Efficient training algorithms for quantum Boltzmann machines

Develop an efficient training algorithm for quantum Boltzmann machines that optimizes the parameters of the transverse‑field Ising Hamiltonian to maximize likelihood (or a principled surrogate) without relying on loose upper bounds, achieving practical convergence and reliable performance on realistic datasets.

Background

The text discusses that current approaches to training quantum Boltzmann machines use an objective based on an upper bound to the desired log‑likelihood, and that this bound can be far from the true value, often yielding poor performance.

An explicit open problem is stated: finding a genuinely efficient and effective training algorithm for quantum Boltzmann machines. Such an algorithm would need to address the challenges of evaluating gradients or proxy objectives under quantum Gibbs states and to provide guarantees suitable for machine learning practice.