Noncommutative Boltzmann Machines*

Building on the 2018 paper on quantum Boltzmann Machines (qBM) by Amin et al [1], the concept of noncommutative Boltzmann Machines (ncBM) is introduced. ncBM contain qBM as a subset, but can be viewed, for example, as machine learning with superoperators. In particular, we study ncBM with the Liouvillian superoperator, and show the negative phase of machine learning becomes easy to calculate in a particular limit. Both Bernoulli data sets [1] and quantum dragon datasets [2] are utilized for both generative and discriminative learning. Possibilities of using near-term adiabatic quantum annealing machines for ncBM will be discussed.

[1] M.H. Amin, E. Andriyash, J. Rolfe, B. Kulchytskyy, and R. Melko, Quantum Boltzmann Machine, Phys. Rev. X 8, 021050 (2018).
[2] M.A. Novotny, Energy-Independent Total Quantum Transmission of Electrons through Nanodevices with Correlated Disorder, Phys. Rev. B 90, 165103 (2014).