  Synthetic data generation has proven to be a promising solution for
addressing data availability issues in various domains. Even more challenging
is the generation of synthetic time series data, where one has to preserve
temporal dynamics, i.e., the generated time series must respect the original
relationships between variables across time. Recently proposed techniques such
as generative adversarial networks (GANs) and quantum-GANs lack the ability to
attend to the time series specific temporal correlations adequately. We propose
using the inherent nature of quantum computers to simulate quantum dynamics as
a technique to encode such features. We start by assuming that a given time
series can be generated by a quantum process, after which we proceed to learn
that quantum process using quantum machine learning. We then use the learned
model to generate out-of-sample time series and show that it captures unique
and complex features of the learned time series. We also study the class of
time series that can be modeled using this technique. Finally, we
experimentally demonstrate the proposed algorithm on an 11-qubit trapped-ion
quantum machine.
