, they do not easily fit conventional approaches to quantum modeling. This paper therefore presents various quantum model architectures suitable for encoding and analysis of time series data. In particular, it investigates their architectural design aspects, such as methods of encoding and reuploading of temporal data, parameterizing quantum circuits, controlling the circuit qubit resources and entanglement, and dealing with issues of state evolution in the model Hilbert space, as well as navigability of the classical parameter space for an optimizer.Each approach enhances or impedes model expressivity, i.e. its ability to effectively represent time series data in quantum space, as well as its trainability, i.e. its capacity to learn and generalize for predictive accuracy and efficiency in the process of model optimization. The paper evaluates different quantum circuit configurations for their impact on the expressivity and trainability of a quantum time series analysis model, and analyzes how these two design qualities influence model performance in training and testing.