Tomography and Generative Data Modeling via Quantum Boltzmann Training

Abstract: The promise of quantum neural nets, which utilize quantum effects to model complex data sets, has made their development an aspirational goal for quantum machine learning and quantum computing in general. Here we provide new methods of training quantum Boltzmann machines, which are a class of recurrent quantum neural network. Our work generalizes existing methods and provides new approaches for training quantum neural networks that compare favorably to existing methods. We further demonstrate that quantum Boltzmann machines enable a form of quantum state tomography that not only estimates a state but provides a perscription for generating copies of the reconstructed state. Classical Boltzmann machines are incapable of this. Finally we compare small non-stoquastic quantum Boltzmann machines to traditional Boltzmann machines for generative tasks and observe evidence that quantum models outperform their classical counterparts.