Learning Hidden Quantum Markov Models
This work provides a method for modeling sequential data with quantum graphical models, which could benefit quantum machine learning researchers, but it is incremental as it builds on prior HQMM work and is limited to synthetic datasets.
The paper tackles the problem of learning Hidden Quantum Markov Models (HQMMs) from data by developing a new algorithm that estimates parameters, showing it matches the predictive accuracy of true HQMMs with the same number of hidden states, while classical HMMs require more states to achieve similar accuracy.
Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing the constraints for modeling HMMs on quantum circuits, and (3) we present a learning algorithm to estimate the parameters of an HQMM from data. While our algorithm requires further optimization to handle larger datasets, we are able to evaluate our algorithm using several synthetic datasets. We show that on HQMM generated data, our algorithm learns HQMMs with the same number of hidden states and predictive accuracy as the true HQMMs, while HMMs learned with the Baum-Welch algorithm require more states to match the predictive accuracy.