  In this paper, we propose circular Hidden Quantum Markov Models (c-HQMMs),
which can be applied for modeling temporal data in quantum datasets (with
classical datasets as a special case). We show that c-HQMMs are equivalent to a
constrained tensor network (more precisely, circular Local Purified State with
positive-semidefinite decomposition) model. This equivalence enables us to
provide an efficient learning model for c-HQMMs. The proposed learning approach
is evaluated on six real datasets and demonstrates the advantage of c-HQMMs on
multiple datasets as compared to HQMMs, circular HMMs, and HMMs.
