Learning Circular Hidden Quantum Markov Models: A Tensor Network Approach
This work provides a novel method for temporal modeling in quantum and classical datasets, offering potential improvements in data analysis for quantum computing applications.
The authors tackled the problem of modeling temporal data in quantum datasets by proposing circular Hidden Quantum Markov Models (c-HQMMs), showing they are equivalent to a constrained tensor network and developing an efficient learning approach that outperforms existing models on six real datasets.
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.