Characterizing quantum Boltzmann machine distributions for generative modeling

Characterize the properties of the probability distributions p(s) = Tr(Λs ρTFIM) induced by the transverse‑field Ising model Gibbs state in quantum Boltzmann machines, including their expressivity, sampleability, and suitability for generative machine learning tasks compared to classical Boltzmann machines.

Background

The paper constructs a quantum Boltzmann machine by replacing the classical Ising energy with the transverse‑field Ising Hamiltonian and defining the model distribution via the Gibbs state ρTFIM = e{−HTFIM/T}/Z. Samples are obtained by projective measurements onto computational basis states, producing p(s) = Tr(Λs ρTFIM).

Although this defines a clear quantum analogue of classical Boltzmann machines, the text explicitly notes that the generative modeling properties of such quantum distributions are not yet understood. This includes questions about what kinds of data structures these models can efficiently represent, how sampling behaves in practice, and in what regimes they offer benefits over classical variants.

References

It is an open problem to describe the properties of this kind of "quantum" distribution with regard to generative machine learning tasks.

— Quantum machine learning -- lecture notes (2512.05151 - Žunkovič, 3 Dec 2025) in Section: Quantised classical models, Paragraph: Quantum Boltzmann machines